The Detection of Faint Light in Deep Underwater Neutrino Telescopes

RHEINISCHWESTF�ALISCHETECHNISCHEHOCHSCHULEAACHEN

PITHA ��

Dezember ��

The Detection of Faint Light

in

Deep Underwater Neutrino Telescopes

Christopher Henrik V� Wiebusch

III� Physikalisches Institut� Technische Hochschule Aachen

PHYSIKALISCHE INSTITUTE

RWTH AACHEN

�� AACHEN� GERMANY

The Detection of Faint Light

in

Deep Underwater Neutrino Telescopes

Von der Mathematisch�Naturwissenschaftlichen Fakult�at

� Fachbereich I �

der Rheinisch�Westf�alischen Technischen Hochschule Aachen

zur Erlangung des akademischen Grades eines Doktors

der Naturwissenschaften genehmigte Dissertation

Vorgelegt von

Diplom�Physiker

Christopher Henrik V� Wiebusch

aus Bonn

Referent� Universit�atsprofessor Prof� G� Fl�uggeKorreferent� Universit�atsprofessor Prof� C� Berger

Tag der m�undlichen Pr�ufung� �� Dezember ��

Abstract

The Detection of Faint Light in Deep Underwater Neutrino Telescopes

The new �eld of high energy neutrino astronomy gives the opportunity to open a new observationalwindow to the universe� This provides a large variety of prospects to investigate new phenomenain astronomy and particle physics� This work concentrates on the two experiments� BAIKAL andDUMAND� Their goal is the permanent operation of large detectors in the deep natural water oflake Baikal and the Paci�c Ocean near Hawaii� These detectors consist of a matrix of highly sensi�tive optical sensors built for the detection of �Cerenkov�light of charged secondary particles� especiallymuons� originating from neutrino interactions� Because the sensors are sensitive to all sources of faintlight such as bioluminescence or radioactivity� these experiments provide interdisciplinary aspects ofresearch in Biology� Environmental and Ocean science� The design of the European Optical Modulefor DUMAND II is presented� This self�contained detector module consists of a new� large area pho�tomultiplier �Philips XP�� fast read�out electronics� power�supplies and monitoring transducerspackaged in a glass pressure�housing� Measured characteristics and the calibration of these modulesshow� that the so called smart PMT has excellent amplitude and time resolution properties� whichwill improve reconstruction accuracy and triggering� A second aspect of this work is the developmentof a general purpose Monte�Carlo program �DADA� for Underwater Neutrino telescopes on basis ofthe GEANT detector simulation library embedded in a data analysis package �SiEGMuND�� In orderto avoid long CPU time consuming calculations� speci�c parameterisations for �Cerenkov�light fromelectro�magnetic� hadronic cascades and secondary energy loss processes during muon propagation arederived and their in�uence on measured detector signals� especially in the BAIKAL NT�� detector�investigated� A comparison of simulation results for atmospheric muons with experimental data ofthe BAIKAL NT�� detector shows good agreement and yields � �� cm��s��sr�� forthe vertical atmospheric muon intensity� The light� which originates from radioactive ��K decays inthe ocean� has to be considered as a background signal in muon measurements� On the other handit provides a constant isotropic photon �ux� A measurement of these signal rates allows a continu�ous measurement of the water transparency� which can be used for detector monitoring and appliedresearch�

This work is supported by the Claussen Stiftung im Stifterverband f�ur die Deutsche Wissenschaft�Projekt�Nr��TS ��

Hardware and Software speci�c names and symbols occuring in this text are often registered trademarksand are acknowledged as such� Extensive use was made of CERN and free software �GNU�� especiallyPAW� GEANT� LATEX� Linux� emacs� gcc� x�g�

c� Christopher Wiebusch� ��

CONTENTS i

Contents

� Introduction �

� High Energy Neutrino Astrophysics �

�� Neutrino production � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Neutrinos from heaven � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Atmospheric neutrinos � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� The sun and the galactic plane � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Neutrinos from hell � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Pulsars � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Supernova remnants � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� X�ray binary systems � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Other galactic objects � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Active galactic nuclei and quasars � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Di�use neutrino �ux � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Neutrino detection on Earth � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Neutrinos from dark matter � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Neutralino annihilation in the Earth and in the Sun � � � � � � � � � � � � � � � � ��

�� Neutrinos from R�parity violation � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Cosmological neutrinos � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� Faint light Deep Underwater ��

�� The Deep Underwater Environment � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� The �Cerenkov e�ect � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Cosmic rays deep underwater � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Muon propagation � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Electromagnetic cascades � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Hadronic cascades � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Optical properties deep underwater � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Natural radioactivity � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Light of biological and chemical origin � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Exotic physics � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� Deep Underwater Experiments ��

�� The BAIKAL Experiment � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� From NT�� to NT��

�� Signal processing � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Calibration � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� The DUMANDExperiment � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� The DUMAND II detector � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Signal processing and triggering in DUMAND II � � � � � � � � � � � � � � � � � � �

�� Other projects � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� AMANDA � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� NESTOR � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� JULIA � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Perspectives of underwater neutrino physics � � � � � � � � � � � � � � � � � � � � � ��

�� Mean visual range and the design of a Deep Underwater Muon Detector � � � � � � � � � ��

ii CONTENTS

� The Optical Sensors ��

�� Optical Modules for DUMAND II and BAIKAL � � � � � � � � � � � � � � � � � � � � � � � ��

�� Optical Modules for DUMAND II � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� The Optical Module for BAIKAL � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Design of the European Optical Module � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� The smart photomultiplier XP��

�� Read�out considerations � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� The smart read�out DMQT � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� The Remote Control Unit � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Mechanical design � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Properties and calibration of the EOM � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Sensitivity � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Signal amplitude � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

�� Time properties � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� Monte Carlo Simulation ��

�� Simulation framework � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� The detector response � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Data analysis � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Extension of the simulation � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� Simulation Results ��

�� Cerenkov light from electromagnetic and hadronic cascades � � � � � � � � � � � � � � � � ��

�� Cerenkov light from muons � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Parametrisation of the e�ective �Cerenkov light from muons � � � � � � � � � � � � ��

�� Cerenkov light from secondary processes � � � � � � � � � � � � � � � � � � � � � � � ��

�� Pointing accuracy of muons � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Muon detection in BAIKAL � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

� Experimental Results �

�� Atmospheric muons in NT��

�� Hit e�ciency and channel multiplicity � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Signal amplitudes of individual channels � � � � � � � � � � � � � � � � � � � � � � ��

�� Time characteristics � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Vertical muon intensity � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

�� Ocean background � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

Summary and Conclusions ��

A Additional calculations ��

A�� Transformation from a track to a �Cerenkov light distribution � � � � � � � � � � � � � � � ��

A�� Timing and amplitude for minimal ionizing tracks � � � � � � � � � � � � � � � � � � � � � ��

A�� Time and amplitude for spherical and plane waves � � � � � � � � � � � � � � � � � � � � � ��

A�� The cumulative Poisson probability � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

B EOM test and calibration measurements ��

B�� Point sensitivity � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

B�� Amplitude and time response � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

B�� Dark noise measurements � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

CONTENTS iii

C Software details ��

C�� The Dada program � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��C�� Geometry de�nition� data structures and initialisation � � � � � � � � � � � � � � � ��C�� Fast tracking � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��C�� Signal generation � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��C�� Internal event generation � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

C�� Event generation � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��C�� Triggering� event selection and reconstruction � � � � � � � � � � � � � � � � � � � � � � � � ��C�� Data processing � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��C�� Calculation of ��K rates � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

D The BAIKAL and the DUMAND collaboration ��

References a

List of �gures h

List of tables j

Glossary k

Index l

Acknowledgement p

�

� Introduction

No on ne straxen� Vs�e pro�id�et�Stradani�� muki� krov�� golod i mor� Meqisqeznet� a vot zv�ezdy ostanuts�� kogdai teni naxih tel i del ne ostanuts� nazemle� Net ni odnogo qeloveka� kotory�i by�togo ne znal� Tak poqemu e my ne hotimobratit� svo�i vzgl�d na nih Poqemu

Aber man braucht sich nicht zu f�urchten� Alles wird

vor�ubergehen� Leiden� Qualen� Hunger� Blut und Massenster�

ben� Das Schwert wird verschwinden� aber die Sterne werden

auch dann noch dasein� wenn von unseren Leibern und Taten

auf Erden kein Schatten mehr �ubrig ist� Es gibt keinen Men�

schen� der dies nicht w�u�te� Warum also wollen wir unseren

Blick nicht zu den Sternen erheben� Warum�

Michail Bulgakov� Bela� Gvardi� �Die wei�e Garde��

In �� Wolfgang Pauli quipped having done a terrible thing� He postulated the existence of anundetectable particle� the neutrino� Fortunately the un�detectability was disproved by Clyde Cowanand Fred Reines with the direct experimental detection in �� Since then the neutrino played adouble role in the process of understanding the fundamentals of nature� On the one hand the neutrinois a miraculous particle� which hardly reveals its properties� It is still uncertain� whether it has amass at all� On the other hand� the neutrino has been one of the most important sources of innovationin modern physics� Very dramatic examples have been the fall of the parity conservation law ��and the detection of weak neutral currents �� Deep inelastic scattering experiments with neutrinosand electrons onto nucleons established the parton model of the nucleon and thus the inner structureof matter� ��

A conclusion may be drawn after almost �� years neutrino�physics� The major challenge for aneutrino�experiment is to cope with an enormous relative background as a result of the tiny probabilityof a neutrino to interact with matter� Whenever experimentalist succeeded with this� they could bealmost certain� that the neutrino probe would provide a very clean view into the subatomic world andoften exciting new results�

Historically the achievement of the �Standard model� is comparable to the invention of the periodicaltable of elements by Mendeleev last century� It allows not only to order all known elementary particles�but also to understand the systematics of their interactions�Within this model� matter is build up by a few fundamental point�like� spin �� particles� quarks andleptons� Both families consist of members� ordered in three generations� each with two members�The charges within one generation are �� and �� for quarks and �� and � for leptons� Each quarkand lepton has a corresponding anti�particle which is identical except for an opposite value for thecharge and the �avour quantum number �for quarks� and the lepton quantum number �for leptons��Three fundamental forces� strong� electro�weak and gravitation� are responsible for all interactionsbetween these particles� They are mediated by another class of fundamental particles� the gauge�bosons� The six quarks �up�� down�� strange�� charm�� bottom� and top�� carry colour� which isthe charge of strongly interactions� They interact strong via eight �also coloured� bosons� calledgluons� In addition they experience electro�weak interactions via four gauge bosons� the photon ��responsible for electro�magnetic interactions� the Z� responsible for weak neutral currents and the W�

responsible for weak charged currents� The six leptons� perform only electro�weak interactions� Threeare charged� electron� muon and tau �e�� Each of them has an uncharged partner� a neutrino��e� ��

�� Because neutrinos are uncharged� they can only interact weakly� �� The neutrinos di�er from the anti�neutrinos � �e� �� by their helicity� which is the projection ofthe spin onto the momentum vector� Neutrinos are found to be left�handed � anti�neutrinos areright�handed� One remaining fundamental question still is� whether neutrinos are identical with theiranti�partners �Majorana type� or not �Dirac type�� With the prerequisite of a �nite mass it would

�Gravitation is far to weak to play a role in particle physics� Also every attempt to put gravitation into the frameworkof quantum physics has failed so far� Thus gravitation will be neglected in the following discussions�

�Though there is strong experimental evidence for its existence� no direct experimental detection of �� neutrinos hasbeen successful yet�

� � INTRODUCTION

be possible for the �rst case to change neutrinos into anti�neutrinos just by a transformation of thereference system� Thus the detection of a �nite neutrino mass could be a hint for new physics beyondthe standard model� ��

Not only on the smallest known scales� in particle�physics� but also for the largest known scales� inastro�physics� neutrinos play an essential role in the understanding of nature�

A fundamental question of cosmology is the fate of the universe� Whether it will expand for ever�open universe� or whether it will �nally collapse gravitationally �closed universe� depends cruciallyon its total mass� Theorists favour exactly the case between these two scenarios� a universe whichasymptotically stops expanding in in�nite time� In observations we see only so called bright matter!matter which is emitting electro�magnetic radiation� This matter adds up to less than �" of themass necessary to close the universe� There are strong experimental indications for large amounts ofinvisible� so called dark matter � but astro�physicists are not sure about its total amount and itsnature� Because of the incredibly large number of neutrinos in the universe even a small neutrino masscould provide a large amount of the missing mass��

A recently developed branch in cosmic ray physics� neutrino�astrophysics� aims at the detection ofneutrinos from extraterrestrial sources�Besides the photon� neutrinos are the only known stable and uncharged elementary particles� Nota�ected by interstellar magnetic �elds� they do not change their direction and do not loose the infor�mation about their origin� The universe has been investigated throughout the total spectral range ofelectro�magnetic radiation� Investigations in a new spectral range were always accompanied by newfundamental results� Neutrinos are not absorbed in dense matter and provide complementary infor�mation to photons� especially from the inside of objects�� This gives rise to the hope to open a new�complementary observation window to the universe� The detection of cosmic neutrinos may provideinformation on another fundamental� still unanswered� question in astrophysics� the origin and theacceleration of high energy cosmic rays� Last but not least some postulated dark matter particles maydecay or annihilate into detectable neutrinos�

These hopes are stirred by two� major breakthroughs in neutrino astrophysics�The detection of solar neutrinos since more than �� years in presently four experiments� gave birth tothis discipline and also raised the until now unsolved Solar Neutrino Problem� These experimentsdetect a smaller number of neutrinos than expected from the Standard Solar Model� There is stilldispute on the signi�cance of these results due to uncertainties in experimental statistics and theoreticalpredictions� A possible solution to this problem could be a �avour change of the initial �e into �� or�� called neutrino oscillation� This would imply a �nite neutrino mass and is the presently mostpromising hint for new physics beyond the standard model� �� Two new projects may helpto clarify the solar neutrino puzzle� The Sudbury Neutrino Observatory �SNO� will be capable ofmeasuring all neutrino �avours and the di�erential energy spectrum� which is necessary to con�rmthe neutrino oscillation hypothesis� The Super Kamiokande detector is designed about �� times largerthan Kamiokande to detect the solar neutrino �ux with high statistics�

The second breakthrough occurred on ��rd February �� with the detection of a total of �� neutrinosin coincidence with the explosion of the supernova SN��A in two proton decay detectors� IMB andKamiokande� and a supporting measurement of � events in the Baksan neutrino�telescope �� Thedetected number of events matches the number expected from our knowledge on the violent deathof a giant star� SN��A released an energy of about �� J � mostly ��"� in form of neutrinos�� producing an estimated neutrino��ux of ��cm�� on earth within a few seconds �� With

�The detection of solar neutrinos is the �rst direct experimental proof for the nuclear fusion processes in the Sun�score�

�A third important topic� the �atmospheric neutrino anomaly� will be discussed in section ��Homestake� Kamiokande II III� Sage� Gallex�

�

Figure �� Principle of a DUMAND � type detector�

only �� events many limits on properties of the neutrino like mass� life�time and magnetic momentwere measured comparably precise or superior to terrestrial experiments �� Kamiokande III issensitive to supernova explosions up to a distance of about ��kpc� An explosion within our galaxywould produce several �� events� No further supernova signal has been observed since �� Futureexperiments will be even more sensitive �� Both experiments� IMB and Kamiokande� used theWater��Cerenkov�technique to detect neutrinos and showed that this is an appropriate detectionmethod for neutrino telescopes�

Crucially for the construction of a neutrino�telescope are both the background due to other cosmicrays and the extremely rare occurrence of neutrino interactions� The �rst problem can be solved bylocating the experiment several km underground with a large amount of matter on top as a shieldingto absorb almost all other cosmic rays� A solution to the second problem is found by enlarging thedetection volume as much as possible�

Within the DUMAND � approach natural water is used as detection medium to study high energyneutrino interactions and to search for high energy astrophysical neutrino sources� A schematic sketchis shown in �gure �� A detector is located deeper than �km under water and connected to a shorestation via cables for signal transmission and power supply� High energy neutrino interactions producesecondary �charged� particles which emit �Cerenkov�light along their track� This light is detected withhighly sensitive optical sensors� The clarity of natural water in this depth and the available spaceallows the realisation of large detection matrices�

The current step is to increase the sensitive volume from about � �� to ��m� realized in undergroundexperiments� to about � ��m�� This attempt has su�ered from several drawbacks� particularlydue to the remote location under free nature conditions� It took several years for approval anddevelopment of appropriate technologies� After two decades of preparation with several test�detectors�the experiments� BAIKAL � NT�� in the deep Siberian lake Baikal �Ozero Ba�ikal�� and DUMAND II

� in the Paci�c Ocean close to Hawaii� are in the stage of turning to permanent operation� A �rstsmall detector� BAIKAL � NT�� is in operation since spring ��

The unique location in a natural environment implies a strong interdisciplinary cooperation between

�DUMAND� Deep Underwater Muon And Neutrino Detection

�MACRO�� m�� Kamiokande�II� � � � ��m�� IMB�� m��Also the AMANDA experiment� using a similar approach in the deep clear ice of the antarctic glacier� is starting with

permanent operation�

� � INTRODUCTION

various scienti�c disciplines� When these detectors are completed� they will act as underwater laborato�ries and measure continuously environmental parameters such as temperature� salinity and currents inthe deep water� Several subjects of research in biology� geology or environmental sciences are obvious�investigation of bioluminescence� sedimentation� seasonal and other long term variations of environ�mental parameters� Within an optimistic scenario a tomography of the inner earth seems possible ifbright and time�stable sources of astrophysical neutrinos are found�Apart from scienti�c subjects� technological aspects play an important role� The remote location deepunderwater with rough conditions like extreme temperatures� pressure and strong corrosion in oceansrequire new technologies and strong checks on quality assurance� Within these experiments severalmajor technological innovations have been born�

A further scienti�c step will be to increase the sensitive volumes further by several orders of magnitudeto a detector of km� size� Several proposals have been made� Experience with present detectors andtechnologies under operational conditions are signi�cant for the further development of this ambitiousproject� ��

Within this treatise astronomical models for possible sources of high energy neutrinos and their de�tectability are reviewed in chapter �� The �Cerenkov e�ect used for the detection of charged particlesdeep underwater as well as other sources of faint light in deep water are described in chapter �� Currentexperiments are discussed in section �� Chapter � gives a close view on the development and propertiesof the highly sensitive optical sensors used in these experiments� The simulation and analysis softwareis described in chapter and results are shown in chapter �� Experimental results from the NT��detector are compared with simulations in chapter �� From these results� conclusions on the detectionof faint light in next generation neutrino�telescopes are drawn�

� High Energy Neutrino Astrophysics

�� Neutrino production

The atmosphere of the earth is steadily bombarded by an isotropic �ux of various elementary particles�mostly protons and heavier nuclei� called �primary cosmic rays�� Energies higher than ��eV havebeen observed� The energy spectrum follows a power�law

dN�E� � E��dE with

�� for E ��TeV� � �� for E ��TeV

��

Instead of the power�law index �� frequently the spectral index � � � � � is used� The spectrumsteepens above � ��TeV �� Above � ��TeV the spectrum seems to �atten again to� � �� The mechanism generally thought to be responsible for the acceleration to highest energies is called�rst order Fermi acceleration� It describes the acceleration of charged particles due to relativisticshock fronts moving through turbulent plasma� Calculations yield a power�law spectrum with � # ��where � is a small number� A power�law spectrum with the value � # �� corresponds to accelera�tion with a constant amount of power per decade energy� A second mechanism second order Fermiacceleration also yields a power law�spectrum� It describes the stochastic acceleration of particlesdi�using through turbulent moving plasma and is less e�cient� It is generally assumed� that cosmicrays are mostly con�ned by magnetic �elds within our galaxy� To compare the theoretical spectrumwith observations it has to be taken into account� that the probability for a particle to escape fromthe galaxy depends on its energy� From the relative absence and abundance of certain elements in thecomposition of primary cosmic rays one �nds a characteristic escape time ��E� � E�� with � � �� below ��TeV � A comparison with the primary spectrum yields

dN�E� � E��dE ��

and thus � � �� This is consistent with the assumption� that the accelerator has a hard spectrum�� as expected for shock acceleration� ��

Though the origin of high energy cosmic rays is uncertain� many models predict point sources whichalso emit large �uxes of high energy gamma�rays and neutrinos� Excluding low energy neutrinossynthesised in the centre of the sun or during supernova explosions� only energies above ��MeV areconsidered during the following discussions�These neutrinos are assumed to be produced in inelastic interactions of accelerated protons with atarget� This mechanism is called astrophysical beam dump� As sketched in �gure �� high energyprotons hit onto matter and secondary pions and kaons are produced� Charged pions decay into muonsand neutrinos and neutral pions into gamma�rays� Di�erent production mechanisms suggest a furtherdistinction by their energy range

Very High Energy �VHE�� E� ��GeV # ��eV

Neutrinos of this energy are produced in collisions of accelerated nucleons with protons in a targetgas around an astrophysical accelerator�

p� p � � �X� ��

� e� � �e � �� e� � �e � �� X

� ��

��

�In contrast to secondary cosmic rays which are measured at the surface of the earth�

� � HIGH ENERGY NEUTRINO ASTROPHYSICS

+

νμ

νe

proton source

μν

μ+π

High energy

p

p p

target matter

e

π0

γγ

p

X

Figure �� Principle of an �astrophysical beam dump

If the material density in the target is too high � ��gcm�� charged pions do not decaybut are reabsorbed! muons loose energy before they decay and the energy spectrum of neutrinossteepens�

Ultra High Energy �UHE�� E� �PeV # ��eVUnlike the case of VHE�neutrinos a dense photon gas acts as a target� a situation realised inactive galactic nuclei �AGN��

p� � � $�

� p� �

� n� ��

The pions decay according to eq�� Other reaction channels are e�g� p� $�� Thepion production threshold depends on the temperature of the photon gas� For optical photons itis typically of the order of PeV in the laboratory rest frame�

The energy spectrum of these point�source neutrinos is expected to follow closely the hard powerlaw spectrum of the accelerator itself �� The matter density necessary for the generationof su�ciently large neutrino �uxes is not very high� Column densities of typical accretions disks�� gcm�� are high enough� but also thin coronae of these disks may produce up to ��" of themaximum possible neutrino yield� �� In general the neutrino �ux resulting from decaying mesons can be parameterized via

dN�

dE�#

N��E��

�� ZN�N

�� A��

� �B�� cos �E��EC

� �� AK��

� �BK�� cos �E��ECK

� ��

��

where A�B�Z are constants which depend on the power�law index� hadronic interaction and decayparameters� � is the incident angle of the proton� The �rst term represents the contributions frompions� the second from kaons and �� further contributions due to other mesons� Each term ismultiplied with a branching ratio factor �e�g� �� for K� �� The competition of the twoprocesses� decay and absorption� is represented by the critical energy factor EC

i � For E� ECi all

parent mesons decay� ��

�� Neutrinos from heaven �

An important aspect for terrestrial observations is the comparison of the gamma and neutrino yield�It is characterised by the ratio

R�� N�

N��

In a simple balance of the production mechanisms �eq�� and �� one gets R�� In moredetailed calculations� the absorption of pions� energy loss of muons� electro�magnetic cascading andabsorption has to be taken into account� Though for high matter densities R�� may become smaller�� More realistic models predict a ratio from � to �� due to absorption of gammas� Depending on thetype and distance to the source� additional absorption mechanism occur and may dramatically reduceN� and thus increase R�� These are

�� Absorption of gamma�rays in matter�

Many sources are encapsulated by thick dust and gas clouds� These clouds are either directlycorrelated with the source� e�g� a thick accretion disk around a massive black hole� or the sourcelives in a region of dense interstellar gas� These sources are called hidden sources�

�� Gamma gamma interaction within the source�

At UHE energies gammas interact with thermal photons via �� e�e�� The threshold energyE� for this process is given by

pE� � Ephot � mec

� and the absorption length is � T��phot� withthe temperature Tphot and the energy Ephot of the photons� PeV �gammas are suppressed bymicrowave photons and TeV �gammas by optical and UV photons� Especially accretion diskcoronae of AGN show high UV�photon densities� that may reduce the gamma �ux down to��

A second process is pair production of gammas in strong transverse magnetic �elds with thethreshold condition E�eV � �B�G� � � �� A transverse magnetic �eld larger � ��G suppressesTeV � and � � ��G suppresses PeV �gammas��

�� Gamma gamma interaction with the micro�wave background radiation�

At high energies gammas may interact with the �K background radiation� The probabilityto become absorbed depends on the gamma energy and rises linearly with the distance to thesource� The absorption is maximal for E� � � ��eV and accounts typically for a factor of � forsources within our galaxy and several orders of magnitude for extra�galactic objects� Thereforethe experimental observation of high energy gammas from distant sources is unlikely� ��

As a conclusion� neutrino �uxes might be of comparable magnitude but can not be directly derivedfrom the �ux of gammas� On the contrary predictions require a detailed knowledge of the speci�castronomical object itself� A simultaneous measurement of both� neutrinos and gammas� is desirable�to reveal the characteristics of the source and thus determine information about the initial protonbeam� ��

�� Neutrinos from heaven

Predictions of neutrino and gamma �uxes from cosmic accelerators depend on speci�c models� How�ever guaranteed sources of high energy cosmic neutrinos do exist and �uxes can be predicted withhigher accuracy�

�� Atmospheric neutrinos

High energy neutrinos are produced in the earth atmosphere due to interactions of primary cosmic raysaccording to eq�� Typical values for the critical energies are� EC

� � ��GeV � ECK� � ��GeV and

� � HIGH ENERGY NEUTRINO ASTROPHYSICS

ECD� � � � ��GeV � Muons with energies larger than � �GeV reach the surface of the earth and stop

before decaying� Detailed calculations of the neutrino �ux and its energy spectrum consider additionale�ects such as� details of the primary cosmic ray spectrum and composition� in�uences of the earthmagnetic �eld �in dependence on the latitude and solar cycle� and energy loss of muons�

The result of these calculations is a uniform but not isotropic angular distribution �see �gure �� A��The energy spectrum follows the primary spectrum with a power�law index � � �� up to � ��GeVand becomes steeper �� above� The spectrum of electron neutrinos� which are produced bymuon decay� is one power steeper� The spectrum has a broad maximum at �� MeV due to decaysof stopped muons and pions� For the ratios of electron� to muon�neutrinos at sub GeV energies� oneexpects

�e��

��

�e�e� ��

��

For high energies � ��TeV the production of charmed mesons �e�g�D�� becomes important� Dueto the high value of EC

D� charmed mesons always decay� Therefore the expected �prompt neutrino�spectrum is isotropic and follows the primary spectrum up to highest energies� Prompt neutrinos maydominate the atmospheric neutrino �ux above ��TeV � Predictions of the �prompt neutrino� �uxare di�cult� because cross sections depend on the small�x behaviour of the gluon structure function��

Atmospheric neutrinos provide a standard source for the calibration of neutrino telescopes but alsoprovide interesting aspects of investigations� So far physicists and other humans believe to haveobserved a few thousand atmospheric neutrino events mostly in the experiments Baksan� IMB andKamiokande� In contratiction to expectations eq�� the measurements in IMB and Kamiokandeshow almost the same number of electron� and muon�neutrinos� These results are supported by theSoudan � experiment but are in contradicted by the Frejus and Nusex experiments! the latter threehave a lower statistics� In addition to the solar neutrino problem �see chapter �� these measurementsmay be an indication for neutrinos oscillations� Larger detectors will provide higher statistics and thusallow the investigation of the ratio in dependence of the zenith angle� This corresponds to a variationof the oscillation length in the range from ��km to ��km� More accurate predictions of the absolute�uxes for each neutrino �avour are necessary to judge whether a de�cit of muon�neutrinos or an excessof electron neutrinos occurs� ��

�� The sun and the galactic plane

Similar to processes in the atmosphere� cosmic rays interact with interstellar gas in our galaxy� Pro�duced mesons are not absorbed and the neutrino spectrum follows the primary spectrum with � � ��The �ux depends on the density of the interstellar gas and the intensity of cosmic rays� Its origin ismainly the galactic plane and is eventually concentrating in point�like sources from gas clouds in spiralarms� Expected event rates in detectors are signi�cantly smaller compared to atmospheric neutrinosand only marginally detectable� Even with the assumption of a locally higher cosmic ray intensitythe total expected event rate for a large ��m� detector is of the order of � �� and e�g�� from thedirection of Orion ��kpc away��

The solar atmosphere is much more tenuous than that of the earth� hence producing a harder ��spectrum at high energies� Calculations predict more events from the direction of the sun comparedto the atmospheric background from the same direction� Unfortunately event rates are small� and thedetection becomes likely only for a large �km�� detector� ��

�Future results� especially from HERA� may help to improve calculations� e�g� ��

�� Neutrinos from hell

�� Neutrinos from hell

In a standard model for the origin of cosmic rays one assumes that the acceleration takes place whenshock waves from exploding supernovae move through the interstellar medium� However� due to the�nite life time of the shock front� acceleration to energies higher than ��TeV is di�cult to explainwithin this model� A popular solution are additional cosmic rays due to acceleration within the extremeconditions of some compact galactic objects and for the highest observed energies in extra�galacticobjects� Two processes� accretion and strong magnetic �elds� allow acceleration to highest energiesin short time�scales� Several astrophysical objects show a tremendous amount of energy output andmay well serve as candidate hells to produce su�ciently large neutrino �uxes� If these objects areindeed responsible for a highly e�cient acceleration to highest energies� they have to be considered asthe hottest regions known in the universe� ��

Mainly three di�erent categories of possible accelerators could gain su�cient power and neutrinoluminosity�

�� Young type II supernovae remnants�

�� A neutron star or a black hole in a X�ray binary system�

�� Accretion of matter onto a super�massive black hole in galactic nuclei�

It must be pointed out� that other models� extending the basic supernova blast model� do not predictpoint sources of neutrinos or gammas� ��

A standard neutrino source may be de�ned as an accelerator of protons with the luminosity Lp � ��

submerged in a cloud of gas with low density located at a distance of R� � ��kpc� The neutrinoluminosity QS

� can be related to the proton luminosity of the source via

QS� �E�dE # %�i �

��

�� LSp �E�� dE ��

where � � �� is the fraction of energy retained by the proton in a nuclear collision� %�i is the neutrinoyield for the �avour �i and depends on the power�law index �� Calculations for � # �� predicttypically %�� "� %�e� �e � ��" and %� � �� "��

�� Pulsars

Pulsars are young� fast rotating neutron stars� These objects have masses of � � � solar massescompressed to an object of � ��km diameter� Due to fast rotation and very strong magnetic �elds atthe surface� they are excellent accelerators for particles up to energies of more than ��eV � Withina so�called light cylinder�� around the rotation axis magnetic �eld lines are closed and co�rotate thestar� Outside the �eld has a spiral character� �see �gure ��

The total amount of stored rotational energy is of the order of � ��erg� The energy loss may beup to ��erg�s and is not expected to be emitted as magnetic dipole radiation� but rather to drivea relativistic wind of electrons and positrons� Especially near the light cylinder also ions may beaccelerated to relativistic energies� The total energy for the Crab pulsar is assumed to �� erg andthe energy loss �� ergs�� Particles may stream along the unclosed polar magnetic �eld lines� Material �ows onto the polarregions� where the magnetic �elds reaches typically� �� G� A rough estimate of the maximum

�The radius is given by Rc � c�� with the speed of light c and the rotation frequency ��This high values can be explained by the reduction of the radius of a progenitor star� A typical main sequence star

has a surface magnetic �eld of ��G�

�� HIGH ENERGY NEUTRINO ASTROPHYSICS

magnetic axis

rotation axis

neutron star

emitted radiation

downstreaming matterclosed field lines

acretion diskinner surface of the

Figure �� Accretion onto a neutron star�

proton luminosity is given by the Eddington luminosity

LEdd � �� Mneutronstar

M�

�erg

s� ��

which corresponds to the maximum X�ray luminosity that does not stop accretion� For the e�ectiveproton luminosity one has to consider a duty cycle in the order of ��" due to the interception ofnew accretion material� Di�erent scenarios consider� shock fronts and turbulent magnetic �elds in theaccretion plasma �ow� di�erences in the rotation of the accretion disk and the neutron star� interactionswith atmospheres of possible companion stars� Which scenario is preferred depends on the magnetic�eld of the neutron star� The accretion onto a neutron star is sketched in �gure ��

Isolated pulsars are weaker candidates for bright neutrino point sources due to the absence of sur�rounding matter� necessary to generate an astrophysical beam dump� However a few objects shouldnot be ruled out as candidates for detectable neutrino sources�

Crab is the remnant of a supernova explosion observed in the year �� by Chinese astronomers� Thissystem consists of a pulsar �PSR �� surrounded by a nebula and is approximately �kpc awayfrom the earth� It is the brightest and most energetic source for high energy gammas detected withenergies up to ��TeV and high statistical signi�cance � �� Opposite to lower energies� Crab showsno pulsed but steady emission at high energies� Its luminosity above �TeV was measured� ��erg�sproducing a photon �ux of �� cm��s�� with a power�law index � # ��

Vela is a similar but older pulsar �� yr�� It is a bright ��ray source at moderate energies witha distance of only ��kpc� ��

Geminga is the brightest gamma ray source in the constellation Gemini� It&s nature has been recentlyestablished as a pulsar giving testimony to a supernova explosion several �� years ago� Thoughprobably an isolated neutron star� its appealing attribute is its extreme close distance to earth which

�� Neutrinos from hell ��

is about ��pc� probably less than ��pc� High energy � observations con�rmed pulsed emission with atotal luminosity of � ��erg�s above �TeV � The power law index between ��MeV and �TeV wasmeasured to ��

�� Supernova remnants

neutron star

ν

ν

νν

ν

pp

p

p

p

ν

supernova shell

Figure �� Neutron star in a young supernova remnant� Accelerated protons hit onto the expanding supernovashell�

Within young supernova remnants protons may be accelerated either in the strong magnetic �eldof a fast rotating neutron star or via accretion onto a black hole or neutron star� As sketched in�gure �� these protons interact with the expanding shell� High proton luminosities may be gained�� ergs�� as well as maximum energies up to ��PeV � Within two typical times t� � � � ��days and t� � � � �� years these objects correspond to a standard neutrino source eq�� Beforet� the shell is too thick� after t� only a fraction of the accelerated protons interact and the neutrinoluminosity decays quadratically with time� ��

In addition neutrinos may be generated in the supernova&s blast wave itself� due to shock fronts refractedfrom stellar winds of the progenitor star� This mechanism is very sensitive on the mass loss of the presupernova and may yield a neutrino signal comparable to the above mechanism for the �rst �� days��

SN��A is the only recently observed close supernova� SN��A shows no pulsar activity above��erg�s and is more distant ��kpc� than typical galactic supernovae ��kpc�� Constraints on theproton luminosity derived from the absence of VHE neutrinos Lp �� ergs�� and gammaobservations Lp ��ergs�� are less stringent than expectations� Neutrino detectors� capable ofsupernova detection� found no evidence for galactic supernova collapses during the recent years� ��


�� X ray binary systems

p

p

p

ν

ν

ν

Figure �� X�ray binary systems as high energy neutrino sources� The system is composed of a neutron staror a black hole together with a massive companion star� Protons gain energy either by accretion ormagnetic acceleration� Both� the accretion disk itself or the close companion star may serve as targetfor a �cosmic beam dump

X�ray binary systems consist of a compact component �black hole or neutron star� together with anordinary companion star� eclipsing at a short distance� Mass from the star is transferred and accretedonto the compact object� Strong X�ray radiation is released during thermalising of the accreting matter�Emissions show a typical phase modulated character which allows to determine dynamical kinematicparameters of the system� This con�guration is sketched in �gure �� These objects are the most luminous objects in our galaxy and may produce proton luminosities upto typically �� erg�s� In early ��& detections of UHE gamma rays with luminosities up to��erg�s have been reported from the two most prominent objects� Cyg X�� and Her X�� Theseobservations have not been con�rmed by much more sensitive experiments� scaling down the upperlimit for steady gamma �ux at UHE energies by an order of magnitude� ��

Cyg X � is obscured by dust of the galactic disk but has to be considered as one of the mostluminous objects in our galaxy� One assumes that a neutron star orbits extremely close to a massiveWolf�Rayet�type star� The neutron star may move through the stars envelope inducing strong shockfronts� It&s distance is about ��kpc and the proton luminosity is estimated to be up to � ��erg�s��

Her X � Her X�� is an optically visible binary system consisting of a main sequence star and aneutron star approximately �kpc away from earth� The pulsar has a moderate period but a strongsurface magnetic �eld �� G�� It&s proton luminosity is estimated up to ��erg�s� ��

Cyg X � This systems consists of the blue giant star HDE�� m � �� m�� with aninvisible companion of �� m�� which is one of the strongest candidates for a black hole� only ��kpcdistant from earth� This object shows indication for the existence of a pulsar� but a high random�likevariability� showing strong radiation bursts of millisecond duration� Its total luminosity is of the orderof �� erg�s� ��

Besides these systems there are further binary objects with X�ray luminosities in the range ��

at distances between �� and ��kpc� Other objects have been found in the Magellanic clouds� Theiremission shows both periodic and random variability with time scales down to milliseconds� Many

�� Neutrinos from hell ��

contain an identi�ed pulsar as compact component� Some have also been reported as very high energygamma sources� ��

�� Other galactic objects

In addition to the frequently occuring X�ray binary systems two other objects within our galaxy� haveto be considered as detectable neutrino sources�

SS�� is strange object� probably a neutron star or a black hole in a binary system� at � � � kpcdistance� This object strongly accrets matter� A jet structure with outstreaming gas allows to estimatethe total luminosity up to ��erg�s� The central engine is strongly obscured by dust preventing thissource to be a brilliant gamma source� Observations suggest a situation similar to active galacticnuclei �see section �� If a rescaling of the AGN model down to stellar dimensions is appropriate�a possibly high neutrino luminosity and its close distance mark this object as a strong candidate for adetectable neutrino source� ��

SGR A� �galactic centre� is a strong radio source� located at the dynamical centre of our galaxy��kpc distance�� a region which is optically invisible� The emission comes from a central region of afew astronomical units� High rotation speeds of clouds lead to the assumption of a massive � � ��M��black hole� Observations show� that the current accretion rate is low� and the total proton luminositydoes not exceed ��erg�s� However the con�rmation or exclusion of SGR�A as a power�full neutrinosource will yield information about the inner nature of our galaxy� ��

�� Active galactic nuclei and quasars

Since the inclusion of the p�� mechanism �see section �� into earlier models� active galactic nuclei�AGN� have attracted a lot of attention � very high neutrino �uxes with hard spectra are predicted�� Observations of AGN show strong variability of typically ��s implying a very small emission region�This leads� together with the high luminosity in all spectral regions� to a generic model of AGNand quasars assuming a very massive central black hole �� M�� which is accreting matterat the Eddington limit �eq�� Quasi spherical infalling matter builds a shock�front at a radiusR # �� Rs with Rs the Schwarzschild radius� Accelerated protons at the shock�front cannotescape due to the instreaming matter� but are dragged into the black hole� p� interactions producehigh energy neutrinos� neutral pions initiate electromagnetic cascades� Photons from these cascadesare coupled back as target for in�owing protons� Due to the high radiation density �but simultaneouslylow matter density� high energy gammas interact via �� e�e�� Thus only UV�� X�ray� and softgamma�ray� radiation escape from the source� The photon gas can be modelled by a combination ofthe power�law spectrum from the AGN engine and a black body thermal component leading to an UV�bump� Models for neutrino emission from AGN are normalised to the electromagnetic spectral shapeand the absolute luminosity of UV and X�ray observations� The total luminosity of AGN ranges from��erg�s up to ��erg�s� depending on the mass of the black hole� This corresponds to a typicalaccretion mass of �M� per year� The proton luminosity depends on the ratio of the Schwarzschild� andthe shock radius and is typically �"� ��" of the total luminosity� The maximum achievable protonenergy is limited due to energy loss processes� It is approximately proportional to the total luminosity�for L ��erg�� Maximum energies of ��eV can be achieved only by the most luminous quasars��

�Other galaxies in our local group may also give lodge to detectable neutrino sources �e�g� LMC�X�� or may bemeasured as a point�like source themselves� e�g� the Andromeda galaxy �M��

�Recently also detected in the X�ray and gamma light��There are indications for are stronger activity in the past�


One limitation of this generic model is� that strong constraints on properties of the accretion disk arerequired in order to satisfy limits on the emission of high energy gammas �di�use cosmic gamma back�ground�� Alternate models do not assume the spherical accretion� but e�g� a proton acceleration in innerdisk�accretion regions or at the bases of the jets� Despite of quite di�erent production assumptions�the resulting neutrino �ux is comparable �due to X�ray luminosity constrains��

Several AGN � �� have been detected recently in GeV gamma rays by the EGRET�experimenton the Gamma Ray Observatory � All these sources are so called Blazars �BL�Lac objects�� whichseem to be AGN with their perpendicular jets pointing into our direction� Acceleration within jetsserves as an additional feature of the AGN and provides a large fraction of AGN luminosity and mayalso produce neutrinos� This is not only supported by several models� but also by the detection of oneEGRET source� Mkn�� in TeV gamma rays by the Whipple observatory �see below�� A con�rmationof even higher energies would clarify if protons are accelerated in AGN� Unfortunately this is unlikely�even for this relatively close AGN due to gamma absorption by IR�background radiation� Thoughmuch more powerful� more distant sources are expected to be undetectable in high energy gammas dueto the strong attenuation� ��

The gross of active galaxies is too distant to produce signi�cant individual neutrino �uxes � only afew are relatively close to earth and have a chance of being detected with large neutrino telescopes�

Markarian �� is the closest �EGRET��blazar to earth �distance ��Mpc� red�shift z # ��This is the �rst active galaxy identi�ed with high statistical signi�cance � �� in VHE gamma rays� �TeV � with a �ux of �� cm��s�� above ��TeV � Its high energy gamma luminosity iscalculated to exceed ��erg�s� A combined �t to EGRET�Whipple results yields a power�law indexof � # �� Recently the Whipple observatory reported the detection of a second Blazar Markarian

�� z # �� with a �ux of � � ��cm��s�� above ��TeV and a statistical signi�cance of about��

�C�� is one of the closest quasars �z # �� Mpc�� The X�ray luminosity is of the order of��erg�s� Though detected by EGRET in the GeV range� the detection of high energy gamma�raysis unlikely� Another often quoted close�by quasar is the bright EGRET�source �C�� z # ��

Cen A �NGC �� a large elliptical galaxy� has a very luminous nucleus with an X�ray luminosityof ��erg�s� Bursts of typically �� days are reported in X�rays� but also at UHE energy gamma raysreach luminosities of ��erg�s� With � �Mpc Cen A is the closest known active galaxy to earth�Two other close active galaxies have to be mentioned� M�� at a distance of �� Mpc� shows strongjets� NGC �� Mpc� is the closest Seyfart galaxy with an X�ray luminosity exceeding several��erg�s� ��

�� Di�use neutrino �ux

Though AGN are individually only marginally detectable� the summation of neutrino emission fromall AGN and quasars yields a large isotropic �di�use� neutrino �ux� The calculation proceeds similarto calculations of the di�use X�ray background via an integration of the AGN�luminosity as a functionof the red�shift� The total �ux is expected to exceed the total atmospheric neutrino �ux above �� TeV � becoming the dominant source of high energy neutrinos on earth� Already detectors underconstruction may con�rm predictions or set new signi�cant constraints on theoretical models� Theseprospects are discussed in more details in section ��

�� Neutrino detection on Earth �

�� Neutrino detection on Earth

Proton

Atmosphere

DetectorMuon

Muonatmosphericatmospheric

Muon bundle

atmospheric

Proton Proton

Muonsgoing

up

Neutrino

Earth

extraterrestrialNeutrino

Figure �� Principle of a muon and neutrino telescope�

When neutrinos reach earth� most of them pass entirely una�ected through it � sometimes interactionsvia the weak force occur � sometimes close to a detector� In case of �anti� muon neutrinos �� a chargecurrent interaction with a nucleon produces a charged muon �� and a hadronic cascade X

�� N � �� X ��

The muon points almost into the initial direction of the neutrino and may travel a long distance �severalkm� through matter� possibly passing a detector� The cross section ��N for this interaction rises linearwith the energy up to � �TeV and changes into a logarithmic growth above� Averaged over � and �below �TeV

��N � �� cm� � E� �GeV � ��

and reaches � � ��cm� for energies � ��GeV � The average scattering angle � between the initialneutrino and the muon below �TeV can be approximated by

p ��

rmp

E��rad� �

�� for E� # ��GeV�� for E� # �TeV

��

��

The detection of a muon in a detector and the reconstruction of its direction allows to operate thisdetector as a muon telescope� Figure �� sketches the principle of an underground muon and neutrinotelescope� Muons from interactions close to the detector pass through the detection medium� Not allarriving muons in an underground detector are induced by neutrinos� As seen from �gure �� muonevents are classi�ed as follows�

�� HIGH ENERGY NEUTRINO ASTROPHYSICSLO

G (

Muo

n flu

x / (

year

deg

ree)

10

Zenith angle (degrees)

Eve

nts

per

year

abo

ve E

μ

�A� �B�

Figure �� Signal and background muon �uxes for neutrino telescopes� �A� shows the angular distribution ofatmospheric muons and muons induced from atmospheric neutrinos in DUMAND II � �B� shows thenumber of upward going muons within �� above a threshold energy for in the DUMAND II detector fromatmospheric neutrinos and an imaginary point�source producing �� events per year with a power�lawindex � �� from ��

��Muons induced by cascades from initial protons in the atmosphere reach the detector from above�These muons provide a large �ux� but can not travel through the earth and therefore do not arrivefrom below� Atmospheric muons may arrive in bundles� which is a group of parallel traveling muonsoriginating from the same initial cascade� ��gure �� A��Muons induced by atmospheric neutrinos arrive from all direction but have a characteristic angulardistribution� Their �ux falls steeply with the energy� ��gure �� A��B��Muons induced by extraterrestrial neutrinos� are expected to arrive from all directions and have ahard energy spectrum� ��gure �� B��An upward going muon� provides a clear signature for a neutrino induced muon� A selection of thesemuons enables the operation of a muon telescope as a neutrino telescope� � �� Besides muon neutrinos all neutrino �avours may be detected via charged current or neutral cur�rent reactions� Usually the �nal state particles induce an electro�magnetic or hadronic shower �e�g��eN X � e�� In contrast to upward going muons� these interactions are harder to detect� This isespecially the case for conventional underground experiments� because the e�ective volume for showersis limited to the geometrical volume of a detector� DUMAND� type experiments are capable of de�tecting �Cerenkov light from these cascades outside of their geometrical volume� This is mainly limitedby the attenuation of the �Cerenkov light� Especially at ultra high energies extremely large e�ectivevolumes are established� At these energies an additional important reaction occurs�

�e � e� W� �

l��l � ��" �l � lepton�hadrons � ��"

��

This reaction� called Glashow resonance� becomes dominant at an energy of E� # m�W��me� �

��PeV � The resonance has a width of ' # 'W �mW�me � ��PeV � The number of resonant eventsNR can be calculated analytically for a power�law neutrino spectrum

NR # ( �Ne � �eff � �� F �e� E��

with Ne the number of electrons in the detector� ( the angular acceptance of the detector� GF theFermi coupling constant and F �e the isotropic neutrino �ux above the resonance energy� ��

�� Neutrino detection on Earth ��

For the search of astrophysical neutrinos� the muons from atmospheric cascades and muons inducedby atmospheric neutrinos have to be considered as background signals in neutrino telescopes� Figure�� A� shows the angular distribution as calculated for the DUMAND II detector �see section ��Though not traveling upwards� atmospheric muons may be falsely reconstructed and appear as upwardgoing muons� so called �fake muons�� The rate of down�going muons Rdown strongly decreases withdepth� Therefore it is possible to reduce this background by locating the detector deeper underground�For the detection of di�use neutrinos like atmospheric neutrinos or neutrinos from AGN� the rateof fake muons Rfake should not exceed the expected signal rate Rup� Therefore the rejection factor�R � Rfake�Rdown must be

�R � Rup

Rdown��

Typical required values are �R � �� for BAIKAL and �R # �� for DUMAND �Searching for astrophysical point sources is easier than for the di�use �ux from atmospheric muonsdue to two reasons

�� The rate of background signals Rback due to atmospheric neutrinos and fake muons is Rback � ��with the mean reconstruction error �� In a straight forward estimate the required rejection factor�R becomes

�R � Npix � Rup

Rdown��

Npix is the number of angular pixels given by the solid angle of observable lower hemisphere�� sr� divided by the size of one pixel �� deg��

Npix � �

��deg��

Therefore a good angular resolution strongly improves the background rejection of both atmo�spheric muons and neutrinos�

�� Both� the cross section and the muon range� rise with the energy� Therefore the resulting muon�ux induced by neutrinos of a hard spectrum is almost �at in the range of �GeV � �TeV � Whilea higher detection threshold reduces a possible astrophysical neutrino signal only marginally� the�ux of atmospheric neutrinos decreases rapidly with the energy� The higher detection threshold�� GeV � of deep underwater muon detectors reduces the background rate compared tocurrently operating underground detectors �� GeV ��

Figure �� B� shows the example of a hypothetic point source� that produces � �� events in theDUMAND II experiment with the expected hard spectrum of a cosmic accelerator �� # �� Thepicture shows� that the rate of background muons due to atmospheric neutrinos falls o� much strongerwith energy� It must be pointed out� that background rates in experiments like BAIKAL NT�� andDUMAND II can be reduced below � per pixel and year� These experiments are not background�limited� but signal�limited and the capability of detecting a point source depends mostly on the�ux of neutrinos� �� The sensitivity to detect a possible neutrino �muon� signal depends on the size of the detector� Assketched in �gure �� a neutrino interaction occurs outside the detector and a muon passes throughthe detector� The perpendicular area around the detector within which muons are detected andreconstructed de�nes the e�ective area Aeff of the detector� The e�ective volume Veff is given by

Veff � R� �Aeff ��

�Because of the annual and daily rotation of the earth a source has no �xed position in local detector coordinates� Afull calculation considers the explicit angular distribution of fake muons and atmospheric neutrinos convoluted with thereconstruction accuracy and the observation time of the source in a certain direction�


ν

μ

μ

μ-Detector

R

eff.Area

eff.Area

eff.Volume

Figure �� E�ective area and volume for underground muon telescopes�

with the mean muon range R��E�� Opposite to conventional underground detectors� DUMAND� typedetectors have no boundaries and are not limited by their geometrical volume� but rather by theircapability of detecting and reconstructing tracks passing outside� On one hand this strongly enlargesthe e�ective volume� on the other it complicates the determination of the quantitative value for thee�ective area� Both the muon range R� and the energy loss rise with larger muon energy giving also alarger Aeff and Veff � The e�ective area is calculated via Monte�Carlo simulations or by comparisonof a measured event rate with a known �ux� e�g� from atmospheric muons or neutrinos� The e�ectivearea depends the e�ciency function of a detector for triggering �trig� reconstruction �rec and qualitycuts during analysis �cut� which themselves depend on the muon energy E� and the direction of the

muon �(��

The actual calculation is performed by simulating a large number NI of random muons vertices on aninitial plane FI and counting the number of events NF � that survive all analysis steps

Feff �E�� (�� # FI � NF �E�� (��

NI��

Published values for the e�ective area are usually given for a speci�c energy and direction or for anevent class� averaged over energies and directions�

To quantify the sensitivity of the neutrino telescope one uses the term�minimum detectable �ux��MDF�� This is de�ned as the minimum neutrino �ux producing a �� excess of a muon signal NS

above a background NB

NS �NBpNB

# ��

To calculate the muon �ux above a detection threshold F�� E�� passing through the e�ective areaof a detector one has to convolute the di�erential neutrino spectrum f��E� with the neutrino�nucleoncross section and the mean muon range� In the next step F�� E�� has to be convoluted with thee�ective area and the observation time of the candidate source� which is the time fraction the sourceis below the horizon � and the operation time of the detector� Typical values for the MDF are�F� � � � ��cm��s�� BAIKAL NT�� and F� � �� cm��s�� DUMAND II � for a thresholdenergy E� �TeV � Comparing VHE gamma �uxes of Crab and Mkn�� one needs a factor R�� see eq�� for these sources to be detectable in DUMAND II � ��

�� Neutrino detection on Earth �

Eve

nts

per

year

abo

ve E

μ

�A� �B�

Figure �� Total event rates from AGN according to several models in comparison with atmospheric neutrinoevents� �A� shows the expected number of upward going muons in DUMAND II versus the muonenergy� �B� shows the number of ��e cascade events in DUMAND II versus the energy� �from ��

GemingaCrabHer X-1SS 433Cyg X-3SN 1987ACen AMkn 4213C2733C279

LOG10(Source distance [pc])

LO

G10

(Lp

[erg

s-1

])

X-Binary

young SN AGN

30

32.5

35

37.5

40

42.5

45

47.5

50

2 3 4 5 6 7 8 9 10

30

32.5

35

37.5

40

42.5

45

47.5

502 3 4 5 6 7 8 9 10

Figure �� Proton luminosity and detectability of individual cosmic neutrino source candidates versus distance�The plot assumes a standard neutrino source eq�� and the production of about �� muonevents per year above ��TeV � Dashed lines show typical sensitivity limits of detectors ranging from��m� to �km� for � year operation� The shaded regions show the areas where typical populations�young supernova remnants� X�ray binaries and AGN reside� The error bars indicate errors of theresulting neutrino �ux and the detectability of this source� Especially in case of Mkn �� the modelof a standard neutrino source yields a smaller � �ux than expected from the VHE � observation� Ifprotons are accelerated in a jet pointing into our direction a larger fraction of the proton luminositycontributes to the � �ux on earth�


The situation is di�erent for di�use extra�galactic neutrino �ux� which is not limited by gamma ob�servations� but rather by the observed X�ray luminosities and measured power�law indices from AGN�Figure �� shows the number of events due to di�use AGN neutrinos expected in the DUMAND II ex�periment� Figure �� A� shows� that the total number of high energy muons exceeds the atmosphericbackground above � ��TeV with a still detectable rate� The importance of the Glashow resonance�eq�� at UHE energies becomes clear with a discussion of �gure �� B�� The �gure shows theexpected number of detectable cascade events in DUMAND II versus the energy� The resonant peak isvisible at E� � ��PeV � producing a clear signal above the background due to atmospheric neutrinos�

It is important to mention� that the earth becomes opaque to neutrinos at UHE energies and the ex�pected angular distribution of events becomes enriched around the horizon� One important applicationis to use the strong attenuation of the isotropic AGN�neutrino �ux to map the inner earth&s densitypro�le� If the �ux rates are large enough� AGN neutrinos provide a probe to measure the inner earth&scomposition� ��

Figure �� shows a summary of estimated luminosities of some discussed candidate sources versus theirdistance� A small detector is generally bounded to close�by sources within our galaxy� Short�timesupernova remnants are detectable within our local group� The visibility of X�ray binaries is limitedto sources within our galaxy� Individual AGN are only detectable for large detectors� The large gap indetectable sources between the scales of our galaxy to cosmological distances is remarkable� The errorbars give only rough estimates on possible errors� Any con�rmation or discon�rmation of expectedneutrino �uxes will improve the understanding of these objects� ��

�� Neutrinos from dark matter

In addition to the previous discussions� cosmic neutrinos are also powerful probes for the investigationof new and exotic phenomena� Especially in case of super�symmetric dark matter particles� neutrinosmay help to identify the nature of dark matter and also to obtain parameters for super�symmetrictheories�

Research on the nature of dark matter gave birth to a large variety of candidates� from axions ��eV �to massive black holes ��M�� a mass range of �� orders of magnitude� A large class of suggestedparticles are thermal relics of the early universe� These stable particles mostly annihilated with theiranti�particles in the early universe� until their density became small and their annihilation probabilitynegligible� Under the assumption� that they are massive enough to close the universe� the cross�section for these thermally created particles turns out to be on the weak scale� and their masses in theGeV � TeV range� Therefore they are named WIMPS�� Several theories� motivated by extensions of the standard model� predict further particles on theelectro�weak scale� which are also in reach for future accelerator experiments� A currently populartheory� the minimal super�symmetric model �MSSM�� will be considered representatively for othertheories� Within the MSSM three possible candidates for the lightest super�symmetric particle �LSP�exist� the neutralino� the gravitino and the sneutrino� The sneutrino is ruled out by direct searches� Ifthe gravitino is strictly stable� cross sections are to small to predict any observable e�ect� � Howeverthe most attractive candidate for the LSP is the neutralino �� a Majorana particle� which is a linearcombination of four neutral spin �� elds

� # Z�)W� � Z�

)B � Z�)H� � Z�

)H� ��

)W�� )B� )H�� )H� are the so called wino� bino and the two higgsinos� The constants Zi dependon the parameters of the MSSM� A postulated discrete symmetry� R�parity� is conserved� To normalparticles R # �� is attributed� their super�symmetric partners have R # ��

Weakly Interacting Massive Particles

�� Cosmological neutrinos ��

�� Neutralino annihilation in the Earth and in the Sun

Though their average density is small� thermal neutralinos are expected to accumulate in the sun andthe earth� due to gravitational capture after neutral current scattering with nucleons� Neutralinosannihilate via

� � �

��

l l �l � lepton�gg �g � gluon�q q ��g� �q � quark�W�W�� Z�Z��W�H�� Z�H�

i � � �

��

The actual branching ratios depends on the choice of the MSSM parameters� Depending on the massm� not all channels �e�g� W�W� or t�t�� are allowed� Decays into fermions are dominated byheavy quarks� because the cross section is proportional to m�

f � Further hadronisation and decays yieldneutrinos� In thermal equilibrium the number of captured neutralinos equals the annihilation rate�� A resulting upward going muon signal either from the direction of the sun or from the core of the earthis expected to exceed the atmospheric neutrino �ux� Future neutrino telescopes are sensitive to a largerange of MSSM parameters and neutralino masses beyond present accelerator limits� A ��m� detectormay yield typically �� events per year for a ��GeV neutralino� Smaller telescopes than ��m� maybe sensitive for m� � �TeV � ��

�� Neutrinos from R parity violation

If R�parity is not a fundamental symmetry� it is likely to be violated and neutralinos may decay�� Inorder to contribute to dark matter� the life time �� must be larger than the age of the universe t�� Anappealing signature for neutrino telescopes are mono�energetic neutrinos with E� � m�� resultingfrom two body decays� If the violation mechanism of R�parity is due to spontaneous R�parity breakingwith a remaining Majoron J �a massless Goldstone boson�� the decay � ��J is the dominant decaychannel� The neutrino �ux is given by

I� � �� t�� GeV

m�cm��s��sr��

The rate of neutrino events inside a detector �� I��N � is independent of m�

N� � � � �� t�� h��kt��a��

with h� the normalised Hubble constant �� Future ��kt�detectors are sensitive down tot�� * Such a weak R�parity violation is far beyond the bounds of accelerator experiments��

�� Cosmological neutrinos

During propagation of highest energy cosmic rays with E � � ��eV through the cosmic microwavebackground� photo�pion production occurs�

p� $� n � �p ��

The cross section reaches its maximum at � � � ��eV � The universe becomes opaque with a meaninteraction length of about �Mpc� The neutrino �ux is calculated by assuming the maximum proton

�In this case also the decay of gravitinos may produce observable results�


energy similar to the maximum observed energies of cosmic rays� The contribution due to close�bysources �d � ��Mpc� is marginal� The �ux may be drastically increased by sources with large red�shifts� due to cosmological reasons� The energy density of the microwave background scales with thered�shift � �� z�� In some cosmological models sources are much more luminous in the youngeruniverse� e�g� during the bright phase of galaxies� The resulting cosmic ray spectra after propagationhas to be normalised on the observations of highest energy cosmic rays� The resulting neutrino �uxmay exceed the expected �ux due to AGNs above ��eV � ��

Several exotic cosmological models involving super�conducting cosmic strings prophesy large neutrino�uxes at highest energies� E�g� strings loose energy into massive fermions �MF � ��GeV �� whichfurther decay� The neutrino spectrum extents up to the Planck mass and is enriched at E ��eVdue to strings at large red�shift� ��

��

� Faint light Deep Underwater

A neutrino telescope deep underwater is composed of a matrix of highly sensitive optical sensors� Thesesensors register optical light which is emitted from charged relativistic tracks via the �Cerenkov e�ect�In order to operate a �Cerenkov neutrino telescope it is essential to examine in details! the propagationof secondaries originating from a neutrino interaction� the optical properties of the deep water� and allambient sources of light�

�� The Deep Underwater Environment

The ocean is a desert with its life underground� and a perfect disguise above�

America Horse with no name ��

Deep water provides extreme but time�stable environmental conditions� Many properties are compa�rable between the BAIKAL experiment� located �� km o�shore at a depth of ��m in the fresh�waterlake Baikal in Siberia� and the DUMAND experiment� located about ��km o�shore the Big Islandof Hawaii at a depth of ��m in the Paci�c ocean� To cope with high pressure � �� atmospheres�and corrosion all components have to be pressure tested and materials have to ful�ll long�term dura�tion requirements� The optical sensors are deployed in high pressure housings made from transparentboron�silicate glass� Connectors and other components are preferably made from titanium�

Water currents are generally low �� cm�s� with slight daily and seasonal variations� Low tempera�tures� ��C �BAIKAL� and ��C �DUMAND �� improve the noise characteristics and time stability ofdeployed electronics� especially of the optical sensors�

Another important aspect for long�term deployment is the sedimentation rate� Though it is small�highly sensitive surfaces of optical sensors are interfered� The accumulated matter is mostly of organicorigin � dead bio mass from the surface water layers� An accidently lost optical apparatus from anearly DUMAND� test�experiment �TTR IV� showed no signs of organic grows on its surface after itsrecovery � �� years later� However slightly warmer surfaces of an apparatus under operation� mayprovide a comfortable climate for dwellings of organic populations� These concerns are not so seriousfor the BAIKAL experiment with � year operation cycles and low power consumption close to opticalapparatus� This was proved by the BAIKAL experiment in the years �� and �� Down�lookingoptical surfaces of the NT�� detector� showed no signi�cant reduction of the sensitivity� Upwardlooking surfaces are stronger a�ected than those looking down and show a ��" reduction of thesensitivity after � year of operation� ��

Surface layers of natural water are dominated by solar radiation� Going deeper the light intensity fadeso� exponentially until one reaches the abyssal zone at � �km in the ocean and ��m in Lake Baikal�Here the solar radiation is below a threshold of � photon cm��s�� Wcm�� The depth for this�ux threshold depends strongly on the surface properties and the �spectral� attenuation length of thewater�

Though long assumed as a cold dead dessert� the abyssal zone is inhabited by about ��" of knownmarine species� mostly bacteria� Little is known about these complex eco�systems� except that directsun�light has only a small in�uence on them� Many of these species produce light themselves� biolu�minescence� Other sources of faint light also become important� cosmic rays and natural radioactivity��

�� The �Cerenkov eect

While passing through matter charged particles loose energy� One major contribution is due to inelasticcollisions with atomic electrons � a quasi continuous ionisation of atoms along the particles path�This process is described by the well known Bethe Bloch formula� Included is a tiny contribution�

�� FAINT LIGHT DEEP UNDERWATER

OMdA

dx

βcvac

vac

cΘ

cΘ

c /n

�A� �B�

Figure �� Geometry of the �Cerenkov cone� �A� Huygens construction� �B� A �Cerenkov cone hitting an opticalsensor �OM��

that occurs if particles travel faster than the speed of light in the medium with index of refraction n�v � �cvac � cmed � cvac�n� This de�nes the �Cerenkov threshold

� � �

n��

Above this threshold some energy is released in form of a coherent electromagnetic wavefront� Ingeneral the index of refraction depends on the frequency of the emitted photons� The total amountof released energy is calculated via an integration over all frequencies � for which n�� ful�lls relationeq��

��dE

dx

�Cerenkov

#� � � �cvac

�Z �n��

��

�� n��d� ��

with the �ne�structure constant �� However in a small frequency �wavelength� window� de�ned bythe optical transparency of the medium and the acceptance of a sensor� the index of refraction doesnot change with the frequency� A calculation for water n � �� yields about ��eV cm�� for opticalphotons ��nm � � � ��nm�� corresponding to � �� emitted photons per cm� The spectraldistribution of the emitted photons is given by

d�N

dxd�#

�

��

n� � ��

��

��

The total �Cerenkov energy loss� typically ��MeV cm�� is marginal compared to the total ionisationloss � �MeV cm�� for minimal ionising particles� The relative importance of �Cerenkov light comesfrom the fact� that all photons are emitted with a �xed angle +c� in a cone around the trajectory! inclose analogy to the emission of acoustical waves released from a plane moving at supersonic speed�In case of relativistic particles �� the �Cerenkov angle is independent on the particle&s energy�Figure �� shows a Huygens construction of the wavefront� The �Cerenkov angle is given by

cos+c #cvac�n

�cvac#

�

� � n ��

�� Cosmic rays deep underwater �

For water �n � �� it is +c # ��

The �Cerenkov threshold energy can be calculated via

Ec mr

��

n�

��

This corresponds �with Tc # Ec �m� � c�� to a kinetic threshold energy of Tc�H�O # �� MeV forelectrons and Tc�H�O # �� MeV for muons in water�

�� Cosmic rays deep underwater

The underground �ux of cosmic rays is dominated by down�going atmospheric muons� This �ux isdecreasing down to a depth of � ��km� where the intensity falls below the �ux of isotropic neutrino�induced muons� Atmospheric muons are created by an initial shower in the top of the atmosphere�e�g�due to a high energy cosmic nucleus� Depending on the primary cosmic ray composition� energy andincident angle single muons or bundles of parallel muons may reach an underground detector� Accessibleto experimental observations are the vertical muon intensity� the energy and angular distribution� themultiplicity and the separation of muons in a bundle� ��The total �ux J� from above is given by

J� #

Z��

j�� sin � d� d� # � Iv

Z��

f�� sin � d� ��

with the directional intensity j�� the vertical intensity Iv and the angular distribution f�� f�� The vertical muon intensity Iv is measured in chapter �� and compared with results ofother experiments in �gure �� The multiplicity �mult may be de�ned as the ratio

�mult #N��N�

��

with Ni the relative abundance of i muons in a bundle� Another characteristic value is the meanmultiplicity N #

PiNi � i� The characteristics of these muons depends mainly on the depth of the

detector�

Several calculations have been performed to calculate these parameters either using empirical formulaeand simulate the propagation of muons down to depths of a detector or by using complex Monte Carlosimulations of the initial shower itself ��

This work concentrates on the approach of Boziev et�al�� as it is implemented in the BAIKAL MonteCarlo Program �� see appendix C�� For the BAIKAL detector �depth� ��m� one gets of�mult � � "� N � �� and for DUMAND� �depth� ��m� �mult � ��"� N � �� These valuesdepend on the energy threshold and the maximum allowed separation necessary for the detection ofthe muons�

In order to search for the needle in the haystack� rare neutrino interactions� one can summarisefollowing signatures�

Electron Neutrinos ��e� �e� perform weak charged and neutral current interactions with atomic nuclei�A hadronic cascade and an electromagnetic cascade� occurs at the point of interaction� Allcharged secondaries in the cascade produce �Cerenkov light� If the shower dimension is smallcompared to the dimensions of the detector volume� the interaction produces a bright point�likesource of light�

�Only for charged current interactions�


At UHE energies an additional channel opens for �e� the resonant interaction with atomic elec�trons at the Glashow resonance� �see eq�� g�� According to branching rations of the W�

decay� bright electromagnetic or hadronic cascades occur in � ��" of the decays� The remaining��" are shared by �� and ��

Muon neutrinos �� perform charged current interactions with nuclei� A hadronic cascade anda muon are generated� The muon travels large distances and emits �Cerenkov light along it&strajectory� This is the standard detection reaction and has been discussed in chapter �� Neutralcurrent interactions produce a hadronic cascade similar to �e interactions�

Tau neutrinos �� are not predicted to be emitted from astrophysical accelerators with a photongas beam dump� If they occur� they perform the same interactions as �� The resulting � decaysimmediately � � � ��s� It&s decay gives birth to a electromagnetic� a hadronic cascade or amixture of both� In about ��" of the decays a muon is generated�

It has been recently proposed that UHE �� interactions may provide a clear signature� whenthey generate an ultra relativistic � traveling several ��m before it decays� The large hadroniccascade from the ��N�interaction and the cascade from the � decay may possibly be identi�edindividually if they occur inside a neutrino detector � generating a so called double�bangevent� These �� may occur in case of neutrino oscillation from an initial �� or �e during thejourney from the cosmic source to earth� ��

The physics of the three phenomenological classes of underground events� muons� electromagneticcascades and hadronic cascades will be exploited further in the following paragraphs�

�� Muon propagation

While passing through matter� muons loose energy via Ionisation� Pair production� Bremsstrahlungand Nuclear interactions� The total energy loss is determined by a summation of the individualcontributions��

�dEdx

#

�dE

dx

I�

�dE

dx

B�

�dE

dx

P�

�dE

dx

N

��

Because the ionisation loss is almost constant above � �GeV and losses due to the other mechanismsrise approximately linearly with the energy� the mean total energy loss is often parameterized via

�dEdx

# aI�E� � b�E� � E��

with b�E� # bB�E� � bP �E� � bN �E� �

A simple approximation can be achieved assuming the parameters aI and bB � bP � bN to be constant

�dEdx

� a� b �E ��

Typical values forH�O� derived from several calculations� are aI # �MeVcm � b # ��cm��

for H�O� �� The solution of the di�erential equation �� gives the energy E as function of the initial energy E�

and the travelled distance r

E�r�E�� #

�E� �

a

b

� exp ��b � r�� a

b��

�In compound materials �like natural water� the individual energy loss for each element has to be summed accordingto their relative atomic weight�

�� Cosmic rays deep underwater ��

The mean range R of a muon is

R #�

b� ln

�bE�

a� �

��

EntriesMeanRMS

1000 974.8 28.52

(A) energy [GeV]

entr

y

EntriesMeanRMS

947 348.3 111.6

(B) energy [GeV]

entr

y

1

10

10 2

10 3

600 800 1000

1

10

10 2

0 200 400

Figure �� Stochastic character of muon energy loss The picture shows distributions of the �nal energy of ��simulated muons �initial energy �TeV � after passing �A� ��m and �B� ��m of fresh water� simulatedwith GEANT �section ��

A detailed description of the muon propagation through matter has to take account of the extremelystochastic character of the individual energy loss processes as demonstrated in �gure �� Even aftera short distance of ��m ��g�� A�� some muons have experienced dramatic energy losses� Thoughafter ��m distance the average energy is still � ��GeV already �" of the muons have been stopped�One has to distinguish between the quasi continuous losses �e�g� ionisation� and so called �catastrophic�losses� mostly due to hard interactions like bremsstrahlung and nuclear interactions�� The catastrophiclosses occur rarely but give birth to large local energy depositions generating electromagnetic andhadronic cascades� Calculated cross sections for all processes are plotted in �gure ��

The phenomenology of these e�ects is demonstrated in �gure �� The pictures show muon tracksincluding all secondary tracks above the �Cerenkov threshold� simulated with GEANT �see section ��Especially for higher energies large densities of secondary tracks may locally accompany the muon� Thetotal amount of �Cerenkov light emitted along the muon track is proportional to the total amount oftrack�length of charged particles above the �Cerenkov threshold� Therefore a high energy muon occursbrighter� but the clear angular characteristic of �Cerenkov light with a sharp angle +c is distorted� Adetailed investigations of the e�ective �Cerenkov light characteristic is performed in chapter ��

�The most catastrophic energy loss process� decay of the muon� has been neglected in this discussion� but is includedin the simulation �chapter ��


100 cm

10 cm

��GeV �

100 cm

10 cm

��TeV �

100 cm

��TeV �

Figure �� Typical muon tracks and charged secondaries above the �Cerenkov threshold for di�erent energies intwo zoom levels�

�� Cosmic rays deep underwater �

�� Electromagnetic cascades

The energy loss of electrons is composed of two parts� electromagnetic radiation �bremsstrahlung�� andionisation loss� The radiative energy loss rises proportionally with the energy� the ionisation lossesonly logarithmically� Above the critical energy Ec radiation processes dominate the energy loss� Thecritical energy may be approximated

Ec � ��MeV

Z � �� MeV for H�O ��

with the atomic number Z� Secondaries from a radiative process experience strong radiative inter�actions themselves and generate new secondaries� As a result of this cascading process electrons�unlike muons� do not travel long distances through water� but immediately produce an electromag�netic shower� Figure �� shows typical electromagnetic cascades for three di�erent initial energiessimulated with GEANT �see section ��

A second characteristic quantity� the radiation length Lrad yields the distance after which the energyof an electron is reduced by a factor of ��e� It may be approximated via

Lrad #�

�� gcm�� AZ�Z � �� ln��

pZ�

�

��

� ��cm for H�O��cm for fresh water��cm for sea�water

��

with the density � and the atomic weight A� For mixtures of materials �e�g� water� the radiationlength is given by

�

Lrad#Xi

wi ��

�

Lrad

i

��

with wi the relative weight fraction of material i� ��

The longitudinal energy deposition of the shower can be parameterized with a gamma distribution

dE

dt# E� � b � �bt�

a�� exp ��bt�'�a�

��

with t # x�Lrad the number of radiation lengths� The total integrated track�length of charged par�ticles is proportional to the initial energy E�� The maximum of the energy deposition tmax scaleslogarithmically with the initial energy

tmax #a� �

b# �� lnY � Ci��

with Y # E��Ec� The parameter Ci is �� in case of an electron induced shower and �� for aphoton induced shower� The ,shower length& is de�ned as

Xs #Lradb

��

��

Numerical values for a� b in fresh water and the e�ective �Cerenkov light is evaluated in chapter ��

�� Hadronic cascades

Hadronic cascades are induced whenever nuclear interactions �e�g� with muons or neutrinos� occur�or the decay of heavy particles gives birth to new hadrons� Analogous to electromagnetic cascades


100 cm

��GeV

100 cm

��GeV

�TeV

Figure �� Typical electromagnetic cascades in fresh water for three di�erent initial energies� Plotted are onlycharged tracks above the �Cerenkov threshold� Though the longitudinal size of the shower does notchange largely� the number of particles increases strongly with the energy� The pictures are postscriptgraphics� which sizes increase as follows� �kB� ��kB� ��kB�

�� Cosmic rays deep underwater ��

�A� �B�

Figure �� Transversal spread of electromagnetic and hadronic cascades� The observer views into the initialdirection of the cascade� �A� shows a ��GeV electron� �B� a ��GeV pion cascade� The pictureshows charged tracks with kinetic energies above ��keV �

secondary hadrons re�interact with nucleons producing a hadronic cascade� The typical longitudinallength scale is determined by the nuclear interaction length given roughly by

�I � ��gcm��A�� cm for H�O��

Hadronic cascades are generally broader than electromagnetic cascades� The average position of theshower maximum is

t� #z

�I� �� ln �E��GeV ��

Hadronic cascades are accompanied by an electro�magnetic component� Individual cascades show large�uctuations in length and corresponding energy deposition� This is mainly due to � e�ects

Generated neutral pions � �� immediately decay � �� The produced gamma�rays induceelectromagnetic cascades� These particles do not contribute further to the hadronic evolution ofthe shower�

Charged pions or other hadrons can decay into muons� These muons do not further contributeto the shower� but may travel farther than the other shower particles�

If these processes happen during an early stage of the shower evolution� they strongly determine thelater development of the cascade� ��

The e�ective �Cerenkov light from hadronic cascades and di�erences to electromagnetic cascades arestudied in section �� Di�erences between electro�magnetic and hadronic cascades are also demon�strated in �gure �� which shows the transversal spread of charged tracks� The electromagneticcascade is very homogeneous� mostly pointing into the forward direction� the hadronic cascade has alarger transversal spread and shows bigger inhomogeneities� The total production of �Cerenkov light isslightly bigger for electromagnetic cascades�


�� Optical properties deep underwater

Unlike conventional detectors in high energy physics water �Cerenkov detectors do not directly measurethe trajectories of particles� but rather detect secondary light and reconstruct these trajectories o��line�The propagation of light strongly in�uences the detectability and the reconstruction accuracy� Mainlytwo microscopic processes a�ect the propagation� absorption and scattering�

Experimentally observable is the di�use attenuation of a beam of light after traveling a path�length xthrough water� One gets an exponential decrease of the irradiance� I� de�ning the di�use attenuationcoe�cient �

I�x� �� # I�� exp �� x� ��

�� the inverse attenuation length� is a function of the wavelength� ��

attenuation coefficient [m-1]quantum efficiency [%]glass transparency [%]Cerenkov photons [0.1nm-1]Cerenkov photons after 10 m [0.1nm-1]

wavelength [nm]

10-2

10-1

1

10

10 2

10 3

200 300 400 500 600 700

�A� �B�

Figure �� Light attenuation for lake Baikal and clearest natural water versus the wavelength� �A� Measured dif�fuse attenuation coe�cient � in lake Baikal �from �� B� E�ective �Cerenkov photon spectrumfor clearest natural water� The initial distribution of �Cerenkov photons is attenuated in water ��mpath� and the glass of the pressure housings� A typical quantum e�ciency curve for a bialkali photo�cathode is plotted �To calculate the e�ective �Cerenkov photon distribution only the relative quantume�ciency distribution was used�� data from ��

The di�use attenuation coe�cient � is an apparent property and is not directly accessible through amicroscopic theory� which yields only inherent properties� It can be calculated from the total �micro�scopic� attenuation coe�cient c and the scattering function �� The scattering function gives thedi�erential light intensity scattered into the direction � from a volume element dV illuminated froman incident beam of light� c is generally written as

c # a� b��

where a is the absorption and b the scattering coe�cient� In order to calculate c for natural water onecalculates c for pure water and adds the scattering and absorption coe�cients derived from calculations

�The value irradiance is de�ned as the radiant �ux through an in�nitesimal area �unit Wm��

�� Optical properties deep underwater ��

for additional dissolved and suspendedmaterials� Absorption and scattering properties are derived fromthe electromagnetic and molecular properties� The scattering coe�cient b can be calculated from thescattering function � via

b # �

Z

�� sin �d� ��

The forward bf and backward bb scattering coe�cients are de�ned as the corresponding integrals�eq�� of � over the forward and backward hemisphere respectively� Approximately � is given by

� � c� bf # a� bb ��

�� Figure �� A� shows several measurements of the attenuation � in lake Baikal �� Small seasonalvariations are observable� The total maximum attenuation length is � ��m� the scattering length �b��was individually measured to � ��m� In comparison an additional curve shows the values for purewater�The attenuation curve has a minimum in the wavelength range from ��nm to ��nm coinciding wellwith the maximum sensitivity of a bialkali photocathode� This allows the use of large area photo�multipliers as optical sensors� The e�ective photon spectrum detectable by a bialkali photocathode isshown in �gure �� B�� The data for clearest natural water is used to calculate the photon distribu�tion ��m away from the �Cerenkov radiating track including the transmission of pressure housings andthe relative response of the photocathode� Geometrical e�ects are not included� The e�ective photonspectrum is bounded by the glass transmission to the UV and by the photocathode e�ciency to thered� ��

(A) distance [m]

phot

on f

lux

/ [m

-2]

Lake Baikal20 m Learned25 m Learned40 m Learned

(B) distance [m]

ratio

Bai

kal /

Lea

rned

Baikal / 20m Learned



10-1

1

10

10 2

10 3

10 4

0 20 40 60 80 1000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100

Figure �� Parameterization of the e�ective photon �ux versus distance� �� A� The photon �ux fordi�erent types of water� �B� Ratio of the Baikal function to the Learned parameterizations�

The density of photons ��d� hitting an optical sensor as calculated in appendix A�� eq��A��depends on the number of generated photons and their attenuation� The function n� � ��d� gives thee�ective number of photons per unit track that survived after traveling the distance d� This functionis calculated by an integration over the distance including the wavelength and distance dependente�ective photon spectrum of �gure �� B�� This is parameterized by J�G�Learned via

��d� � n� #a�

�d� a��a�� exp��a�d��


for several types of water� characterised by di�erent sets of attenuation data� Numerical results areplotted in �gure �� in comparison to the attenuation used in the BAIKAL simulation program� Thecomparison yields a constant ratio � �� between the BAIKAL parameterization and Learned for ��mattenuation� The consequences for the detection of these photons and the design of a detector arediscussed in section ��

The usage of photomultipliers as optical sensors implies the usage of pe as a natural unit for theamplitude of individually registrated signals� The number of pe gives the number of coincident mea�sured photo�electrons due to simultaniously converted photons at the photocathode� Both� the initialnumber of photons and the electrical signal of the photomultiplier� in case of ideal photomultiplier� arelinearly related to the number of pe� Though naturally an integer number� the pe value represents a�oating value due to the �nite pulse�height resolution of the photomultiplier�

�� Natural radioactivity

Natural radioactivity is an inherent property of ocean water� Especially ��decaying isotopes contributeto the underwater photon �ux� if the energy of the resulting electrons �or positrons� is above the�Cerenkov threshold� Whereas the contamination and thus the resulting photon �ux is negligible forfresh water� deep ocean experiments su�er and pro�t from additional light due to ��K� which is thedominant isotope� Potassium is an abundant ingredient of salinity in the ocean� A small fraction ofpotassium isotopes� ��"� is made up by the ��K� which has a half�life period of �� years�The activity can be calculated from the salinity� S via

A # �� S�Bqm��

Typical salinity values range between �� and �� in open oceans� It&s value is generallyconstant at one location� The value S # �� gives a ��K activity of �� Bq m��

Two dominant ��K decay modes occur via a ��decay ��K ��Ca � �� e with a branchingratio of ��" and via electron capture �EC� followed by a prompt ��decay ��K ��Ar��e��Ar� ��Ar� � with ��"� The electron from the ��decay has a maximum energy of �� MeVand an average energy of �� MeV � About ��" of ��decays produce an electron above the �Cerenkovthreshold� The � from EC�decays has �� MeV energy� which is converted into Compton electronscapable of emitting �Cerenkov light� ��

For electrons with the mean ��energy one gets about �� detectable �Cerenkov photons� However in�cluding the energy spectrum of electrons yields a mean value of typically �� photons �� nm�per decay with an electron above the �Cerenkov threshold! a continuous distribution which extends upto � �� photons for the maximum � energy� A volume integration of the activity convoluted withthe optical attenuation yields a typical isotropic photon �ux of � ��cm��s�� It is important to note� that the angular distribution of emitted photons has a strong in�uence on thepulse�height distribution of individual registered �Cerenkov signals� Due to multiple scattering of theelectron the photons are not emitted into a sharp �Cerenkov cone around the initial direction� Theopposite assumption� an isotropic emission also leads to wrong results� Scattered electrons have alower energy and therefore a smaller �Cerenkov angle� Hence most photons are emitted into a solidangle ( � sr around the forward direction� Within this angle the distribution is approximatelyisotropically� In addition electrons scattered at large angles provide a small fraction of light into all

�The ratio needs not necessarily to equal �� because Baikal water has a stronger attenuation to smaller wavelengths�see �g��A�� than ocean water� The result is a smaller value for n� � The used BAIKAL parameterization includes thesignal�amplitude of the speci�cally used optical sensor� The back calculation of the photon �ux provides a systematicerror of about �� Following values have been assumed� quantum e�ciency� � � �� radius R � � cm�

�The salinity S expresses the weight percent contribution of dissolved materials� Usually it is calculated from thechlorine C content via S � �� C�

�� Light of biological and chemical origin �

directions� The size of the angle ( strongly in�uences the ratio of the rate of larger to smaller registeredsignals� ��

It also has to be noted� that the detection of higher amplitudes than �pe is generally unlikely � morethan ��" of registered signals are �pe� The capability to discriminate against these low energy signalsimproves the triggering and reconstruction of muons signals� ��

To evaluate� the rate of registered signals larger than a certain amplitude Ape in the optical sensors�in units of photoelectrons pe� one may integrate the probability of each space point to produce asignal

R� Ape� #

Zd�r � A � P � Ape� m��r��

with the ��K activity A� the probability P � Ape� m� to produce a signal Ape from the space point�r and m��r� the mean expected number of photoelectrons from the space point �r� The probabilityP � Ape� m� is given by a summation over the cumulative Poisson probability to produce a signal Ape� This is given by the incomplete gamma function G�PE� m� � � see appendix A��

P � Ape� m��r�� # G�Ape� m��r�� (

� ��

with the mean solid angle ( for the emission angle of �Cerenkov photons� The integration can beperformed via a Monte�Carlo integration� which allows ot include additional e�ects such as the dis�tribution of electron energies� The calculation is described in details in appendix C�� and results arecompared to experimental data in section ��

The integration method can be also used to calculate the coincidence rate of several N optical sensorsdue to a single decays� Assuming the optical sensors are located at space points �Ri� the probabilityfunction P � Ape� m� in eq�� has to be replaced by

)P � Ape� m��r�� #

�(

�

N�NYi��

G�Ape� m��r� �Ri��

The coincident rates due to single decays have to be compared to random coincidences due to inde�pendent ��K�decays� This random rate can be calculated from the individual counting rates Ri andthe coincidence window � � Calculations show� that coincident signals due to one decay are rather un�likely for typical detector con�gurations� with distances between the optical sensors larger than a fewmeters� Only for close distances of optical sensors � �m� the rate reaches the same order of magnitudeas random coincidences� ��Figure �� shows the characteristics of registered deep ocean light signals� �A� shows count rates ofsignals with about Ape � ��pe� An almost constant count rate due to ��K is superimposed by largephoton �uxes due to bioluminescence �see chapter �� The cumulative distribution of measured ratesis shown in �gure �� B�� It shows that the rate of ��K is a constant inherent source of signals witha rate ��kHz in case of the OM&s used in DUMAND II �see also section ��

�� Light of biological and chemical origin

If the reader considers� that a large fraction of our planet is covered with oceans and that the productionof light is an inherent attribute of all kinds of marine species� she may come to the conclusion� that the

�It has to be noted this method is also appropiate for the calculation of other physic processes� such as expected hitrates in coincidence with a close supernova explosion�

�The large count rates in one optical module �OM �� results from internal noise signals� which occur if the ultrasensitive cathodes have been exposed to bright sun light before usage� This noise decays away down to typically � �kHz�Within the time of measurement ��h the rate of this OM decreased by ��


OM 3

OM 2

OM 4

Measurement No.

Rat

e [k

Hz]

0

100

200

300

400

500

600

700

800

900

1000

1100

x 10 3

0 100 200 300 400 500

�A� �B�

Figure �� Ocean noise measured during the �rst phase of the installation of the DUMAND II detector� Dec��The data contains �� subsequent �snapshots of the count rate of � optical modules in a timewindow of ��s and a delay of ��s between each measurement� The measurement spans about ��hours of real time corresponding to a live time of �� minutes��A� Count rate of three neighbouring optical modules ��m distance��B� Fraction of all rate samples that are above a rate threshold �from ��

production of light is also an inherent property of life on earth� Luminescent organisms can be foundin all kinds of marine species ranging from bacteria and fungi� to larger �sh� Also underground and infreshwater luminescent animals have been found�� Reasons to produce light� some are still speculative�are mainly obtaining food �Illumination or luring of prey�� defence �camou�age� alarm or blinding� andpropagation of species �mating ritual and attraction�� In order to do this many animals possess highlydeveloped light emitting organs� others emit luminescent clouds or are engaged in symbiotic relationsto luminescent bacteria� Bioluminescence is observable in situ and in the laboratory� An importantfeature is� that the emission of light can be stimulated mechanically or photically� Bioluminescence isgenerally produced in a continuous spectrum whose peak emission lies mostly in the region of maximumwater transparency ��max � �� nm�� Several types of chemical reactions are used by organismsto generate light� The simplest reaction occurs via the oxidation of the organic molecule luciferin Lvia the enzyme luciferase

LH� �O�luciferase� light �

The intensity and time characteristics of the light emission depends strongly on the speci�c species�The emission duration ranges from short ms�pulses up to several minutes� The pulses often show afast rise time and a long decaying tail� with more or less complex substructures �e�g�depending on thestimulus�� Intensities can be small� exceeding the photons due to ��K only at short distances �� m��up to the emission �� photons s��

As seen in �gure �� pulses from bioluminescence occur occasionally above a constant backgroundrate due to ��K� Most rate excess peaks in this data set show no correlation between the neighbouring

Biological light is also a major source of background light in lake Baikal�

�� Exotic physics ��

sensors� suggesting a uniform distribution of individuals with low intensity� The duration times followan exponential distribution with � � ��s� However a few extremely bright pulses have durations ofseveral minutes� Also some coincidences are visible� e�g�OM�� and OM�� at measurement�� and� �� Already on basis of the distributions of duration times� count�rates and coincident rates estimates ofthe spatial distribution� density and species are possible for the small data�set above� Most importantfeature in the analysis is� that di�erences in spatial distribution and intensities are di�erently a�ectedby attenuation� The result is a changed distribution of the excursion rate versus the frequency of occur�rence� Without attenuation one expects for a volume density �� of roughly equally bright individuals�intensity I�� a frequency distribution N�q� of recorded �ashes larger the size q

N�q� � � � I�� q��

Including attenuation into calculations allows to separate � and I� in the distributions� The dataof a series of background measurements for the DUMAND I experiment was analysed and yields themean intensities of the population� Strong mechanical stimulations are observed� when the detectoris moving through water� The intensity�depth relation in the paci�c ocean � �km� was found todecrease roughly exponentially with ��e � �km� ��

Future permanent underwater laboratories allow investigations with high statistics on a long termbasis� The optical sensors sample the time characteristics of individual pulses down to � ��ns� Afterthe selection of pulses according to di�erent time characteristics� an analysis according to eq�� canreveal the characteristics of individual species� The complex infrastructure allows to deploy additionalmeasurement devices e�g� to perform stimulations and to do video recordings�

�� Exotic physics

Due to the large amount of monitored volume� underwater neutrino telescopes are extremely sensitiveto a class of predicted super�heavy exotic particles� that may move through the water with non�relativistic speed� Most popular representatives are magnetic monopoles as predicted by theoriesbeyond the standard model� further uni�ng the known fundamental forces� These monopoles havemasses ranging from �� GeV�c� with a velocity of typically � � �� The key signature todetect magnetic monopoles is the Rubakov�e�ect� which predicts a magnetic monopole M to catalysethe decay of protons along it&s trajectory

M � p �

��

M � e� �� M � e� � �� M � �� K� �M � �� K� � � �

This results in subsequent deposition of the energy of typically �GeV thus with �Cerenkov radiatingparticles along the track� The characteristic distance between two proton decays� depending on thevelocity and the catalysis cross section� is typically of the order of less than a meter� characteristic timesin the order of ��s� It is possible to identify the track directly or to search for an excess of the countingrate of two coincident optical sensors within a small time�window of a few �s above the backgroundgiven by a poisson distribution� The second method was applied by the BAIKAL experiment in twoseries of measurements in the years �� and �� These prototype experiments alreadygained the same sensitivity as comparable searches� Results yield upper �ux limits in the parameterspace of the cross section �cat and the velocity � comparable and better to the previous knowledge��

�A count�rate of �Hz in OM�� corresponds to an excess of the maximum count�rate of typically �MHz� This happens� times during the measurement in �gure ��

�� DEEP UNDERWATER EXPERIMENTS

� Deep Underwater Experiments

A large variety of factors determine the detection capabilities and possible success of a neutrino tele�scope� A detailed comparison of the current projects is di�cult due to many speci�c individual charac�teristics and the absence of experience under full operational conditions� Therefore a �nal judgementof the best design must be awaited until these projects are completed�

�� The BAIKAL Experiment

The BAIKAL experiment is the �rst project� which managed to deploy a � dimensional grid of opticalmodules and to run a muon telescope under permanent operation��

�A� �B�

Figure �� Location of the BAIKAL experiment �A� Geographical location �B� Sketch of the site

The experiment is located in the southern part of Lake Baikal ��N� ��E� at about �kmdistance from shore ��gure �� Lake Baikal is the deepest lake on earth and contains a signi�cantpart of our planets fresh water� The water transparency reaches almost the quality of deep ocean water�see �gure �� A�� The depth at the site is ��m� The dominant background light originates frombioluminescence � its intensity is comparable to natural radioactivity in the deep ocean��

As sketched in �gure �� B�� the detector consists of several strings attached to the centre and the �arms of an umbrella�like glass �bre enforced epoxy frame� called HEPTAGON� The construction is bal�anced with buoys and its exact position is measured via a hydro�acoustic triangulation system allowingto monitor the positions of optical modules with an accuracy of ��m� The detector is connected toshore via � multi�wire cables� A third optical cable is deployed but not yet in operation��

Lake Baikal is usually covered with a up to �m thick layer of ice during the months March and April�This natural stable platform is one of the big advantages of this project� It is possible to move heavyinstrumentation like winches trucks and Kung&s right on top of the detector� During the yearly winterexpeditions the HEPTAGON is hauled up to a depth of a few meters below the ice surface� Thisallows yearly maintenance� repair and improvement of the detector� Strings with optical modules areinstalled or removed from the arms of the HEPTAGON through small holes in the ice� All modules areattached directly to string cables� The assembly of cables happens during installation of other devices�There is plenty of space on the ice�� Several working�groups may work in parallel on di�erent strings�During the total deployment the detector is connected to the shore station� The detector or individual

�� The BAIKAL Experiment �

strings may be lowered to deep water at any time� allowing to perform detailed tests on subparts orthe complete system in situ� ��

�� From NT � to NT �

(SEM)

Svjaska

200m

7.5m

5m

17.4m21m

21mString 2

String 3

String 1

Svjaska5mSystem Module

String 5

String 4

Calibration Laser

Installed 1993/94

Installed 1995

Central

(CEM)

StringElectronic Module

Electronic Module

Optical Module(OM)

Svjaska SystemModule

Further strings(in preparation)

(in preparation)Bottom Half-strings

To Shore

OM

Channel

OM

Channel

OM OM

Figure �� Sketch of the NT�� detector and its predecessors NT� �� and NT�� Not toscale��

The present goal of the BAIKAL experiment is the installation of the NT�� detector� NT standsfor Neutrino Telescope� �� for the number of optical modules� �� After the succesfullperformance of smaller test experiments the installation of cables and infrastructure since �� theHEPTAGON�frame was installed in �� together with an ��module test�string �NT�� which wasremotely operated from the shore station for two days� In �� the two string array� NT�� wasdeployed and operated for six months� The full permanent operation as a muon telescope with thecapability to reconstruct muon tracks in three dimensions began �� with the deployment of the��string array NT�� In �� the radius of the HEPTAGON was enlarged from ��m to ��m and someelectronic systems modi�ed� The next step towards NT�� took place �� with an upgrade to the� string detector NT�� However the experiment is still limited by a relatively high failure rate ofOM&s� which reduces the e�ective area of the detector� It is aimed to solve these problems within thenext recursion steps� ��


Figure �� shows a sketch of the NT�� detector including the smaller NT�� and NT�� detectors�The full detector contains � long strings� The detector has a radius of ��m and a height of � ��m withan enclosed mass of � ��kt� The distance to the bottom of the lake is � ��m� The detector aimesat an e�ective area of ��m� �for muons at �TeV � with a pointing accuracy of �� and a minimaldetectable �ux of �� s��cm�� The smaller NT�� detector �� reaches the e�ective area of��m� with an angular resolution of �� for moderate cuts� ��

Optical modules �OM&s� are arranged in pairs with the same geometrical orientation� switched to alocal time coincidence� Such a pair de�nes a so called channel� The electronics� such as coincidencelogic� fast readout and power supply is provided in a separate module� the System Module �SM��Each SM serves � OM&s �� channels�� These modules together build a hierarchical unit called Svjaska�Sv�zka��

The original layout assumes that half of the channels have an orientation with the photo�cathodespointing downwards� the other half pointing upwards� The distances for two channels within oneSvjaska are �m� looking into opposite directions� the distance between two modules of di�erent Sjaskasis ��m� However it has to emphasized� that this geometrical design is not �xed but rather underdevelopment� Especially for the two new strings of NT�� this geometry was modi�ed� aiming a largerspacing with the majority of the channels �� out of �� looking downwards��

Each half�string is equipped with a so called String Electronic module �SEM�� The total detector iscontrolled via the Central Electronic Module �CEM� located � ��m above the detector� A fast laserfor time calibration is located above the detector� It is directly connected to all channels via optical�bres of the same length� For additional calibrations each OM is equipped with an LED� Centralelement of the optical module is the hybrid PMT Quasar�� with a cathode diameter of ��cm� whichwill be discussed in details in section ��

�� Signal processing

Signals are processed in a strong hierarchical order� with the aim to reduce the data already withinthe detector�

On the lowest level the Svjaska�SMs form the local coincidences of the OM�pairs and a fast charge totime conversion of the OM amplitudes using a complicated logic scheme �� This logic is describedin the following in a simpli�ed way� If both OM&s of one channel show a signal above � ��pe within atime�window of typically � ��ns� the local trigger condition is accomplished and a pulse is transmittedfrom the SM to the string electronic module �SEM�� The leading edge of this signal represents theresponse�time of the channel� given by the time of the earliest of the OMs� The summation andcharge�integration of the two PMT�signals with an integration time of about ��ns determines thechannel amplitude and the width of the resulting signal� The local coincidence reduces the signalrates of ��kHz��kHz per individual OM&s down to a rate ��Hz��Hz� The amplitude is measuredfrom �pe up to � ��pe with good linearity up to � ��pe� An additional mode for adjustment ofthe thresholds and calibration allows to stretch the scale for the amplitude or to exclude one or bothOM from the amplitude measurement� ��

Upon receiving a pulse from a channel� the SEM sends a trigger signal to the central electronic module�CEM� and starts the digitisation of the response�time and the channel amplitude with TDCs� Ifwithin the typical time of � ��ns� necessary for a muon to pass through the detector� the numberof signals arriving at the CEM ful�lls the detector trigger condition� a signal is transmitted back tothe SEMs� which stops the time�TDCs� If within ��s no detector trigger arrives at the SEM thedigitisation is cancelled� The time�TDC&s yield an accuracy of � �ns ��bit�� The TDC&s for theamplitude digitisation have a resolution of ��bit with typically �bit�pe� ��

The detector trigger is de�ned by two numbers A�B� with A the minimum number of hit channelsand B the minimum number of hit strings� A typical trigger� �� yields an event rate of a few Hz

�� The BAIKAL Experiment ��

in NT�� In addition to this a second trigger may be applied at the shore station �typically ��The digitised hits are read out from the SEM&s via a special First�in��rst�out bu�er� multiplexedand transmitted to the shore station via serial modem� The data connection may transmit data up to�kByte�s� �� An additional signal branch in the SEM&s is designed to search for events due to slowly moving particlese�g� magnetic monopoles� which may catalyse several Baryon decays in the detector within a timewindow of ��ms � �ms� The number of hits in each channel are counted within this time window�yielding a strongly Poisson�like frequency�distribution� If the number of hits in a channel exceeds athreshold of typically � � hits this value is transmitted to shore� �� Heart of the DAQ�system at the shore is a transputer�farm� which is hosted by the Main�PC connectedto a local area network of PC&s� The transputer system extracts events from the data�stream andperforms a preliminary error analysis� These events are written to a mass storage ��mm�Exabytetapes�� One major feature of the transputer system are complex online�monitoring capabilities� AMonitor PC allows to interactively display various characteristic histograms such as pulse�height dis�tributions during the run� The parameters of the electronic modules in the detector are controlled byan additional computer� which handles requests from the Main PC to the detector and reads backdetector information� ��

�� Calibration

The calibration of the detector is done during speci�c calibration runs� The analysis of these runsallows the determination of characteristic constants� for the calculation of times �ns� �time calibration�and amplitudes �pe� �amplitude calibration� from the raw digitised values� The raw�data �les aretransformed into calibrated data��les allowing further analysis� �� To carry out the time calibration one needs to calculate the true time t from a digitised ��bit worddt using the time o�sets t�j and a scale factors �j for the channel j�

tj # dtj � �j � t�j ��

The factors �j are measured using a special mode� where the digitising TDCs are started by anuncorrelated noise signal and stopped with a �MHz�signal� The result are uniform distributions oftimes within the TDC ranges� The width of these distribution gives ��j � �� The measurement of the time o�set t�j is a more complicated process� The calibrated time t does notrequire a high accuracy in terms of absolute world�time but an accuracy of � �ns relative to theother channels� Thus one needs to measure the time�di�erences between OM response times and areference�signal� A natural approach is to use the time�di�erences between two channels due light fromdowngoing atmospheric muons� Due to the broad angular and spatial distribution of these muons� thismethod allows an accuracy of a few ns� but depends on Monte�Carlo simulations �� The experimentuses a direct method instead� A calibration laser �see �gure �� is located above the detector andconnected to each channel with optical �bres of equal length� Thus an equal arrival time of the lightat each channel is guaranteed� The Laser�system consists of a Dye�laser � ��nm� driven by an N�

laser� which yields a maximum amplitude of � ��pe at each channel and a time�accuracy of ��ns�The light intensity can be controlled by certain fractions� determined by an attenuating disc� whichis rotated by a stepper motor� The system automaticly runs sequences of typically �� laser shots atdi�erent intensities� The events within one sequence� which have a �xed frequency � ��Hz� have tobe �ltered out of the data�stream including background hits due to atmospheric muons� An analysisof these events allows a measurement of the tj� with a statistical error better than �ns� � ��

To perform the amplitude calibration one calculates an amplitude A ��pe�� from the digitised �� bitvalue daj via

Aj # �daj � dpedj � � �j ��


using the pedestal dpedj and the scale factor �j � The pedestal can be directly derived from amplitudedistributions of noise�

The constant �j can be determined via � methods� For the �rst �standard� method one uses theamplitude of �pe signals� The OMs are operateded in a mode which expands the amplitude�distributionwith a �xed factor �� Using the mean amplitude da of �pe pulses this yields

�j #�

da � dpedj

��

The two alternate methods use the amplitude distributions of multi�pe pulses� The distributions aregenerated by the calibration�laser or an LED� which is attached to each OM� The calibration constant�j may be calculated from the mean daj and the width �dj of the distribution via

�j # daj � dpedj

��dj ��

� �j ��

The value �j depends on the energy resolution of the OM� which can be measured with the width ofthe distribution of single photoelectrons signals �see eq�� Di�erent intensities allow to check thelinearity of the Q�T integration� ��

The water parameters are measured independently with a hydrological string close to the detector�� The response of the detector to distant sources of light was measured �� and �� using alaser�system� analogous to the calibration laser� shining directly into the water� Di�erent optical setupswere used for the geometrical light emission� e�g� an isotropic emitting ball or a straight laser�beam��

�� The DUMANDExperiment

The beginning of the DUMAND � experiment may be dated back to a �rst workshop in �� DU�

MAND is thus the oldest underwater neutrino project� The experiment intends to install a detectorarray in a subsidence basin about ��km o�shore the big Hawaiian island Hawaii at a depth of ��km�The array is connected to a shore station in the areal of the Hawaii Natural Energy Laboratory atKeahole point �see �gure �� The headquarter of the experiment is located at the UniversityHawaii in Honolulu on the Hawaiian island Oahu� The Hawaiian islands provide an excellent infras�tructure� especially concerning marine technology� ��

The experimental program started �� with a series of test experiments� mostly examining lightbackground due to radioactivity and bioluminescence� This stage ended �� with a successful testexperiment �DUMAND I �� the deployment of a short prototype string �SPS� from a ship� This stringcontained all subsystems� necessary for the permanent operation of a larger detector� The experimentoperated several hours at various depths� The vertical �ux of atmospheric muons was measured� Thedetector gained an e�ective area of � ��m� for down�going atmospheric muons� ��

The next step is to construct the permanent underwater detector DUMAND II � in two stages�

The �rst step is the installation of an array consisting of � strings and total �� OM&s� the TRIAD�DUMAND II will be completed with the installation of further strings to a total of �� OM&s� theOCTAGON � The TRIAD reaches an e�ective area of � ��m� �E� ��TeV � with an angularresolution of � �� The OCTAGON aims at the e�ective area of � ��m� �at E� ��TeV � with anangular resolution better �� The minimal detectable neutrino �ux for DUMAND II is ��cm��s��

above �TeV ��

�� The DUMANDExperiment ��

�A�

�B�

Figure �� Location of the DUMAND experiment

�� The DUMAND II detector

Figure �� shows a sketch of the proposed OCTAGON� Eight strings are arranged in an octagon arounda centre string� The horizontal spacing is about ��m� Each string contains �� optical modules �OM�with a vertical spacing of ��m� The total string length is � ��m� the instrumentation starts about��m above ground� Floats at the top and within the strings provide the necessary string tension�Central element in each string is the so called String Controller �SC�� which performs both� the fastdigitisation of signals from the optical modules and the control of all modules in the entire string �see

�Deep Underwater Muon and Neutrino Detection


JB

40m

53m

To shore

230m

100m-4800 m

TRIAD10m

-4400m

OM

SC

CM

HY

CTD

VL

FL

SM

NBU

300m

Figure �� The DUMAND II detector �Not to scale�� OM� Optical Module� SC� String Controller� CM� Cal�ibration Module� HY� Hydrophone� NBU� Neil Brown Unit� CTD� Conductivity�Temperature�Depthmeter� VL Video � Light� FL� Floats� SM� Sonar Module� JB� Junction Box�

�� The DUMANDExperiment �

section �� Two di�erent types of OM&s are used� the JOM�� based on the conventional largearea photomultiplier Hamamatsu R �� and the EOM�� based on a new type hybrid photomultiplierPhilips XP �� which uses a combination of an electro�optical pre�ampli�er with a small conventionalPMT� The diameters of the Hamamatsu and Philips photomultipliers are ��cm and ��cm� �see section��

Calibration modules �CM�� alternating one or two per string� are mechanically and electronically similarto OM&s but contain a laser calibration system for the detector� A scintillator ball� �m distant from theCM is illuminated by two lasers and produces isotropic bright UV��ashes� which are measured by theOMs in the detector� A small photomultiplier inside the CM monitors the reference time of the �ashand sends it to the SC� This allows the calibration of the relative response�times and and pulse�heightsof the OMs as well as the in�situ measurement of the light attenuation length� ��

The power to the detector ��kW � �kV DC� is provided via an electro�optical cable and a sea return�using a pair of platinum electrodes� one at the shore the other at the detector� The cable ends at apassive box at the bottom of the ocean� the junction box �JB�� Each of the total �� of optical �bres inthe cable is lead to a single port� Each string is plugged into one port� either using a deep submergencevehicle or a remotely operated robot� This allows a direct link between each string controller and theshore station� ��

Several systems to monitor environmental data are integrated within the detector� Attached to the JBis a small environmental string �JBEM�� which is mechanically integrated into the centre string� It isalso directly connected to the shore� using one of the spare optical �bres� It contains a conductivity�temperature�depth meter �CTD� and a video�camera system and acoustical devices� Each string con�tains a Neil�Brown�Unit �NBU�� which integrates a current meter together with a CTD� Integrated inthe SC�pressure housing is an additional environmental system including a compass and a tiltmeter��

The experiment is equipped with a sophisticated acoustical system� containing �� hydrophones �HY�� in each string� � at the JBEM� � elsewhere� for two reasons� First the accurate reconstructionof muon tracks requires a very precise monitoring of the positions of the OM&s and CM&s� Secondlyit is intended to study the possibility of an acoustical detection of UHE neutrino interactions� Thismethod� if successful� could provide an inexpensive experimental technique for the realisation of verylarge detection volumes� The acoustic properties of the deep ocean are measured continuously andprovide long�term environmental data� The locating system gains an accuracy better than ��cm forthe relative locations of modules and an absolute geographic position accuracy of a few meters �limitedby the GPS accuracy� allowing to maintain celestial coordinates better than �� The data�stream fromthe HYs is digitised in the SCs� ��

The �rst attempt to begin the installation of the TRIAD detector in December �� was only partlysuccessful� The �rst string was deployed together with the junction box and the shore cable� Howeverafter a few hours the central string controller failed due to a hair�leak in one of its connectors� Thecentral string operated for a few hours� measuring mostly light due to radioactivity and bioluminescence�see �gure �� and section �� This demonstrates the disadvantage of a strongly hierarchical designof a remotely operating experiment� since the failure of a central element may signi�cantly harm thetotal detector� The string was recovered after triggering an acoustic release in January �� Since thejunction box and the shore cable are still operating it is intended to �nish the installation of the threestrings of the TRIAD early �� It has to be noted� that the DUMANDproject is strongly handicapedby an inadequate funding and the unreliability of avaliable ship�time to perform installations� ��


Power(48V)

Control,Power(48V)

Tref

optical linksingle mode

(500 Mbd)

Control,

Ocean cable (30km)

String-Controller (SC)

DataDigitisat.(1ns)

Position

#1..#24 #1..#5OM CM HY

#1..#4SM

JBEM

String #1..9

#1..#2

Trigger processor

Power supplyOnline computer

Fast link to the world

Detector control

Shore-Station

(Koax 1000V DC)

(12 fibre, full duplex link)

All Data Power

(350V DC)

Junction Box (JB)

Enviroment

#1

NBU

Data storage

Enviroment(Ocean bottom)

Sea water return

Figure �� Schematic overview on the DUMAND II detector

�� Signal processing and triggering in DUMAND II

Figure �� shows a schematic diagram of the DUMAND II detector� Each string controller is connectedto the shore�station via a passive connection at the junction box� Each OM is connected to the SCvia two cables� a coaxial cable for power�supply and slow modem�link and a multi�mode optical �brefor fast data transmission� A computer in each SC� equipped with a �� microprocessor runningan OS�� operating system� controls the power�supply of all modules in the string� The modem�communication� which is superimposed onto the DC�power�supply allows to connect to each OM�

�JOM� Japanese Optical Module�EOM� European Optical Module

�� The DUMANDExperiment ��

which are also equipped with a computer running OS�� This link allows to individually control andmonitor each OM&s internal parameters� e�g� high voltages �see section �� Both types of opticalmodules� JOM and EOM� are interchangeable in terms of communication and system compatibility�Besides the micro�computer the OM&s are equipped with a fast�readout for the photomultiplier signals�which is designed to the speci�c photomultiplier� The EOM�readout performs a fast charge integrationand produces a charge to time �QT� converted signal� The JOM measures the pulse�duration above anamplitude threshold �Time Over Threshold� TOT� and performs� in case of a higher amplitude� alsoa QT conversion �see section �� These resulting pulses are immediately transmitted to the SC viathe optical link� ��

The arrival time and pulse�width of each OM signal is digitised in the SC and transmitted to shorevia a full duplex optical link with ��MBd� Heart of this system is a monolithic multi�hit time�to�digital converter chip� This chip was especially developed for DUMAND II and contains about�� transistors implemented in a GaAs gate array� It is driven by a frequency doubled clock with��MHz to �GHz� providing a digitisation accuracy down to �ns� It achieves continuous digitisationof �� channels without dead�time� a pipelined bu�ering of a total of � �� pulses and a continuoustransmission rate of up to ��kHz per OM� ��

Because of the full transmission of the raw detector data to shore� complex trigger strategies for variousphysical purposes may be implemented at the shore station� The nine serial data streams from thestrings are put onto parallel busses and fed into a four level trigger�processor� whose �rst three levelsare resident in a single VME�crate� The �rst level� implemented in a custom built circuit board� parsesthe data stream and searches for local coincidences on a single string level� The next two levels� whichsearch for higher level coincidences involving several strings� use commercially avaliable digital signalprocessors� Finally the data is transmitted via Ethernet to the fourth level� a cluster of workstations�This cluster performs control and monitor functions of the underwater systems� a preliminary data�analysis and the data storage� It is intended to enable access to data and the detector operation viaworldwide network communication� ��

The presence of high background noise rates and the absence of local triggers in the detector requires afast� e�cient� trigger scheme� The expected number of noise hits per ��s is of the order of �� assuminga single noise rate of �kHz per OM�� which is in the same order as the expected signal from a muonevent� Even a trigger with more than �� hits per �s would yield a rate with random noise events of� �kHz� ��

Since the noise signals are almost entirely �pe signals� but muons generally produce higher signals �atleast in one PMT�� a simple energy trigger on the number of photoelectrons larger than a speci�cvalue yields a better suppression of noise� This trigger condition is called TE xpe� This approachcan be improved employing optical modules with a good energy resolution in the multi�pe regime� Thisapproach requires a linear read�out for the pulse�height of the OM signal �see section ��

The majority of muon hits involve a hit coincidence in three neighbouring OM&s in any string� Thetime di�erence $t ful�lls the relation

$t � j jt� � t�j � jt� � t�j j ��ns ��

yielding an e�cient trigger called T�� An alternative is the combination of a local energy triggerwith a local coincidence� requiring a large amplitude in one of two OM hits in coincidence or generallya larger TE on basis of one string� ��

A combination of these triggers can be implemented in the �rst stage trigger processor� reducing therate of the noise by a factor of � �� and e�ciently trigger muon events on a single string basis� ��

For analysis in later trigger�stages� more e�ective triggers mainly use the combination of above triggers


for several strings� A useful notation is

T � a� b� c with

��

c � Value of the coincidence� e�g� � # T��b � Number of c�coincidences in each string� e�g� � times T��a � Number of strings with b coincidences of type c each�

��

As an example e�ective trigger combinations to reduce the noise rate below �Hz without dramaticreduction of the e�ective area were found for the TRIAD detector to� T � � � � � �� T � � � � � ��T � �� TE ��pe� in case of �kHz OM noise rates and �T � �� T � �� T � �� T � �� T � �� TE ��pe� for ��kHz OM noise� It has to benoted that � hit neighbour OMs ful�l the �T � �� condition� � ��

It has to be noted that the above trigger�conditions are not valid for non relativistic particles� Theserequire additional hardware components in the trigger processor�

�� Other projects

Two other experiments� AMANDA and NESTOR � are also important in discussion of current highenergy neutrino detectors and the design of a future km� detector� The community of the four currentprojects is sometimes named BAND� A further in�situ test experiment was carried out in the Atlanticocean by the JULIA project early ��

�� AMANDA

Within the AMANDA experiment the extremely transparent deep ice of the antarctic glacier is used asdetector medium instead of deep water� Despite of this it has a similar physical approach and madeenormous progress over the last years� It is the only experiment at the southern hemisphere and is thuscomplementary to neutrino experiments at the northern hemisphere� The experiment is directly locatedat the south pole using the local infrastructure of the U�S� research station� Amundsen�Scott� Duringthe months of the antarctic summer holes are melted into the ice and strings with optical modulesare installed in depths deeper than �km� The detector is not accessible during the rest of the year�On the one hand this installation technique provides the advantages of an easy installation with thepossibility to walk and work right on top of the detector� on the other hand it is impossible to recoverparts of the detector for repair� It thus requires a very robust design and choice of components� Thedetector can be expanded very �exible without limitations due to previous installations� Close to theexperiment is the location of the SPASE air shower experiment� which allows to measure coincidencesbetween down�going muons and air showers detected at the surface� � � ��A further advantage marks out this experiment� The ice is a sterile medium with a constant temper�ature � ��C� This provides stable operation of electronic components and low noise�rates of thephotomultipliers� Furthermore the ice itself contains no radioactive isotopes like ��K and biologicalmatter� Therefore the total signal rate per OM is low �� kHz� allowing simple trigger schemes� � �During winter �� four strings with total �� OMs have been installed in a depth of ��m to ��m�Since the data acquisition electronics is located close to the detector it is possible to transmit theanalogical PMT signals directly to the surface via coaxial cables� In consequence the optical modulewas designed in a very simple and reliable way containing only ��cm �� diameter photomultipliers�

without further electronics� Each OM is directly connected to the laboratory without a hierarchicaldata acquisition scheme inside the detector� During winter �� the data acquisition and calibrationsystems were upgraded together with an additional system to detect neutrinos from supernova bursts��

�Baikal Amanda Nestor Dumand�

�This PMT has about �� of the sensitive area compared to BAIKAL and DUMAND II �

�� Other projects �

Unfortunately it turned out� that the scattering length is very small at this depth but slowly improvingwith the depth ��cm�� Emitted �Cerenkov photons are multiple scattered and perform a randomwalk� Thus they loose their initial time information preventing a good reconstruction of the initialmuon� However several muons have been detected in coincidence with the air shower array� Thestrong scatter properties of the ice originates mainly from small air bubbles enclosed in the ice� It isexpected� that these bubbles disappear at depths below ��m due to a phase transition� At thesedepths the scattering lengths may reach several ��m� limited by dust enclosed in the ice �e�g� due tohistoric volcanic eruptions�� Despite of this it turned out in absorption measurements that the ice ismore transparent than expected� in the optical region ��nm� yielding � �m� similar to attenuationin puri�ed water� Furthermore� several independent methods show indirect evidence for an extremelylarge attenuation length at smaller wavelengths up to more than ��m below ��nm� In consequencethe number of detectable �Cerenkov photons per unit track rises in comparison to water �see �gure��

The aim for winter �� is to deploy further strings� containing �� OMs to a depth of ��m to��m� With regard to the expected improvement of optical properties� the spacing between OM&s willbe signi�cantly enlarged� The deep location requires a modi�cation of the optical modules� in order tobe able to transmit the OM signals with the required accuracy� ��

�� NESTOR

The Nestor is an European experiment located in the Mediterranean� approximately ��km south�eastof the coast of the Peleponnisios �Greece�� at a depth of ��km� Though many technological aspectsare closely related to DUMAND II the geometrical design is di�erent in order to achieve a lower energythreshold for the detection of muons� ��

The �rst phase consists of a tower� ��m tall� which is built of �� hexagonal �horizontal� structureswith a vertical spacing of �� m between each hexagon� A hexagon consists of arms with a radiusof of � m� Each hexagon consists of �� large area OMs with two in the centre and two at the end ofeach arm� The OMs of each pair look into opposite directions� one down � one up� in order to achievea � sr sensitivity for the detector� In further expansions of the detector it is intended to deploy additional towers at distances of about ��m��m around the �rst tower� yielding a detector with ane�ective area of � ��m� and �� OMs� ��This design may lower the energy threshold for muon detection below �GeV making this detectorsensitive for long baseline neutrino oscillation experiments� This may be done by measuring theatmospheric neutrino �ux versus the zenith angle� yielding oscillation length from ��km to ��km�As an alternative� a long baseline oscillation experiment with a neutrino beam from CERN to NESTORwould yield several �� events in one tower and thus a good coverage of small mixing angles� ��

First experimental tests have been performed in situ� lowering one hexagon attached to a cable todepths below �km� The small detector was equipped with batteries� CAMAC�electronics in pressurehousings to process the data and a computer to record the data to tape� Relative muon �uxes atseveral depths have been obtained� ��

�� JULIA

The aim of the JULIA � project was to construct a neutrino telescope with a strong inherent aspect touse this detector as a permanent deep underwater laboratory for interdisciplinary research� ��

During a small test experiment in the Atlantic ocean� close to the Canary island Gomera� a small

�Previous laboratory measurements showed only absorption lengths in the order of �m�Joint Underwater Laboratory and Institute for Astro�Particle�Physics

�This was done in a cooperation between the University of Technology RWTH Aachen �III�Physikalisches Institut�Institut f�ur Lagerst�attenlehre� and DESY IfH Zeuthen together with the companies Philips and AEG �Kabel Rheydt��

� � DEEP UNDERWATER EXPERIMENTS

string containing three optical modules was lowered from a research vessel� The purpose of this cruisewas to test advanced but robust technologies for future detectors� Main research aspects have been�

Each OM was individually connected to a DAQ�system aboard the ship� to avoid a hierarchicalstructure and thus sophisticated signal processing underwater� This requires a signal transmissionlink capable of transmitting asynchronous signals from an OM via several km distance preservinga time�jitter better than �ns� Links with several km mono�mode optical �bres have been tested�Results show only a marginal degeneration of the time resolution after �km �bre ��ps�Under experimental conditions this system gave proof of reliable working� despite of a water leakin the signal cable� This opens the possibility of transmitting individual signals from OMs overseveral tens of kilometers� e�g�to a shore station� without signi�cant dispersion and loss of timingaccuracy� ��

Construction of prototype optical modules containing the new type hybrid photomultiplier�Philips XP� �� together with a fast� self triggering charge integrating readout� The EuropeanOptical Modules� described in section �� are based on this development� ��

The JULIA project did not receive further funding� but experiences have been useful for the BAIKAL

and DUMAND II experiments� � ��

�� Perspectives of underwater neutrino physics

Detector year Vgeo Aeff reference��m�� m��

First stageNT�� TeV �� TeV � ��NT�� atm�� NT�� TeV �� TeV � �� DUMAND II �TRIAD� � �� TeV �� TeV � ��DUMAND II �Oktagon� � �� TeV �� TeV � �� AMANDA � �� NESTOR ��rst tower� � �� TeV �� TeV � ��

Second stageBAIKAL II � � � �� AMANDA II � �� NESTOR �� tower� � ��

km� stageKM� �Halzen� � �� KM� �Learned� � � ��

Table �� Parameters of various underwater detectors

In �� several workshops were held with the aim to form international working groups to design alarge �km�� detector for high energy neutrino astrophysics� Several design proposals have been done�Table �� gives a summary on various detectors� which are proposed or under construction� ��

�� Mean visual range and the design of a Deep Underwater Muon Detector �

�� Mean visual range and the design of a Deep Underwater Muon Detector

The history of the past years showed that considerations such as a robust experimental strategy�easy access to the experimental apparatus and low costs for deployment expeditions have a muchlarger impact than expected in the early years of the projects� Therefore the primary managementconsideration is not necessarily the costs of the optical sensor itself�Despite of this� a fundamental question is the optimisation of a geometrical detector con�gurationunder the prerequisite of a given ��xed� number of optical modules �� A second important item isthe choice of the appropriate optical sensor itself and the design of the optical module ��

Assume a cubic grid with the side length L and N optical modules �xed to vertical strings� �lling thevolume of the detector� The optical modules are horizontally and vertically separated by the spacingb� The number of sensors N is

N #

��

L

b

�� L�

b��

Since the total volume is given by V # L� the detector volume per optical sensor v is

v #V

N� b� ��

In order to maintain a big �inexpensive� detector volume� it is highly desirable to achieve a large spacingb of optical modules� The best spacing is derived from a full analysis of the detector perfomance�especially concidering e�ective area and good track reconstruction capabilities �see also chapter ��and ��

In order to determine the largest possible spacing a �rst order estimate may be achieved� investigatingthe mean visual range Lvis of an optical module� Lvis depends mainly on the light attenuation in thewater� the sensitivity of the optical sensor and the minimal detection threshold per OM� Sensitivityand attenuation are closely connected� A more sensitive OM may detect smaller photon �uxes froma more distant muon� A stronger attenuation requires a more sensitive sensor to maintain the samevisual range� �see also chapter �� and appendix A�� The minimal detection threshold depends onthe speci�c detector� In order to understand this the reader may assume a muon passing through adetector with several layers of optical modules� For a small detector a clear identi�cation requires ahit in every layer� which is not necessary for a detector with a larger number of layers� Therefore therequired detection probability and thus the minimal detection threshold is smaller for larger detectors�Obviously a smaller detection threshold is equivalent to the use of a more sensitive optical module�A calculation of Lvis requires a full integration over the probability P of a muon to generate a signalabove the threshold Ape

Lvis #

s� �Z

�r � P � Ape� m�r�� dr��

m�r� is the mean number of photo�electrons�� for a muon passing at the perpendicular distance d� # r�The probability P to produce a signal above the threshold Ape is given by the incomplete gammafunction analogous to section �� which yields the cumulative Poisson probability function to producea signal above Ape ��

P � Ape� m�r�� # G�Ape� m� ��

Figures �� demonstrates the above discussions� The diagram shows the mean number of photoelectrons m�r� �� from a minimal ionising muon track for di�erent light attenuation� Using the contour

It has to be noted� that due to the geometry of the �Cerenkov e�ect the distance d� the light travels is longer than theperpendicular distance d� to the track� which is equivalent to Lvis� It is d � d�� sin c � �� d��

� !m�r� is given by eq��A�� using d � r� sin c��This is calculated from the photon density ��gure �� using eq��A�� appendix A�� assuming a peak quantum

e�ciency � � �� and the diameter �R � � cm for a full illuminated optical sensor�


perpendicular distance [m] n

mea

n PE

6

5

4

3

2

1

perpendicular distance [m]

mea

n PE

0 20 40 60 80 1001 2 3 4 5 6

10-3

10-2

10-1

1

10

10 2

10-4

10-3

10-2

10-1

1

10

20 40 60 80 100

Figure �� Number of photoelectrons from a minimal ionizing track versus distance for several types of water�� n � � � � � corresponds to attenuation lengths� �m� �m� ��m� ��m� ��m� ��m� �mcorresponds to lake Baikal water� ��m to DUMAND � water� ��m to clearest observed ocean waterand ��m to puri�ed water of proton decay experiments�

lines in �gure �� A� or drawing a horizontal line into �gure �� B� at a given threshold yields thevariations of the mean visual range for di�erent attenuations� A less sensitive �smaller� sensor or anillumination from the side corresponds to a higher threshold in the �gures� It can be seen� that forhigh thresholds �small OM&s� the in�uence of the attenuation is much smaller than for low thresholds�large OM&s��Considering the detectability of a certain muon �ux the visual area Avis � L�

vis becomes important�see eq�� Avis depends on the radius of the optical module R�� Neglecting attenuation and usinga sensitivity proportional to the OM area �� R�

�� one gets

Avis � R��

However especially for low detection thresholds and a large radius R�� this is not realistic� Using theparameters of present experiments one gets a much weaker dependency

Avis � R��

It has also to be noted� that it is not realistic to increase the sensitivity of optical modules in the deepocean above the present values� because of a strong increasion of the count rates due to ��K decays��

Another important aspect is the use two OMs switched to a local coincidence �BAIKAL � instead ofindividual OM&s �e�g�DUMAND ��

�� Mean visual range and the design of a Deep Underwater Muon Detector �

20 m

20 m (coinc)

40 m

40 m (coinc)

(A) perpendicular distance [m]

hit p

roba

bilit

y

MC - Generator

MC - Reconstructed

DATA NT-36 (1993)

(B) perpendicular distance [m]

hit p

roba

bilit

y0

0.2

0.4

0.6

0.8

1

0 10 20 30 40 500

0.2

0.4

0.6

0.8

1

0 10 20 30 40 50

Figure �� Hit e�ciency versus distance to the OM� �A� shows the calculated hit probability for full illuminatedsingle and coincident OM s� each for �m and ��m water� �B� shows experimental and Monte Carlodata from the NT� detector� The MC�data includes a simulation of atmospheric muon bundles anda reconstruction �� Plotted are the distributions for all generated tracks �MC�Generator� and forall reconstructed tracks� which pass all quality criterias �DATA�MC�Reconstructed��

This brings the disadvantage that the required number of optical modules is doubled and due to thecoincidence condition the mean visual range on becomes smaller� Lvis may be calculated modifying Pin eq�� via

P � G�Ape�� m�� G�Ape�� m�� # G�Ape� m��

The right part of the equation is valid for identical sensors and thresholds�

The advantages are a much easier signal processing �see sections �� and �� and the possibleuse of simple and fast reconstruction algorithms without the need of sophisticated noise reductionalgorithms��

Figure �� A� shows the calculated hit probability for ��m and ��m attenuation length of the waterfor single OM&s and two coincident OM&s� Assumed is an OM with fully illuminated photocathodeand ��" trigger e�ciency for �pe signals �Ape # �� For short distances the hit probability forcoincident and single OM&s does not di�er largely�

Figure �� B� shows a comparison between Monte Carlo and experimental data for the NT�� de�tector� The hit probability does not reach � for small distances� because sometimes modules show nohit for close tracks� This is an e�ect of di�erent orientations of optical modules to atmospheric muonsand the dead�time of the modules themselves� Because NT�� is a small detector� tracks more distantthan ��m from an OM&s mostly pass outside of the detector� Therefore these tracks are likely to failtrigger conditions or quality criteria after reconstruction�

Eq�� can be generalised to n identical optical sensors with the same threshold located at the same

��To demonstrate the di�erence� Each event in DUMAND II contains about �� hits which are due to noise� In theBAIKAL NT�� detector only �� of all events contain one channel with a noise hit�


space�point� Requiring at least m hit OMs out of n yields

P #nX

k�m

�nk

�� G�Ape� m��k � �� G�Ape� m��n�k��

As an example the requirement of at least � hit out of � OM gives

P # G� � � � G� � �� G� �

20 m water

40 m water

60 m water

APE

Lvi

s [m

]

0

20

40

60

80

100

120

140

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Figure �� Mean visual range for a single OM versus amplitude threshold for �m and ��m water

A calculation of the mean visual range requires setting Ape to the appropriate value and performingthe integration eq�� An ideal photomultiplier allows only natural values for Ape # �� However using the argument for a big detector �page �� that not necessarily each OM� which shouldhave a hit� must indeed have a hit� a fractional value of e�g� Ape # �� may be interpreted as anamplitude threshold of �pe with a hit e�ciency of only �� Figure �� shows the results for Aperanging from ��PE to �PE� For smaller amplitudes the di�erences between the di�erent attenuationlengths become larger� Thus a large km� detector with a lower threshold allows a signi�cantly largerspacing if the detector operates in clearer water�

� The Optical Sensors

�� Optical Modules for DUMAND II and BAIKAL

Optical modules may be designed in a large variety� While the OMs for AMANDA consist only of anaked photomultiplier glued into a glass pressure housing� the OMs for DUMAND II also contain acomplex control system and fast readout for the photomultiplier� As an example �gure �� shows asketch of the European Optical Module �EOM� for DUMAND II �

Electrical penetrator

Vacuum port

Pressure sphere Silicone gel

Electronic

HV (25kV)

Electronic

Optical penetrator

Voltage divider

432 mm345 mm

Philips XP2600

Small PMT

HV (2kV)

Figure �� Sketch of the EOM�

Two types of optical modules� the EOM for DUMAND II and the Baikal OM �BOM�� contain a newtype of large area photomultiplier �PMT�� The principle of a hybrid PMTs and its advanced propertieswill be discussed exemplarily for the EOM in the following�

�� Optical Modules for DUMAND II

DUMAND II contains � di�erent OMs� which have been designed in a parallel development in Japan�JOM� and Germany �EOM�� They are interchangeable in respect of the interfaces to the rest of thedetector� ��

The EOM was developed on basis of the JULIA OM� using the large area phototube� Philips XP� ��and the fast read�out� DMQT� The phototube is constructed according to a new principle� thecombination of an optical pre�ampli�er with a small ��mm�diameter photomultiplier XP�� This

� THE OPTICAL SENSORS

technique yields advanced characteristics with respect to time and amplitude resolution �smart PMT�� The fast read�out DMQT performs a fast charge integration and produces a rectangular signal�whose leading edge gives the response�time of the photomultiplier and whose width is proportional tothe integrated charge �number of pe�� For high amplitudes the width scales logarithmically with thenumber of pe� A detailed description of the design is given in section �� and its properties in ��

The JOM is a signi�cantly improved descendant of the OM used for the DUMAND I experiment�Similar to the EOM� the JOM is composed of a large photomultiplier with a fast read�out� power�supply and a remote control unit �RCU� based on a ��CPU� Heart of the JOM is the ��cmdiameter photomultiplier Hamamatsu R�� Major advantage of this PMT are short pulses� allowingto detect consecutive hits� which are separated by more than ��ns� It is aimed to take advantage of thisfor the identi�cation of muon bundles� The timing and pulse�height characteristics are injured by thegeneral approach� to increase the cathode area to a large diameter with a spherical shape and do notreach excellent values of small photomultipliers� However the timing characteristics and pulse�heightresolution have been signi�cantly improved compared to its predecessor due to an optimisation of thecathode shape and the dynode structure� The PMT reaches a transit�time�accuracy �FWHM� of about ns for �pe signals in full illumination� The transit�time di�erences with respect to di�erent angles ofillumination are of the order of �ns� A single photo�electron peak is visible in distributions of darknoise� In order to achieve a full sensitive cathode area� the PMT has to be shielded by a ��metal gridagainst the earth magnetic �eld� �� The fast readout measures the pulse duration �time over threshold� TOT� and additionally measuresthe integrated charge �Q� for pulses larger �pe� The OM produces a rectangular pulse� whose leadingedge gives the response�time of the PMT and its width the TOT� If a Q measurement is present asecond ��ns delayed pulse is produced� with a width proportional to the logarithm of the integratedcharge� ��

�� The Optical Module for BAIKAL

The optical module for BAIKAL consists mainly of the photomultiplier Quasar�� This hybridphotomultiplier is an advanced copy of the Philips XP�� It has a mushroom shape� which isoptimised in respect of transit�time di�erences from di�erent cathode points� Values better than �nshave been achieved� Other properties are similar to the XP�� The glass pressure housing was especially developed for the BAIKAL experiment� Because BAIKAL

is located relatively shallow �� km� the housing has thinner walls compared to deep ocean pressurehousings� The optical contact between the cathode and the pressure�sphere is achieved by liquidglycerine� which is sealed by an equatorial ring of poly�urethane� The OM is not transparent from theback�High voltage�supplies� a voltage divider and a LED are included inside the OM pressure�sphere� Thecontrol and read�out electronics is housed by the Svjaska Electronic Module �see sect�� Thepulse�charge is linearly integrated� A Q�T transformed pulse is transmitted whose width is linearlyproportional to the number of pe� The dynamic range goes from �pe to several hundred pe� A goodlinearity is guaranteed up to ��pe� ��

� Design of the European Optical Module �

�� Design of the European Optical Module

CPU Modem

Comunication

Power &

DATA (optical)Q-T

DC/DC

DMQT

Pulse

LED

XP2600

Philips PMT

Remote Control Unit

DAC

ADC

To String Controller

Driver

Tresholds

Fast Circuit

Count rate

2kV25kV

SensorsTemperaturesLeakageCurrentsVoltages

High Voltage

Figure �� Schematic diagram of the EOM

The EOM is a self�contained detector for faint light� All functional parts are included in a glasspressure housing ��cm outer diameter�� which is available for standard deep ocean applications� Thefunctional units are schematically drawn in �gure �� and a sketch is shown in �gure �� These are�

The large photomultiplier �section ��

The fast electronics �section ��

PMT�signals are charge integrated in a fast circuit called DMQT� The Q�T signal is convertedto an optical signal and directly transmitted to the outer world via a multi�mode optical �brethrough an optical penetrator in the pressure sphere�

A Remote Control Unit �RCU�� called the slow electronics�section ��

A specially designed ROM�based micro computer handles monitoring and setting of variousmodule parameters� It communicates to the outer world via a serial modem link� which issuperimposed onto the power�supply to the OM�

The OM receives ��V DC power via an electrical penetrator� DC�DC converters generate thesupply voltages for the electronic circuits�

The Philips PMT requires two high voltage supplies� One of these is �xed to ��kV � but can beswitched on and o� by the RCU� The other is adjustable from � to ��kV �

In order to discuss further details of the design it is necessary to introduce the concept of a hybridPMT with the Philips PMT taken as example�

� THE OPTICAL SENSORS

�� The �smart� photomultiplier XP ��

34,5 cm

25 kV

6cm

Scintillator

PMT XP2982

Voltage dividerPMT XP2600

Photocathode

γ

Y Si O : Ce

Sb K Cse-

5

Figure �� The �smart photomultiplier Philips XP� ��

The photomultiplier consists of the combination of an electro�optical pre�ampli�er with a conventionalsmall phototube�

Photoelectrons� emitted from a large area hemispherical photocathode� �� cm diameter� are accel�erated by a high voltage ��kV � to an aluminium coated scintillator placed near the centre of theglass�bulb� This scintillator is read out by a small� fast� ��stage phototube �Philips XP�� placedin a recess at the back of the photo tube�

�� cathode ��cm

e��pe��kV

scintillator

�z �optical pre�ampli�er

� �� conventional fast PMT

� ��pe�

This method yields several major advantages ��

�� The photomultiplier achieves a very high gain� typically �� in the �rst stage� Usually statistical�uctuations in the �rst stage dominate the energy�resolution and the time resolution of a PMT�

� Design of the European Optical Module

This high gain provides excellent time and energy resolution�properties for low pe energies� Thetime jitter is � �ns and the energy resolution � ��"�FWHM�� for �pe signals�

�� The scintillator converts the photo�electron energy isotropically into secondary light� This avoidstypical problems of large area PMTs� The gain �secondary emission factor� is independent of thepoint on the cathode� from which a photo�electron originates and thus the PMT shows a uniformamplitude response� Also no pre�pulsing due to badly focussed electrons occurs�

�� The high voltage provides a high collection e�ciency �� "� and thus uniform sensitivity overalmost the total cathode area� The PMT is only weakly in�uenced by magnetic �elds and doesnot have to be shielded against the earth�magnetic �eld� A Mu�metal cylinder around the smallPMT provides a good shielding for the later ampli�cation stages�

A sketch of the PMT is drawn in �gure �� The glass bulb is covered up to � sr with a bialkali�SbKCs� photocathode� which has a high quantum e�ciency combined with a low thermionic emission�Due to its spherical shape and it&s backward transparency the PMT is capable of detecting light fromall directions�

x1 = 243σ = 30ΔE/E = 47% (FWHM)g1 = 33

integrated charge [a.u.]

entr

y

#11

Q-T [ns]

entr

y

m = 3.1 P.E.c1 = 153 [ns]c1 = 40 [ns]c0 = 23 [ns]nlog= 3.0 P.E.

#19

0

250

500

750

1000

1250

1500

1750

2000

2250

0 200 400 6000

50

100

150

200

250

300

500 1000

�A� �B�

Figure �� Typical charge distributions of the �smart PMT��A� A distribution of the integrated charge of dark noise pulses �PMT ! �� A Gaussian with thewidth � and the centre value x� is �tted to the distribution��B� Pulse�width �QT� distribution of EOM ! �� for illumination with a fast LED �mean intensity��m ��pe�� Clearly visible are peaks due to �� and � converted photo�electrons� A fourth peakoccurs due to a change of the energy scale from a linear to a logarithmic scaling at � �pe� Theamplitude function� described in section �� is �tted to the distribution� Contributions due todi�erent photo�electrons are plotted with dotted lines below the distribution�

Figure �� shows typical energy distributions� Dark noise pulses consist mainly of thermionic electronsemitted from the cathode and have thus mostly an amplitude of �pe� The distribution of �pe signalscan be described well by a Gaussian ��gure �� A�� Typical values for the energy resolution rangebetween ��" and ��" �FWHM� for di�erent PMTs� If one assumes a constant secondary emissionfactor g for the small PMT� the gain of the �rst stage g� can be calculated from the energy resolution

�FullWidth Half Maximum

�� THE OPTICAL SENSORS

via

g� # ��

�

g � �

��$E

E

��

�� The distributions of individual photo�electrons are clearly visible and allows a good separation up toseveral pe �see �gure �� B��

A good energy resolution is important for following purposes�

For triggering in the ocean it is highly desirable to discriminate against the background due to��K decays� which consists almost entirely of �pe pulses� E�g� for ��" energy resolution and atrigger threshold at ��pe it is possible to reject ��" of �pe signals with the loss of only ��"of multi pe signals� With the energy resolution of �" it is still possible to reject �� " of �pewhile loosing ��" of multi pe signals� ��

An OM with good energy resolution can be calibrated in situ without external light� using theclear signature of the �pe dark noise peak �see �gure �� A� and appendix B�� Internaldiscriminator thresholds and the high voltage can be adjusted until dark noise below �pe �dueto the small PMT� is e�ciently cut out�

0

10

20

30

40

50

0 100 200 300 400

Time (ns)

Vol

tage

(m

V)

Time (ns)

Vol

tage

(m

V)

0

10

20

30

40

50

60

0 100 200 300 400

Figure �� Pulse structure of the �smart PMT� The �gure shows two typical �pe pulses sampled with a FADC��MHz� bit amplitude resolution ��

The achievable time resolution is mainly limited by two reasons which are discussed in details in section�� The �rst is due to geometrical transit time di�erences for the emission of photoelectrons fromdi�erent points of the photocathode� Typical transit time di�erences are ��ns between zenith angles�� and �� in point�illumination� With the construction of the Russian smart PMT Quasar�� itwas demonstrated� that it is possible to reduce transit time di�erences below �ns using a mushroomshape of the PMT� It was calculated� that this is also possible for the Philips XP�� Forfull illumination and amplitudes higher than �pe the time uncertainty due to geometrical transit�timedi�erences is much smaller � �ns�� The second contribution occurs mainly due to the internaltime jitter of the PMT during the signal conversion� Figure �� shows two typical PMT pulses� Onesees the stochastic emission of photons from the scintillator� which are individually detected by the

� Design of the European Optical Module ��

[ns]

[mV

]

τ = 58.8 ns ± 6.6 ns

Integration gate [ns]ΔE

/E (

FWH

M)

[%]

0

5

10

15

20

25

30

35

40

0 100 200 300 400 5000

20

40

60

80

100

120

0 100 200 300

�A� �B�

Figure �� Scintillator decay and integration time for the �smart PMT��A� shows the scintillator decay of �PMT �� pe pulses� which were sampled with a FADC��MHz� �bit amplitude resolution �� are superimposed� An exponential decay is �tted to thedata� �B� shows the energy resolution �FWHM� for the �pe peak as a function of the time used forthe charge integration�

fast small PMT �time resolution � ��ns�� For the XP�� the time resolution is mostly limitedby the long decay time � �� ns� of the scintillator� Figure �� A� shows a measurement of thescintillator&s decay time� which was done for each EOM �� Several pulses have been sampled andsuperimposed� An Exponential with the decay time � is �tted to the distribution�

A characteristic quantity for time resolution is the value ��g�� where g� is the gain of the �rst stage�This value can be improved by both� �rst a faster and second a more e�cient scintillator� In additionthe light yield in the �rst stage can be increased with a better optical coupling of the small PMT tothe scintillator� This was done during the assembly of EOMs �see section �� An improvement ofthe light yield also improves the energy resolution� ��

�� Read out considerations

A general consideration for the design of a fast read�out is the decision between charge integration �Q�T� or the measurement of the time�duration above a threshold �TOT�� Advantage of the TOT methodis� that it can be realized in a very fast circuit with almost no dead�time� On the other hand thismethod gives only a logarithmic dependence to the pulse�charge and small pulse �uctuations stronglyin�uence the energy resolution� It is obvious from �gure �� that in case of the EOM a TOT methodis ruled out� due to the bunched time structure of the PMT signals�Another choice is a linear charge conversion to a Q�T signal �as done for the BOM� or a logarithmicconversion �as done for the JOM� with the aim to achieve a higher dynamic range� In case of the BOMthe dynamic range is limited to a few ��pe� and in order to see the distribution of �pe dark noisepulses the BOM has to be run in a special operational mode� In case of the JOM the integrated chargeis measured only for signals above �pe and the TOT method �which is equivalent to a logarithmicdependency� yields in general only a poor energy resolution�The EOM performs a mixture of linear and logarithmic conversion of the charge� Though the read�outitself performs a strictly linear charge conversion� the measurement turns over to a logarithmic scalingabove typically �pe� An ampli�er with a dynamic input range of �V is switched before the fast readout� As result the signal&s charge above this threshold is not integrated and the charge conversion


Amplitude Pulses above this threshold ��RMS

Mean

pe �� pe � ��pe � �peTrue ��

EOM�QT �� JOM�QT � ��

JOM�TOT �� pe �� pe � ��pe � ��pe

True �� EOM�QT �� JOM�QT ��

JOM�TOT �� pe � �� pe � ��pe � ��pe

True �� EOM�QT �� JOM�QT � ��







JOM�TOT ��

Table �� Comparison of the JOM�TOT� the linear EOM QT and the logarithmic JOM QT read�out� �� pulseshave been simulated using the description of the JOM �� and the EOM �section �� The tableshows the percentage of pulses above a threshold after re calculation of the initial amplitude� It givesalso the RMS�deviation divided by the mean of the input amplitude� Simulations have been done for�xed signal amplitudes �pe �� and Poisson distributed mean amplitudes � �pe � � � � ��

becomes similar to a time over threshold measurement�� This yields a larger dynamic range with anexcellent resolution for a few pe�

In order to preserve the energy resolution capabilities and to separate between �� and more pho�toelectrons a linear read�out is necessary� A logarithmic read�out produces asymmetric non�Gaussiandistributions� If an additional jitter� e�g� due to the electronic and the signal transmission� is convolutedwith the signal� a back transformation becomes rather unstable and has the tendency of imitating largepulse energies� This can be seen in table �� which shows simulations of the pulse�amplitude for theEOM and JOM including electronic e�ects�

�For very high amplitudes �� pe� internal saturation e�ects in the PMT and the voltage divider yield a furtherlogarithmic �attening of the PMT gain�


From the investigation of the JOM�TOT conversion it can be concluded� that on the one hand theenergy resolution is too poor to e�ciently discriminate �pe signals �ocean noise� against higher ampli�tudes� E�g� assuming a �pe ocean noise rate of ��kHz the imitation rate of signals above �pe is still��kHz� On the other hand the TOT method is stable with a constant energy resolution achievinga dynamic range up to �� pe� The TOT is the fastest read�out method� which enables a doublepulse resolution of subsequent OM hits� if they are separated several tenth of ns�Comparing the linear and logarithmic charge integration it can be seen� that for intermediate�amplitudes�pe� ��pe� both methods yield comparable results and thus an equivalent quality concerning muondetection� Since the JOM Q�pulse�width is limited below a maximum value of ��ns the back con�version becomes rather unstable for high energies �pe � �� The charge can not be e�cientlymeasured� e�g� for �� signals �Poisson distributed� pe # �� the reconstructed energy reaches upto ��pe� Therefore JOM QT�widths equivalent to more than a few �� pe can not be physicallyinterpreted� The logarithmic charge conversion in the JOM does not yield a larger dynamic range ase�g� the linear read out of the BOM�

�� The �smart� read out DMQT

The EOM read�out� DMQT� was initially designed by F�Beissel and V�Commichau according to thefollowing requirements ��

The circuit is directly fed from the PMT anode signal� Its rectangular ECL output drives anLED driver circuit� The leading edge of the output signal has a delay of about �� ns to the startof the original PMT signal�

The circuit is self triggering� In order to reject noise from the small PMT a high discriminatorthreshold is set to an amplitude corresponding to about ��pe�

The circuit measures the response�time of the PMT� A second discriminator threshold is set toa small value �� pe�� This threshold obtains the leading edge of the PMT�signal withoutbeing a�ected by �uctuations of the rise time� A coincidence to the high threshold de�nes thetrigger and starts the output pulse�

Both thresholds are externally set and monitored by the RCU�

The circuit linearly measures the integrated charge of the PMT signals� The duration has tobe proportional to the measured charge� As seen in �gure �� B� the minimal integrationtime should be about ��ns to obtain a good energy�resolution� Higher amplitudes require alonger integration� Commercially available charge integrating circuits using a �xed integrationgate of about ��ns have conversion times of the order of micro�seconds� This is unacceptableunder the consideration of the dead�time involved by ��kHz ocean noise� Therefore a di�erentsolution was found� After a short time �� ns� the conversion already starts during the chargecollection� Furthermore the conversion is done with variable duration� This leads to smallconversion times for frequently occuring �pe PMT�pulses and requires only long integrationtimes for rarely occuring large PMT signals� This gives a typical dead�times of ��ns for �peplus ��ns for each additional pe� These values were achieved with the DMQT prototypes forthe JULIA experiment�� However due to timing problems on the produced circuits�boards forEOMs this dead time had to be increased to typically ��ns per pe� Also the energy resolutiondoes not reach the excellent values of the DMQT prototypes �see table B�� A sketch of thecircuit is shown in �gure ��

�No QT�signal is generated in the JOM for small amplitudes �� pe��This conversion time is limited by the length of the PMT signals� It is possible to signi�cantly decrease these values

for PMT with shorter pulses


delay6ns Low

High

40ns-80ns

6ns

Integration

6: 0V

5: 0V

4: 0V

3: 0V

2: 0V

1: 0V

analogin

inputamplifier

input comparators AND

gate-timer

currentcontrol

bi-polarcurrent source

I+

I-

capacityintegration

comparator outputcomparator

OR

scaler

count-rate

driverLED6

5

4

3

2

1

Deintegration

Figure �� Block and timing diagram of the DMQT�

The circuit has a soft transition from a linear to a logarithmic charge measurement for highinput amplitudes of the PMT �typically above �pe�� This is achieved via a limited dynamicinput range� which cuts o� pulse�heights above about �V �see section ��

A block diagram of the fast read�out and the internal timing is shown in �gure �� A bipolar currentsource charges and discharges the integration capacity� The current is controlled by the input pulseamplitude and the current control� which starts the conversion after a �xed time� The circuit is builtin ECL and has a power consumption of about ��W � More detailed information can be obtained from��

In order to test the linearity of the QT conversion a photomultiplier was illuminated with a LED �xedto a mean intensity of about �pe� Each PMT signal is measured with a charge sensitive ADC �Lecroy��A� and the DMQT circuit� The correlation between these two measurements is plotted in �gure

� Design of the European Optical Module �

integrated charge [a.u.]

Q-T

[ns]

100

200

300

400

500

600

700

800

200 400 600 800 1000 1200

Figure �� Measurement of the linearity of the DMQT� The plot shows the correlation between measurementof the integrated charge and the width of the QT signal for about � � �� photomultiplier pulses� ��scale units on the x�axis and ��ns on the y�axis correspond approximately to �pe�

�� showing an excellent linearity�

�� The Remote Control Unit

Main purpose of the RCU is to set and monitor internal parameters of the EOM �see �gure �� Heartis a microprocessor TMP �� Toshiba�� which integrates three serial interfaces� a � bit parallelinterface and a �� core� The computer has a � bit data bus accessing �� kbyte random accessmemory and �� kbyte read only memory �EPROM�� The ROM holds an OS�� operating systemand the basic application software� Communication to the OM is possible via a serial modem link��Bd�� which superimposes signals onto the power supply line� The implemented software allowsthree di�erent communication modes� In the standard mode� a control�program is executed� whichsets all internal parameters to default values and enables a bidirectional communication to the stringcontroller according to a special protocol� The control program also monitors and reports the internalparameters on demand� or in case of special emergency conditions �e�g� a water leak�� A second modeallows to download software onto a ram�disk� via the kermit protocol �e�g� a new control�program��Finally it is possible to execute a terminal program and operate the computer on a command shell��

Four internal parameters are set via an �bit DAC �

The two DMQT thresholds in the range � to ��mV �

The high voltage of the small PMT from �V to ��V �

The ��kV supply for the large PMT can be switched on and o��

In addition it is possible to switch on the LED �of the fast circuit� for a certain amount of time�Following parameters are continuously measured via a ��bit ADC�

The thresholds of the DMQT�

�This is the default mode after booting�


& Leak sensorsTemperature

(A)

(C)

(B)

DC/DC ConvertersModem

CPU DMQT

EOM/AHV (small PMT)

48V

ADC and DAC

EPROM LED

HV (25kV) with EOM/B (mounted below)

PMT-signal

6 ns delay cable

Figure �� Electronic circuits boards of the EOM �A� EOM�A� the �power�board� �B� EOM�B� the �fast�board � �C� All electronic devices assembled onto a retaining aluminium ring�

The high voltage of the small PMT and the on�o� state of the ��kV supply�

Three temperatures at di�erent locations�

The three supply voltages� ��V � ��V �

The current for each of the three voltages�

Detection of water inside the module via a leak sensor�

The counting�rate of the PMT is pre�scaled by a factor of � and is measured witht the timer input ofthe CPU� ��


�A� �B�

Figure �� The mechanical assembly of the EOM �A� Glueing of the PMT into the pressure housing� �B� AnEOM in a DUMAND string during the test experiment of September ��

�� Mechanical design

Due to the lack of available space inside the pressure housing� the electronic circuits are realized intwo sickle�shaped � layer circuit boards� which are populated �with mostly SMD� circuits� from bothsides� The �rst board EOM�A� the so called power board contains the DC�DC converters� themodem� DAC and ADC units� The second board� EOM�B� the &computer�board� contains the fastcircuit DMQT� the LED� and the RCU�computer� Connections between the boards are realised withwire�wrap cables� Figure �� shows a photos of these circuit boards ��A��B�� All electronic parts areattached to an aluminium ring which itself is �xed to the neck of the PMT �see �gure �� and ��C��

The PMTs are glued into a pressure housing made by Nautilus Marine Service with optical transparentgel� The pressure housing consists of two hemispherical parts made from borsilicate glass with a goodtransmission � ��"�� It is transparent down to � ��nm ��"� �mm glass�� The refraction index is�� The halves are combined at their equatorial cut and sealed with neoprene tape� The optical gelWacker Semicosil �� is a solvent free addition�curing RTV�� silicone rubber with good transmissionproperties down to ��nm� It is a two component gel which vulcanises within several hours �roomtemperature� to a low viscosity �depending on the mixture ratio� gel with distinct tackiness� Figure�� A� shows the glueing of a PMT into a pressure housing� The PMT is �xed to an adjustable

�Surface Mounted Device


support �xture� which allows to position the PMT with an accuracy of � �mm� ��

The complete OM is mounted into an acrylic hardhat� which is �xed to the string� Figure �� B�shows an EOM assembled in a DUMAND II string�

Two penetrators connect the OM to the outer world � the electrical E�&�style produced by CrouseHinds and an optical penetrator suitable for multi�mode optical �bre� which was designed by BernUniversity and manufactured by Diamond SA� A titanium vacuum port allows to control the insidepressure� Three holes for these penetrators are drilled into the top half pressure sphere� The sphere ispressure tested with installed penetrators up to ��bar� ��

The small PMT is glued into the the recess of the large PMT with optical gel in order to improve theoptical contact to the scintillator � This operation signi�cantly improves the energy resolution of thePMT� A measurement of PMT - �� yielded an improvement of the energy resolution from � " to��"� �see �gure �� A�� A complete �lled recess with too sti� gel leads to strong tensions� whichmay damage the PMT� This is the reason for two lost EOMs� A third EOM was lost due to insu�cientspace inside the pressure housing� The spheres shrink several mm under high pressure in the deepocean�

�� Properties and calibration of the EOM

The �nal calibration of DUMAND II OMs is done in a large water tank at the University Hawaii� Thisincludes measurements of the angular sensitivity� amplitude and time response to a laser light�sourceand �Cerenkov light from muons passing through the water �� Prior to the delivery� several sequencesof test� and pre�calibration measurements have been performed with the EOMs at the University Kiel�Table B�� gives a summary of all tested EOMs� The test procedure covers following points

The relative angular dependency of the sensitivity of the photocathode is measured by pointillumination of �� locations� �see appendix B��

The amplitude and time response is measured for selected cathode points� di�erent light inten�sities� thresholds and high voltage �see sections �� and ��

Measurement of the counting�rates and amplitude distributions of dark noise pulses as a functionof the thresholds and the high voltage� �see appendix B��

Measurement of the amplitude response for high light�intensities and high pulse rates� ��

Measurement of the after�pulse rate as a function of the delay time� ��

For each PMT �� typical PMT pulses have been digitised with a ��MHz FADC for ��s�This measurement yields the decay constant of the scintillator and the characteristics of pulsesand after�pulses� �see �gure ��

Estimation of standard settings for the high voltage and the thresholds as well as the calibrationof all internal DACs and ADCs� �see appendix B��

�� Sensitivity

Optical Modules� which are hit by �Cerenkov light from a muon� are usually exposed to an almostplane�wave light front� Therefore the angular sensitivity of a fully illuminated OM is an importantquantity� which has to be calibrated�

In addition to the standard calibration in the water tank� one EOM �- �� was measured in fullillumination from a green LED approximately �m distant to the OM at DESY IfH Zeuthen� The

� Properties and calibration of the EOM �

Calibration

a = 0.445

b = 0.443

c = 0.112

COS(θ)

S

0

0.2

0.4

0.6

0.8

1

1.2

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Figure �� Relative angular sensitivity of the EOM� The measurement was done with full illumination of a greenLED� E�q�� was �tted to the data�

measurement� was done with �xed intensity of the LED at � di�erent azimuth angles as a function ofthe zenith angle ��

The relative angular sensitivity S�� was parameterized with

S�� # a� b � cos�� c � cos��

The result of this measurement is shown in �gure ��

Because the full illumination is an integral measurement� local di�erences in the cathode quality arehard to detect with a fully illuminated OM� The cathodes of �� OMs have been examined in point�illumination� A LED was directly attached to the surface of the PMT� Results of this measurement areshown in appendix B�� Most PMTs show a very uniform photo�cathode� which is sensitive to zenithangles larger than �� For some PMTs the sensitivity increases at �� corresponding to an emissionof photoelectrons from the photo�cathode from the opposite side of the PMT�

�� Signal amplitude

During the standard DUMAND calibration scheme the mean pulse�width response of OMs is measuredversus the distance of muons passing through a water tank� Several applications� especially in MonteCarlo� require in addition a parameterisation of the actual shape of the amplitude distributions for agiven incident light intensity�

It was shown in �� that the amplitude distribution of the smart PMT is well approximatedby superimposed� equidistant Gaussian distributions Gi� Their relative weights are given by a Poissondistribution Pi for the mean number of photoelectrons m

Pi # mie� m

i*��

�More details on this measurement are given in �"��


The width of the i�th Gaussian �i scales as

�i #pi � ��

with the width �� of G�� The distance between two Gaussians is given by the constant c� and thepedestal of the distribution by c�� Thus the centre value of the i�th Gaussian xi is

xi # c� � i � c� ��

The energy resolution $E�E �FWHM� can be calculated via

$E

E#

� � � � p� � ln �c�

# �� c�

��

It is thus possible to describe the pulse�height distribution of the PMT for arbitrary light intensitieswith only three parameters c�� c��

For a parameterisation of the amplitude characteristics of the complete EOM one has to consider alsothe Q�T conversion in the fast read�out� The pedestal is changed and the energy resolution may becomeworse� e�g� due to electronic defects� The PMT amplitude is cut o� above an amplitude � �V � Thiscorresponds to the threshold value nlog �in units pe� above which the integration becomes logarithmic�The equivalent pulse width xlog is given by

xlog # c� � nlog � c� ��

A description of the EOM pulse shape in the logarithmic region can be achieved via the approximation�that the ampli�ed input signal to the DMQT is described by an exponential decaying function withan in�nite rise�time� which is cut o� above a certain threshold� Further electronic distortions areneglected� This yields the relation for the position of the i�th peak �i nlog�

xi # xlog �� ln

i

nlog

��

and a logarithmic transformation of the initial Gaussian distributions� The complete amplitudefunction describing the EOM in the linear and the logarithmic region is

G�x� #

i�nlogXi��

Pi�p

� � �iexp

��x� xi�

�

� � ��i

�

��

�X

i�Nlog

Pinlog � c�p� � �i � xlog

exp

�x� xlogxlog

�c��

B�nlog � e

�x� xlogxlog

� i

�CA�

� � ��i

�

with xi� �i from equations �� and ��Appendix B�� shows �ts to measured EOM QT distributions� It can be seen that the above estimationsdo not yield a good description of the logarithmic region� but shows the right scaling behaviour at thecost of only one additional parameter nlog� The description can be improved by e�g� an additionalparameters c� in eq�� which respects an incorrect logarithmic conversion performance

xi # xlog � �� c� � ln�i�nlog��

� Properties and calibration of the EOM ��

pulse width [a.u.]

m_

[PE

]

pulse width [a.u.]

m_

[PE

]

2

4

6

8

10

12

14

0 2 4 6 8 10

2

4

6

8

10

12

14

0 2 4 6 8 10

2

4

6

8

10

12

14

0 2 4 6 8 10

�A� �B�

Figure �� The �amplitude function� The parameters have been set to c� � c� �� nlog ��The pictures show two dimensional plots of the pulse width for di�erent mean values of photoelectrons� �m�� A� shows the distributions for �� di�erent values �m� The sizes of the boxes represent thefunction value� �B� a contour plot of the amplitude function�

Figure �� shows a plot of the amplitude function for di�erent light intensities�The energy resolution for various EOMs as calculated via eq�� are given in table B��

In case of a linear read�out and Gaussian amplitude distributions it is possible to calculate the meannumber of photoelectrons for high amplitudes from the mean x and deviation � of the energy dis�tribution� Using the expectation values for Poisson and Gaussian distributions one evaluates for thecombination of both

m #

� x

�

��

where � is closely related to the energy resolution of the OM�

� # � �

��c�

��

If the pedestal constant c� �# �� the values x has to be corrected to the pedestal x x� c� before itis inserted into eq��

�� Time properties

The time accuracy of an OM is the most critical parameter to allow a successful reconstruction of amuon track� A PMT signal appears delayed by a certain signal transit time relative to the time of the


incident photons� The time accuracy is given by the deviation relative to the intrinsic transit time ofthe OM�

θ = 00

1 2 3

(A) pulse width [ns]

entr

y

θ = 900

1 2 3

(B) pulse width [ns]

entr

y

θ = 00sum

123

(C) transit time [0.1ns]

entr

y

θ = 900sum

123

(D) transit time [0.1ns]

entr

y0

200

400

600

800

1000

1200

0 500 10000

200

400

600

800

1000

0 500 1000

0

1000

2000

3000

4000

5000

6000

7000

300 350 400 450 500 5500

1000

2000

3000

4000

5000

6000

7000

8000

300 350 400 450 500 550

Figure �� Energy and time distributions for two di�erent zenith angles� EOM ! was illuminated with a fastgreen LED �point illumination�� A� and �B� show the distributions of the pulse energy� The energy isdivided into three regions �� C� and �D� show the transit time distributions for pulses of eachenergy region separated� The summed time distribution is plotted on top of these distributions�

Figure �� shows energy and transit time distributions for two di�erent zenith angles �� The intensityof the LED is �xed� but due to a di�erent relative angular sensitivity of the OM the relative weight ofeach peak �the contributions for each photoelectron level� changes� The positions of the peaks remainconstant� The corresponding transit time distributions are plotted below �sum�� They have a width ofabout ��ns �FWHM�� To investigate the transit�time for di�erent energies� � regions of energy havebeen de�ned �� The transit�time distributions of the pulses which fall into one of these energyregion are separated and plotted below the sum curve� In these pictures one can identify the threemajor e�ects� which determine the time�accuracy�

Geometrical transit time di�erences Photoelectrons emitted from di�erent regions of the photo�cathode have to traverse di�erent path�lengths� The distributions �C� and �D� show a shift ofabout �ns in the transit�time� For full illumination the distributions for cathode areas of di�erentzenith angles are superimposed� weighted with their relative sensitivity� Assuming a mean zenith

� Properties and calibration of the EOM ��

angle �� with uniform transit time deviations $t # �ns one achieves a mean time uncertainty

�t�geo��pe � $tp��

# ��ns��

This value is to be taken as a worst case� Due to the spherical shape of the photocathode andinhomogeneous sensitivity usually one cathode region dominates the transit�time� This e�ectdecreases for high amplitudes because the cathode region with the fastest transit time dominatesstochastically�

Time jitter This quantity is related to the intrinsic time�spread of the photomultiplier� which occursduring the conversion of the photoelectron� It is measured by the width of the transit time dis�tributions in �gure �� For the XP� �� it is dominated by the stochastic emission of secondaryphotons from the scintillator �� For signals with a higher amplitude the time�jitter becomessmaller�

Time slewing Signals of high amplitude have a faster rise�time relative to smaller signals for a �xeddiscriminator threshold� The response time due to signals of di�erent amplitudes are superim�posed in the resulting transit time distribution� This e�ect can be clearly seen in �gure �� C�and �D�� The peaks of the time distributions are shifted to faster transit times for larger ampli�tudes� This uncertainty can be corrected after calibration if the signal amplitude is measuredcorrelated to the response time� It has to be noted that changes in the high voltage and thesmall threshold also lead to a signi�cant transit time slewing� E�g� a change of ��" in the lowthreshold of the DMQT leads to a time slewing of about �ns�

A good analytical description of the time distributions is gained� if a Gaussian distribution is convo�luted with a decaying Exponential � which is motivated by the scintillator decay�� Evaluation of theconvolution integral �� gives

S�t� #

p�t�

� exp��t��

� t� t��

�� erf

��p��t� t��t

� �t��

��

with the error function

erf�x� #�p

Z x

�e�u

�

du �

The timing�function depends on three parameters� t�� relative transit time! �t� the width of theGaussian and � � the exponential decay constant� Fits of this function to time distributions are shown inappendix B�� A parameterization of the parameters allows an analytical description and interpretationof transit time di�erences� the time jitter and the time slewing� ��

The analysis of the EOM time properties is done as follows� A fast green LED is attached to the surfaceof the OM at three di�erent zenith angles� For each LED pulse the pulse energy and response time ofthe OM are written to disk� The energy distributions are �tted with the amplitude function to obtaina calibration of the pulse�width scale �see appendix B�� The transit time distributions of signals�whose energy falls into a selected energy region� are plotted and �tted with the timing function�Examples of these �ts are shown in appendix B�� Resulting quantities are plotted versus the numberof photoelectrons npe� The mean ��gure �� A�� and rms ��gure �� B�� of the distributions are�tted with

mean # a� �a�npe

rms # b� �b�npe

��

�This is done manually and the power to the OM has to be switched o� between each change�


(A) Q-T [PE]

mea

n [n

s]

mean = 40.1 + 5.7/PE

(B) Q-T [PE]

rms

[ns]

rms = 1.2 + 4.7/PE

(C) Q-T [PE]

t 0 [n

s]

t0 = 38.7 + 1.5/PE0.5

(D) Q-T [PE]

τ [n

s]

τ = 0.6 + 4/PE

(E) Q-T [PE]

σ t [ns

]

σ = 0.8 + 0.3/PE

(F) Q-T [PE]

σ Δt [n

s]

σΔt = 0.9 + 3.9/PE

40

45

50

0 5 100

2

4

6

8

10

0 5 10

35

37.5

40

42.5

45

0 5 100

2

4

6

8

10

0 5 10

0

1

2

3

4

5

0 5 100

2

4

6

8

10

0 5 10

Figure �� Response time characteristics for OM !�� Plotted are the mean �A� and rms �B� of the timedistributions� the parameters t� �C�� D� and �t �E� of the �tted �timing function and the time

uncertainty ��t p��t � � �F� versus the pulse energy�

The time uncertainty ��t is calculated from the �t parameters � and � via

��t #p��

These parameters are �tted ��gure �� D��E� and �F�� also via

� # d� �d�npe

� # e� �e�npe

��t # f� �f�npe

��

Finally the parameter t� is �tted ��gure �� C�� with

t� # c� �c�pnpe

��

Results for all EOMs are given in table B�� It has to be noted that the LED has an intrinsic jitteritself� which is about �ns for �pe and still �ns for several pe� Therefore the presented results are upperlimits on the true time accuracy� The absolute transit times include time o�sets of the measurementsetup and do not give the intrinsic transit�time of the OM�

� Properties and calibration of the EOM �

OM mean �� mean �� t� �� t� ��ns� �ns� �ns� �ns�

��

Table �� EOM geometrical transit time di�erences for point illumination� The values have been derived via twomethods� a� from the di�erences in the mean of the transit time distributions� b� from the parametert� of the �timing function� The relative time for �� was set to zero� OM �� was measured in fullillumination with a fast laser�

The geometrical transit time di�erences are obtained by the comparison of the mean measured atdi�erent zenith angles� A second characteristic value for the transit time is the parameter t� � � � �� isthe expectation value of the Exponential�� In order to avoid time slewing e�ects� the asymptotic valuefor an in�nite number of pe is taken� Thus

$tgeo�� # a�� a�� or $tgeo�� # c�� c��

Table �� shows the results for several OMs� The mean transit�time is smaller at large zenith angleswith a di�erence of about �ns� Two OMs show strong di�erences of this behaviour �-�� and -��These OMs have a low sensitivity at � # �� implying that the majority of emitted photoelectrons areemitted from photons hitting the opposite cathode area�The time jitter $tjit can be characterised by the rms of the distributions or via the parameter��t #

p�� The rms yields less stable results� due to statistical �uctuations of the distribu�

tions� especially for large pulse energies� and due to a long tail in the distributions� As a result of thetail in the transit time distributions� the measured FWHM are signi�cantly smaller �typically �ns for�pe� than the rms values �� The results are given in table ��The time slewing $tslew is given by the change of the transit time for di�erent energies� Thus one gets

$tslew�xpe� #a�xpe

or $tslew�xpe� #d�xpe

�c�pxpe

��

Results are shown in table ��

One EOM �-�� was measured in full illumination using a fast laser with pulse width smaller �ns ��After the same analysis procedure as above one gets signi�cantly better results for the geometricaltransit time di�erences� which are ��ns between �� and �� The other quantities are comparableto the results obtained in point illumination�


OM rms��pe� ��t��pe� ��t��pe��ns� �ns� �ns�

��

Table �� EOM transit time jitter for point illumination� Printed are the �t results for the rms for �pe and ��t for�pe and asymptotically in�nity pe� The values for �pe depend strongly on the calibration of the energyscale which is less accurate for OMs !�� !� and !�� OM �� was measured in full illuminationwith a fast laser�

OM mean t� � ��pe � pe � pe �pe � pe � pe�ns� �ns� �ns� �ns� �ns� �ns�

��

Table �� EOM transit time slewing for point illumination� Printed is �tslew obtained from changes in the meanand t�� for �pe� pe and �pe� The values depend on the calibration of the energy scale which is lessaccurate for OMs !�� !� and !�� OM �� was measured in full illumination with a fast laser�

��

� Monte Carlo Simulation

so lass mich dich heissenwie ich dich liebe�Siegmund � so nenn� ich dich�

Richard Wagner ��

Many programs have been developed for the simulation of deep underwater experiments� They havebeen designed with respect of a speci�c experiment and have proven to be very capable performingspeci�c tasks� such as the the optimisation of a detector geometry for the detection of neutrinos�� Unlike large accelerator experiments the data stream from underwater experiments is simpleand contains essentially only times and amplitudes of hit OMs� The approach of the SiEGMuND� program package makes use of this and attempts to provide a high �exibility in combination withstandard analysis methods of particle physics� It implements a new philosophy which puts mainemphasis on the following aspects�

A modular structure according to the logical steps of the analysis�This provides both a transparency of the analysis and a high variability in the exchange of certainmodules for speci�c steps of the analysis� It is designed independently of the actual experiment�Due to the modular structure it is also possible to include experiment speci�c tasks on demand�

A close connection to particle physics�It is possible to simulate deep underwater experiments using the concepts developed in largeaccelerator labs� such as CERN� This enables detailed studies of the detector response consideringspeci�c particle reactions using standard event generator programs �like Pythia �� and adetector simulation on basis of the GEANT simulation package �� GEANT provides a fullsimulation of the processes responsible for the generation of secondary particles and the stochasticcharacteristics of energy loss�

One data stream for all analysis steps�The interface between program modules requires a stringent de�nition� This is supported by aprogram library rdmc�� The interface between the modules is independent of the actual dataformat as long as this format is supported by the library� Di�erent programming languages suchas C or Fortran�� may be mixed�

The standard data format was chosen to be a line�oriented ASCII format �adapted from an exist�ing DUMAND� format �� which provides a highly machine independent data structure� OnUnix�platforms this philosophy enables the usage of standard IO�pipes for an elegant processingof data through all analysis steps� An analysis may be done interactively on a command line �or asimple shell script�� or via a more sophisticated user interface� It is easily possible to use standardUnix tools within the analysis steps� e�g� awk for small analysis purposes or the selection ofspeci�c events� gzip allows automatic �de��compression in the data stream� Compressed ASCII�les require approximately ��" of the disk space used by ordinary binary formats� ��

�� Simulation framework

Figure �� gives an overview on the logical analysis steps during analysis within the SiEGMuNDpackage� The units represent individual programs� which exchange information via data streams� Thisallows to exchange individual programs or to concatenate several programs sequentially e�g� for therealisation of various trigger and �lter conditions� A program library provides standard functions andmemory structures for I�O and the processing of these data streams� �see appendix C��

�SiEGMuND stands for� Simulation of Events with GEANT for Muon and Neutrino Detectors� It was developed

in cooperation with O�Streicher �DESY IfH Zeuthen�� "��

�� MONTE CARLO SIMULATION

(GEANT) DADA

Hardware Trigger

Software Trigger

(e.g. Muon, Cascades ...)

Analysis

Event Generation

Event Selection

Reconstruction

(FFREAD)

Run Parameter

Physics Parameter

Geometry Parameter

Material Parameter

Tracking Parameter

GEANT Parameter

Detector Simulation Dadabase

(Various independent programs)

OM ParameterIndependent programs

Specific programs (physics)

General purpose programs(Histogramming, Statistics)

Figure �� SiEGMuND program modules and their relationship

The generation of the initial kinematics and track parameters of particles is independent of the detectorsimulation itself� Possible event generator programs range from the simulation of muon tracks with acertain direction and kinematics� complex atmospheric shower Monte�Carlo programs� detailed eventsimulation like charged current neutrino nucleon interactions to the generation of exotic phenomena�e�g�neutrinos from neutralino annihilation�� Generators may be custom�written� The portage of alarger event generator program into this framework requires only an implementation of a known data�format� Events are written to disk� E�g� to study e�ects of di�erent optical sensors the same eventsmay be tracked several times through the detector simulations with each di�erent parameters for theOMs� Appendix C�� gives more details on the implemented event generators�

�� The detector response �

A major element of the SiEGMuND concept is the detector simulation program Dada� �see section

�� Its purpose is the simulation and digitisation of the detector response� It implements a variablegeometry and allows to change various physical parameters� which determine the simulation of particlesin the detector� The program retrieves its parameters from a database� It is written on basis of theGEANT�package�

During the further processing of events it is necessary to account for detector speci�c hardware triggers�which a�ect the experimental selection of events� �e�g� the local coincidence trigger in the BAIKAL

experiment�� It is also useful to apply �lters for the selection of speci�c events �e�g� events withlarge OM signals�� This is realized by a set of �lter programs� which may be concatenated in anarbitrary sequence� It is possible to apply the same �lter programs on Monte�Carlo data as well as onexperimental data� Thus further analysis is identical for both types of data�

The most important step during analysis is the reconstruction of events� A standard task is thereconstruction of muons tracks and the identi�cation of up�going muons after applying cuts ��lters��

More details on the analysis utilities are described in appendix C��

If program units require information not included in the data stream� they may gather archive datafrom the database� Dadabase� The database was originally designed to provide information for thedetector simulation and thus uses the FFREAD package� which is also internally used by GEANT� Itcontains besides GEANT speci�c parameters various steering information like parameters of detectors�See appendix C�� The SiEGMuND philosophy is not chained to a certain programming language� The detector simu�lation and event generators are written in Fortran�� the analysis tools are written in C�

�� The detector response

The Dada program follows the general scheme of GEANT applications ��

Initialisation ��loop N eventsz � �

Simulation of one event �� Termination

During the initialisation phase internal data structures are initialised� such as the detector geometry�particles� materials� tracking parameters and cross sections of the di�erent materials� As result thedetector is built by geometrical volumes� which may contain di�erent materials and sets of trackingparameters� The program reads necessary information from the external database using the FFREADpackage� Several prede�ned con�gurations may be selected for detector geometry and tracking ac�curacy� The program is capable of simulating an almost arbitrary detector con�guration� Detailedinformation on initialisation� termination and limitations are given in appendix C�� After the initialisation� execution control is handled to GEANT� which is responsible for tracking andthe simulation of physical processes� For speci�c purposes GEANT calls user supplied routines �E�g�for the digitisation of the optical module response� Figure �� shows schematically the execution �owduring simulation of one event�After the initialisation of the kinematics of the event tracking is performed by GEANT� During thetracking secondary interactions are simulated and newly generated particles are stored as new tracksin a stack� GEANT loops over all tracks until all primary and secondaries particles have disappeared��

With the beginning of each track� or upon the entry of a new detection volume� the distance tothe next interaction point is calculated for all valid physical processes according to all valid physicalprocesses and pseudo processes allowed for the current medium� The later are e�ects� which in�uence

�Dada �Digitisation And Detector Analysis�

�E�g� due to decay� disappearance in a reaction�the exit of the simulation volume or the energy has fallen below atracking threshold�


Generate Cerenkov light

Loop (all OM’s):

Store Hits in a Stack

Check Cerenkov Hits

Read Event / Init Kinematic

Init Tracking Datastructures

Digitisation: Water Attenuation

Digitisation: Optical Modules

Output to Datafile

Tracking:

Loop:

Loop: all tracks

YesNo

new Secondaries

all tracking steps

Fast tracking for this track?

Generate / Store

Execute once

Figure �� Execution �ow during the simulation of one event

the tracking apart of the physical mechanisms�� This distance is calculated according to the inverseof the cross section for the speci�c mechanism� The necessary cross section values are calculated andtabulated during initialisation�

For each tracking step the distance to the next interaction point is simulated� The particle is beingtransported along a straight line� and the �nal state is generated� If the particle survives the process� thedistance to the next interaction point of the current physical process is recalculated and the distancesto the other processes are updated� The transportation of the particle from one point to the next iscalled tracking step�

Dada makes use of the GEANT environment for all physical processes �including some patches tothe original GEANT code�� but not for the generation of the �Cerenkov light and the digitisation ofthe detector� At the end of each tracking step a user routine is executed� New secondaries are storedin a GEANT�stack� and the �Cerenkov angle is calculated� if the current track ful�lls the �Cerenkovconditions� The program loops over all optical modules and detects �Cerenkov hits�� The time of hit�

�E�g�the step size due to continuous energy loss or a boundary crossing between two di�erent tracking media��This is the most CPU time consuming part of the program�

�� Data analysis ��

the distance to the OM� the length� of the hitting track� the angle between the �Cerenkov cone and thePMT axis and a track identi�cation are stored in a stack for later digitisation� �see appendix C��

Neutrino detectors naturally involve extremely large volumes together with a low tracking thresholddown to the �Cerenkov thresholds of electrons �T � ��keV �� The above approach leads to a largeamount of CPU time for the tracking of one event�� One the other hand large statistical samples ofevents are required� e�g�to check large rejection factors for down�going muons �O��

This problem has been solved by the inclusion of additional fast parameterization �e�g�the e�ective�Cerenkov light from showers�� These parameterizations are deduced in chapter � from full GEANTsimulations� If a fast tracking�mode is active for the current step� tracking is not performed byGEANT but rather the �Cerenkov light is generated directly for the current track including the lightfrom secondary particles�

After all particles have been tracked through the detector� the data in the stack is reduced via arecombination of hits from the same track at about the same time� Then the photon �ux hitting eachOM �see section �� and appendix A�� is calculated� The photon �ux� the time of hit and a referenceto the hitting particle are stored in a new stack! hits occuring at the same time are combined�

The response of the optical modules depends on the type and the characteristics of the individualmodule� The OMs may be simulated with di�erent accuracy� The digitised time of hits and theamplitudes are stored with the reference to the tracks� which caused the hit� After the digitisation is�nished the event is written to a data �le� One special mode allows to calculate the number of photonshitting the geometrical OM area instead of the full simulation of the OM response� If the numberof photons are written instead of photoelectrons to the data�le a later digitisation with an externalprogram in the data stream �e�g�referring to an OM database� becomes possible�

Figure �� shows the cross sections for �� e�� and � for fresh water and a set of trackingparameters down to the �Cerenkov threshold� as they are calculated by GEANT� The maximum energyof GEANT is limited to ��TeV � Above this value� cross sections may be tabulated but have to be usedwith caution� Figure �� shows the extrapolation up to ��TeV �

The muon interactions are calculated according to �� Though bremsstrahlung and nuclear interactionevents occur relatively rarely� they involve a large energy transfer �e�g�� and may initiate brightlocal cascades �see chapter ��

During the analysis of muon events in the Fr.ejus detector a discussion arose about the correctness ofthe implemented bremsstrahlung cross section �� The cross section used in �� refers to �� Thedi�erential cross section d��dy �y is the fractional energy transfer� is proportional to an atomic andnuclear screening function /� which di�ers between �� and �� for atomic numbers Z �� Forfresh water the di�erence between both formulae is not serious� because most ingredients have atomicnumbers Z �� Dada implements both cross sections but keeps the original GEANT as default�This di�erence becomes stronger for ocean water�

It is possible to set several options for debugging and physical cuts� An interface to the HIGZ packageallows to plot the detector� its components and also to visualise trajectories during tracking time� Thegraphical output may be written to a graphical meta��le �e�g� postscript�� Histograms �e�g� crosssections or statistical output� may be generated and written to an HBOOK data �le ��

�� Data analysis

The general philosophy of data analysis within the SiEGMuND environment is to concatenate indi�vidual programs in a serial data stream to process or �lter out events of interest� This philosophy is

�In fact not the length � but rather the relative length L� as de�ned in eq��A��"� is stored��The realisation of this approach to perform a detailed tracking for large scale neutrino telescopes has only become

reasonable due to recently available computing power� The necessary amount of computing time increases strongly withthe number of tracks� the number of steps during tracking and the number of optical modules in the detector�


μ Bremstrahlung

μ Pair production

μ Delta ray production

μ Nuclear Interaction

energy [GeV]

Cro

ss s

ectio

n [c

m-1

]

e- Bremstrahlung

e- Delta ray production

e+ Bremstrahlung

e+ Delta ray production

e+ Annihilation

energy [GeV]C

ross

sec

tion

[cm

-1]

γ Compton effect

γ Pair production

γ Photo effect

γ Rayleigh Scattering

energy [GeV]

Cro

ss s

ectio

n [c

m-1

]

π+ Inela.Hadr. (Gheisha)

π+ Elas. Hadr. (Gheisha)

π+ Delta ray production

energy [GeV]

Cro

ss s

ectio

n [c

m-1

]

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1

10-2

10-1

1 10 102

103

104

105

10-6

10-5

10-4

10-3

10-2

10-1

1

10-4

10-2

1 102

104

105

10-6

10-5

10-4

10-3

10-2

10-1

1

10-4

10-2

1 102

104

105

10-4

10-3

10-2

10-1

1

10-3

10-1

10 103

105

Figure �� GEANT cross sections for �River�water and standard tracking parameters

strongly supported on Unix�platforms�

input�file program� �options program� �options � � � output�file

This allows any combination of analysis applications in any order according to a box of bricks yieldinga high degree of �exibility and speed in data processing�The tools include a muon reconstruction program �� a graphical display program �� trigger and�lter programs �� and programs to generate histograms and N�tuples for the further processingwith Paw �� More details on the concepts and programs are given in appendix C�� and C��

�� Extension of the simulation

Several extensions of the detector simulation are under consideration�

Implementation of ice instead of water as a detector material�

Scattering of �Cerenkov light�

Variable OM positions during tracking� to study e�ects of water currents in the detector�

�� Extension of the simulation ��

Further extensions to GEANT� e�g tracking routines for slow moving magnetic mono�poles�Rubakov e�ect�� or an extension of the valid energy range�

In addition it is intended to add further program modules

Development of further event generation programs�

Further reconstruction programs� E�g� for the reconstruction of point�like light sources�

A �lter based on a neural network to reject down�going muons�

A detailed simulation program for individual optical modules�

Implementation of a graphical user interface� e�g� on base of Khoros or Tcl�Tk�

SiEGMuND was ported to various Unix �avours such as DEC�Ultrix� DEC�OSF�� HP�UX� IRIX�Convex� Linux � � � � It is desirable to expand this list also to non�Unix systems�

�� SIMULATION RESULTS

� Simulation Results

Alea jacta est

This section investigates fundamental characteristics of �Cerenkov signals in underwater �Cerenkov de�tectors� As mentioned in section �� the execution of a GEANT based program for these experimentsrequires a large amount of CPU�time� The parameterizations obtained in section �� and �� allowthe implementation of a fast simulation mode�

�� Cerenkov light from electromagnetic and hadronic cascades

Within the following simulations a parameterization of the total �Cerenkov light output and it&s angulardistribution is calculated for electromagnetic and hadronic cascades� Each simulation has been carriedout by positioning an initial particle with the energy E� at the coordinates �r� # �� The initialmomentum points into positive z�direction ��p� # p� � �ez�� The resulting cascade is tracked until theenergies of all �secondary� particles falls below the �Cerenkov threshold� These simulations have beendone with various initial particles at di�erent energies�

Electromagnetic cascades� e�� MeV � ��MeV � ��MeV � �GeV � ��GeV � ��GeV � �TeV � ��TeV �e�� GeV � �� GeV � �� GeV �

Hadronic cascades� �� GeV � ��GeV � �TeV � ��TeV � p�� GeV � ��GeV � ��GeV � �TeV �K�� GeV �

In order to get rid of statistical �uctuations� the simulation is repeated m�times and averaged�The angular �Cerenkov light distribution is calculated via a transformation method� which transformsthe angular distribution of all shower tracks to the resulting �Cerenkov distribution� Explicit detailsare described in appendix A�� The calculation proceeds via the following steps�

�� A histogram of zenith angles of all charged tracks pieces with energies above the �Cerenkovthreshold is created and the length of the current step is �lled into the histogram versus thezenith angle� de�ned as

cos� #�p � �p�j�pj � j�p�j ��

Thus the histogram contains the distribution dl�d�� called the Angular track�length distribution

dl

d��

Xtracks

Xsteps

li � ��i� ��

with li being the length of the current step and ��i� a delta function of the current directionangle� This distribution contains the di�erential distribution of the total amount of �Cerenkovradiating track�length versus the zenith angle to the initial direction �see �gure��A��

�� In order to preserve the longitudinal information of the shower� a second histogram is created�It contains the distribution

dl

dz#

Xtracks

Xsteps

��z� � li ��

with the Dirac delta function ��z�� This histogram corresponds to the distribution of the totallongitudinal �Cerenkov radiating track lengths along the shower axis�� This distribution is calledLongitudinal track�length distribution �see �gure ��B��

�The maximal step�size during tracking is small compared to the bin width of the target histogram�

�� Cerenkov light from electromagnetic and hadronic cascades �

(A) Zenith angle [deg]

Tra

ck d

irec

tions

dl/d

α [

cm]

(B) Distance [cm]

Tra

ckle

ngth

per

10c

m [c

m]

(C) Zenith angle [deg]

Cer

enco

v di

stri

butio

n dn

/dφ

[deg

-1]

(D) Zenith angle [deg]

Cer

enco

v di

stri

butio

n 4

π/N

* d

n/dΩ

1

10

10 2

10 3

0 50 100 15010

-11

10

10 2

10 3

10 4

10 5

0 500 1000 1500 2000

10-1

1

10

10 2

10 3

0 50 100 150

10-4

10-3

10-2

0 50 100 150

Figure �� Track and �Cerenkov distributions for ��GeV electron�cascades��A� the absolute angular track�length distribution� �B� the longitudinal track�length distribution� �C�the absolute angular �Cerenkov light distribution� �D� the e�ective angular �Cerenkov light distribution�normalised to ��

�� According to the method described in appendix A�� the distribution dl�d� is transformed into adistribution dn�d�� The distribution dn�d� contains the mean number of photons emitted intothe zenithal direction �� This distribution is called the Angular �Cerenkov light distribution �see�gure ��C��

�� In order to calculate the photon �ux at a given distance and angle� the distribution dn�d�is further transformed �see appendix A�� into the distribution dn�d( which is the numberof photons per unit solid angle� called E�ective Angular �Cerenkov light distribution �see �gure��D��

Figure �� shows the simulation results for ��GeV electron cascades� The absolute angular track�length distribution is plotted in �gure �� A�� The tracks are pointing strongly into forward directionbut also tracks with large angles occur� A longitudinal track�length distribution is shown in �gure�� B�� The result of the �Cerenkov light transformation can be seen in �gure �� C� and �D�� Thephoton distributions are strongly peaked around the �Cerenkov angle� Above an energy of � �GeVthese distributions are almost similar for electromagnetic cascades� Below � �GeV the distributionsbecome broader with decreasing energy until they are almost �at for � �MeV with no visible �Cerenkovpeak� shown in �gure ��



Cer

enco

v di

stri

butio

n 4

π/N

* d

n/dΩ

E = 1 MeV

(B) Zenith angle [deg]

Cer

enco

v di

stri

butio

n 4

π/N

* d

n/dΩ

E = 10 MeV

(C) Zenith angle [deg]

Cer

enco

v di

stri

butio

n 4

π/N

* d

n/dΩ

E = 100 MeV

10-3

0 100

10-4

10-3

10-2

0 100

10-4

10-3

10-2

0 100

Figure �� Relative e�ective �Cerenkov light distribution for low energy electrons

The following points have to be noted considering limitations and interpretation of the above trans�formation method�

The e�ective angular �Cerenkov light distribution gives the angular distribution per unit of thelongitudinal evolution of the shower� All tracks are assumed to be on the shower axis� Only incase of a point�like light source the photon �ux at a given distance can be explicitly calculatedfrom dn�d(� In general dn�d( has to be convoluted with the longitudinal evolution of a shower�

The calculation assumes a constant �Cerenkov angle and a constant �Cerenkov photon yield forall particles� This is not the case for low energy particles� The e�ect of the low energy tail ofshowers is respected by an empirical formula �eq�� applied to the actual implementation ofthe parameterizations described below�

Longitudinal distribution

In general the longitudinal energy deposition for electromagnetic cascades can be approximated with agamma distribution �see section �� eq�� The longitudinal track�length distribution has been�tted with

dl

dt# ��cm �E� �m �K � b � �bt�


��

with t # z�Lrad # z��cm the number of radiation lengths� K a normalisation factor� E� the initialenergy� a� b the shower parameters and m the number of simulated cascades�

In case of hadronic cascades� an additional process occurs� the decay of mesons into muons� Thesemuons do not further contribute to the evolution of the shower� but may produce long tails in thelongitudinal track distribution� Though this process is rare it has to be taken into account for summarydistributions of several cascades� This is done in eq�� with an additional exponential term to

�� Cerenkov light from electromagnetic and hadronic cascades ��

MeanRMS

422.6 152.2

P1 13.63P2 7.646P3 0.6473

(A) Distance [cm]

Lon

gitu

dona

l tra

ck p

rofi

le [

a.u.

] MeanRMS

43.42 25.33

P1 41.27P2 2.324P3 -0.6817E-01P4 17.60P5 0.4013P6 0.8752E-01P7 0.1356E-01P8 0.1311E-01P9 23.61P10 -0.7685


Cer

enco

v di

stri

butio

n 4

π/N

* d

n / d

Ω1

10

10 2

10 3

10 4

10 5

10 6

0 500 1000 1500 2000

10-4

10-3

10-2

0 50 100 150

Figure �� Fit to longitudinal track and angular �Cerenkov distributions for ��TeV electron cascades�A� the longitudinal track�length distribution� The �t parameters P�� P�� P� correspond to theparameters K� a and b of eq�� B� the e�ective angular track�length distribution normalised to�� The �t parameters P�� P�� P�� P�� P�� P�� P� P� P�� P�� correspond to the parameters �c� �� N�� N�� N�� of eq��

MeanRMS

504.0 262.7

P1 4.067P2 3.855P3 0.7277P4 0.4494E-03P5 1231.

(A) Distance [cm]

Lon

gitu

dona

l tra

ck p

rofi

le [

a.u.

] MeanRMS

46.27 31.11

P1 41.59P2 2.924P3 -0.2336P4 19.82P5 0.4044P6 0.4583E-01P7 0.1393E-01P8 0.1202E-01P9 25.21P10 -0.7572


Cer

enco

v di

stri

butio

n 4

π/N

* d

n / d

Ω

10 2

10 3

10 4

10 5

10 6

0 1000 2000 3000 4000

10-4

10-3

10-2

0 50 100 150

Figure �� Fit to longitudinal track and angular �Cerenkov distributions for �TeV pion� cascades�A� the longitudinal track�length distribution� The �t parameters P�� P�� P�� P�� P� correspond tothe parameters K�� a� b� k� and � of eq��B� the e�ective angular track�length distribution normalised to �� The �t parameters P�� P�� P��P�� P�� P�� P� P� P�� P�� correspond to the parameters �c� �� N�� N�� N�� ofeq��


K = 13.58

a = 2.03 + 0.604 * log(E)

b = 0.633

(A) Energy [GeV]

K1 = 3.02 + 0.147 * log(E)

a = 1.49 + 0.359 * log(E)

b = 0.772

(B) Energy [GeV]

0

2

4

6

8

10

12

14

1 10 102

103

104

0

1

2

3

4

5

6

7

8

1 10 102

103

104

Figure �� Parameters of the longitudinal �t versus energy �Plotted are the �t parameter K� a and b� �A� shows the �t values for electromagnetic cascades� �B�shows the values for hadronic cascades�

Particle Energy m K� a b K� ��GeV � ��events� �GeV �� GeV �� cm�

e� � �� e� �� e� �� e� �� e� �� p� �� p� �� p� �� p� �� K� ��

Table �� Fit results for longitudinal cascade parameterizations� Input parameters have been Lrad �� cm forelectromagnetic and �I ��cm for hadronic shower�

eq��

dl

dt# ��cm �E� �N

�K� � b � �bt�


�K� � exp�� z

�

��

Table �� gives the �t results for electromagnetic and hadronic cascades� No longitudinal �ts have beenapplied for electrons with energies smaller �GeV and hadrons smaller ��GeV �


Figure �� A� shows a typical �t for ��TeV electromagnetic showers� The �t parameters �eq��are plotted versus the energy in �gure �� A�� The scaling of the constants is �tted with constant ora linear �in log�E�� function�Figure �� A� shows the �t for �TeV pion cascades� A long tail is visible which is �tted with theexponential term of eq�� The �t results are tabulated in table �� and plotted versus the energyin �gure �� B�� The �uctuations for hadronic cascades are larger than for electromagnetic cascades�Thus the �t results are less stable� The scaling of the parameters is parameterized and shown in �gure�� B��

Particle Energy Events �c �� N� N� N�

�GeV � �� e�� e� �� e� �� e� � � � �� e� �� e� �� e� �� e� � � �� e� ��

�� p�� p� �� p� �� p� �� K� ��

Table �� Fit results for angular cascade parameterizations � The �ts for particles in "�� show bad convergenceand thus these results are given only for terms of completeness�

Angular distribution

The angular distribution has been �tted with following function�

dn

d(#

�

� ��N� � exp

�� +c

�� +c�

��

��

�N� � exp�� +c

�� +c�

��

� N� � exp�� +c

�� +c�

��

�

Each Exponential contains a width parameter �i and a skew term �i�The �t results for both electromagnetic and hadronic cascades are printed in table �� A typical �t isshown in �gure �� B� for ��TeV electron cascades� The scaling of the electromagnetic �t parametersversus the energy is plotted in �gure �� The �Cerenkov angle �C �tted as a free parameter is constant

� � SIMULATION RESULTS

Θc

(A) Energy [GeV]

Θc

[deg

]

N1N2N3

(B) Energy [GeV]

Nor

mal

isat

ion

Ni

σ1σ2σ3

(C) Energy [GeV]

Wid

th σ

i [d

eg-1

]

ε1

ε2

ε3

(D) Energy [GeV]

Skew

term

εi

05

101520253035404550

10-4

10-2

1 102

104

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Figure �� Parameters of the angular �t for electrons versus energy�A� shows the �t result for the �Cerenkov angle �c� �B� shows the �t result for the normalisationconstants N�� N�� N�� C� shows the �t result for width constants �� D� shows the �tresult for the skew terms � � � � �

�

above � ��MeV � The input value �� of the simulation is reproduced to better than �� gure��A�� The other parameters Ni� �i and �i are constant above �GeV ��gure ��B��D��

Analogous a typical angular �t is shown for ��TeV pion cascades in �gure ��B�� The results of theparameterizations are plotted in �gure �� versus the energy� The �t results for hadronic cascades arestable except for the increasing normalisation parameter N�� This corresponds to small changes in thecorresponding parameters �� and ��

The following strategy is used to yield a good approximation for non point�like showers� If the initialenergy E� is above �GeV � it is divided into n energies� n vertices starting from the original vertexare generated into the momentum direction according� to the Incomplete Gamma function� Thus alarge cascade is approximated by n smaller cascades which are assumed to be point�like light sources�

As noted above non�relativistic tracks produce less �Cerenkov light with a di�erent angular distribution�In order to include this e�ect the angular distribution dn�d( is corrected with an empirical formula�

dncor��

d(#dn��

d(� �a� b � cos��

�The cumulative distribution of the Gamma�distribution is given by the the �Incomplete Gamma�function� �eq�A��


Θc

(A) Energy [GeV]

Θc

[deg

]

N1

N2

N3

(B) Energy [GeV]

Nor

mal

isat

ion

Ni

σ1

σ2

σ3

(C) Energy [GeV]

Wid

th σ

i [d

eg-1

]

ε1

ε2

ε3

(D) Energy [GeV]

Skew

term

εi

05

101520253035404550

10 102

103

104

0

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104

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103

104

-0.8

-0.6

-0.4

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0

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0.6

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103

104

Figure �� Parameters of the angular �t for hadrons versus energy�A� shows the �t result for the �Cerenkov angle �c� �B� shows the �t result for the normalisationconstants N�� N�� N�� C� shows the �t result for width constants �� D� shows the �tresult for the skew terms � � � � �

�

This strategy is implemented in Dada for fast simulations� The parameters a and b are obtained bya comparison with simulations including the explicit calculation of the �Cerenkov angle and the photonyield� A simulation in the TRIAD gives values a # �� b # �� for electromagnetic cascades anda # �� b # � for hadronic cascades� An electron initiated cascade with ��GeV pointing upwardshas been simulated �� times in the centre of the TRIAD detector� This simulation has been done withthe full GEANT tracking� The same simulation was repeated with the fast simulation once includingthe longitudinal evolution and a second time assuming a point�like light source� Figure �� A�shows the mean number of photons hitting each OM� While the longitudinal simulation reproducesthe full simulation well� the fast simulation gives only the right order of magnitude� The di�erenceof the arrival times for the full GEANT and the fast simulations is shown in �gure �� B� Arrivaltimes for a point�like simulation �P�G� show large time di�erences to the full GEANT simulation �up to��ns�� whereas the longitudinal simulation �L�G� agrees well with the full GEANT simulation� Opticalmodules at a large distance from the cascade have a low hit probability� Due to only few recordedphotons in this simulation they show larger statistical �uctuations�


(A) OM number

Num

ber

of p

hoto

ns

GEANT Point Sim. Long.Sim.

(B) OM number

Rel

. tra

nsit

time

[ns]

t (L-G) t (P-G)

10-2

10-1

1

10

10 2

0 20 40 60

-40

-30

-20

-10

0

10

20

0 20 40 60

Figure �� Comparison of the full GEANT and fast cascade simulations� Simulated are �Cerenkov photons hittingOMs for electron showers ��GeV � in the centre of the TRIAD detector� �A� The mean numberof photons hitting each OM� �B� The arrival time of the �rst photon minus the arrival time of theGEANT simulation� �P�G�� Point�like# �L�G�� Longitudinal

em. cascades L = 488.9 * E

hadr. cascades L = 407.6 * E

Energy [GeV]

Tot

al tr

ack

leng

ht L

[cm

]

10-1

1

10

10 2

10 3

10 4

10 5

10 6

10 7

10-4

10-3

10-2

10-1

1 10 102

103

104

Figure �� Integrated track length for electromagnetic and hadronic cascades

The total integrated track length

L #

Z ��

�d�

dl

d�#

Xtracks

Xsteps

li ��

is proportional to the total amount of emitted �Cerenkov photons�

�� Cerenkov light from muons �

Figure �� shows the total integrated track�length L �see appendix A�� eq�� versus the energy ofelectromagnetic and hadronic cascades� The track�length depends linearly on the initial energy with

L�cm� # E�GeV � ��

�� for e�m� cascades�� for hadr� cascades

�cm�GeV �

The track�length is roughly proportional to the total amount of generated �Cerenkov photons� Ifone applies the correction eq�� to the angular distribution of the resulting �Cerenkov distributionone gets a correction factor �� for electromagnetic and �� for hadronic cascades for the totalphoton yield� This corresponds to approximately �� Cerenkov photons per GeV energy for anelectromagnetic cascade and � �� for hadronic cascades �assuming �� photons per cm track��

COS(Zenith)

dn /

dΩ [

sr-1

]

This simulation (with correction)

This simulation (without correction)

Belyaev

Hauptman

10 4

10 5

10 6

10 7

-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1

Figure �� Comparison of the e�ective angular �Cerenkov light distribution in point�like approximation with earlierparameterizations by Belyaev and Hauptman� The e�ective angular �Cerenkov light distribution isshown with and without the correction according to eq�� Shown are the distributions for ��GeVelectrons assuming an in�nite distant observer�

Figure �� shows the parameterization of the e�ective angular �Cerenkov light distribution with andwithout the correction by eq�� The results of two previous simulations are plotted in comparison�These parameterizations are implemented in the phocas�function �� which bases on two calculationsby Belyaev et�al�� and J�Hauptman� The �gure shows the e�ective photon �ux per steradian resultingfrom ��GeV electrons� No light attenuation was used and the cascade is assumed as a point�like lightsource� All distributions di�er in their integral by less than ��"� It has to be noted� that the assumptionof a point�like light source does not yield a proper description �see �gure �� A full longitudinalsimulations broadens the sharp �Cerenkov peak� Therefore this simulation is not in disagreement to theHauptman parameterization� which already takes account of the longitudinal distribution�

�� Cerenkov light from muons

The primary challenge for a neutrino telescope is to detect muons and reconstruct the direction of themuon track using the arrival time and amplitude of �Cerenkov light measured with the OMs� Due toenergy loss processes a muon is accompanied by secondary particles� which also produce �Cerenkov light�see section�� Therefore the amplitude and time of the measured �Cerenkov signal does not match


the expectation for a pure muon track� Processes with large energy transfers �e�g� bremsstrahlung�give rise to bright local cascades� Processes with smaller energy transfer �e�g� ��ray production� occurmore frequently and can be approximated as a quasi continuous process �see also �gure �� A��

A muon including the low energy quasi�continuous particles will be named naked muon in thefollowing� in contrast to a minimal ionising muon� which represents only a pure muon�

�� Parametrisation of the e�ective �Cerenkov light from muons

Emax=0.1GeV

λ/10

cm [c

m]

Emax=0.5GeV Emax=2.5GeV Emax=5GeV

Distance [cm]

0

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300

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�A�

τ = 3.3

mean = 3.1

Emax=0.1GeV

Rel

ativ

e pr

obab

ility

τ = 5.4

mean = 5

Emax=0.5GeV

τ = 13.5

mean = 10.8

Emax=2.5GeV

τ = 28.3

mean = 13.1

Emax=5GeV

λadd/10cm [cm]

10-2

10-1

0 50 100

10-2

10-1

0 50 100

10-2

10-1

0 50 100

10-2

10-1

0 50 100

�B�

Figure �� Low energy secondary tracks accompanying �TeV muon tracks� �A� the integrated track�length� per ��cm of the covered distance by a muon� Four muon tracks are shown with di�erent upperboundaries on the maximum energy of secondary particles� �B� Shows the frequency distributions ofthe occurrence of additional track�length �add per ��cm for the same tracks� A decaying Exponentialis �tted to the distributions�

In order to investigate the characteristics of the quasi�continuous secondary light production� muonsare tracked in a test volume from the position �� for ��m into positive z�direction� The integrated�Cerenkov radiating track�length � including secondaries is summed every ��cm along z �in analogy tothe longitudinal track�length distribution of a shower eq�� Obviously one expects �� # ��cm�Cerenkov radiating track�length per ��cm covered distance for a minimal ionizing muon� Including


secondaries one gets

� # �� add ��

Figure �� A� shows a simulation of four �TeV muons� An upper limit Emax on the maximumenergies of generated secondary tracks is varied� For small Emax only small local energy depositions arevisible� For values of Emax ��GeV larger local �uctuations occur� which cannot be approximatedas continuous processes� Figure �� B� shows the distribution of �add per ��cm muon track� Anexponential distribution gives a su�cient description for small values Emax�

MeanRMS

9.909 22.75


Tra

ck d

irec

tions

dl/d

α [

cm]

(B) Distance[cm]

Tra

ckle

ngth

per

10c

m [c

m]

MeanRMS

42.53 16.98

(C) Zenith angle [deg]Cer

enco

v di

stri

butio

n 4

π/N

* d

n/dΩ Entries

MeanRMS

50 5459. 282.7

(D) Total tracklength [cm]

Ent

ry

10-2

10-1

1

10

10 2

10 3

0 50 100 15002468

1012141618

0 1000 2000 3000 4000

10-4

10-3

10-2

10-1

0 50 100 1500

0.5

1

1.5

2

2.5

3

5000 5500 6000 6500

Figure �� Track and �Cerenkov distributions for ��GeV muons including only low energy quasi continuoussecondary tracks �Emax � ��GeV � averaged over �� tracks� �A� Angular track�length distribution��B� Longitudinal track�length distribution� �C� E�ective angular �Cerenkov light distribution� �D�Distribution of the total track�length�

A parameterization of the �Cerenkov light due to quasi�continuous processes is obtained in close analogyto the simulation of cascades �section �� All �� muons have been simulated for di�erent energies andaveraged� The threshold Emax is set to ��GeV for secondary e� and �GeV for secondary �� Using theangular track�length distribution eq�� the e�ective �Cerenkov light distribution is calculated �seeappendix A�� Figure �� shows the results for ��GeV muons �see also �gure �� The e�ective�Cerenkov distribution shows a sharp peak at the �Cerenkov angle and a broad distribution of light dueto secondary particles� The calculation of the �Cerenkov light neglects the smaller �Cerenkov light yieldand changed angular distribution of non relativistic tracks� A consideration of this would reduce thetotal amount of light especially into backward direction �analogous to eq��

Figure �� shows a parameterization of �add versus the energy of the muon� The total track�length�tot for a muon track �� can be expressed via

�tot # �� log�E��GeV ��


(A) Energy [GeV]

Tot

al tr

ackl

engt

h [c

m]

(B) Energy [GeV]

A

dditi

onal

trac

klen

gth

[%]

Mean=17.2+3.24*LOG(E)

0

1000

2000

3000

4000

5000

6000

7000

10 102

103

104

0

10

20

30

40

50

60

70

80

90

10 102

103

104

Figure �� Additional track�length due to quasi�continuous secondaries versus the muon energy� �A� the meantotal track�length for ��m muon tracks� �B� The relative additional track�length�

The above parameterization is implemented in the Dada program� The GEANT tracking parametersare set to ��GeV for mechanisms generating e� and to �GeV for produced �&s� If a mechanismgenerates a secondary above the tracking thresholds a local cascade is simulated according to theparameterization in section �� The loss of low energy tracks is compensated by adding �add to eachmuon track piece �� assuming an Exponential distribution with the decay constant �add �see �gure�� B�� The angular distribution is neglected��

This method� called Fast GEANT� yields an enormous increase in the execution speed by typically afactor �� and enables a mass production of muon events� Though it neglects small �uctuations ofcascades and the stochastic generation of low energy secondaries along a muon track� it keeps the fullstochastic tracking with respect to the production of charged high energy secondaries with E � ��GeV �

Figure �� shows a comparison of the fast parameterization with a full GEANT simulation� A speci�c�TeV muon track is simulated through the centre of the TRIAD detector� The photons� which hit theOMs are simulated instead of the full digitisation of OMs� The same track is repeated and results areaveraged� Three di�erent simulations are applied� full Geant� fast Geant and simulation of a minimalionising muon track�

The mean number of photons hitting each OM �A�� and the total number of photons per event �B�matches well between the fast and the full GEANT simulations but disagrees with the simulation ofminimal ionising muons� The time residual is de�ned as di�erence between the time of hit and theexpected time derived from the track kinematics

$t � thit � texpected��

assuming a pure �Cerenkov cone� �C� shows the distribution of the time residuals in all hit OM� Eachentry in the distribution is weighted with the number of hit photons� Thus the distribution shows thearrival times of photons� Minimal ionising muons generate a small peak� The simulation of the muonincluding secondary processes leads to a long tail of photons arriving at later times� The secondarylight causes a distortion of the clean �Cerenkov signature� which makes a reconstruction of the track

�Photons� which are not emitted under the �Cerenkov angle� usually arrive later and thus generate only subsequenthits within the dead time of the OM�

�� Cerenkov light from muons �

(A) OM number

Num

ber

of p

hoto

ns

Full Geant Min.Ionizing Fast Geant

(B) Number of hit OM

ent

ry

Min.Ionizing

Full Geant

Fast Geant

(C) Δt [ns]

pho

tons

Min.IonizingFull GeantFast Geant

(D) Δt [ns]

Hits

Min.IonizingFull GeantFast Geant

10-1

1

10

10 2

0 20 40 600

0.02

0.04

0.06

0.08

0.1

0.12

0.14

20 40 60

10-2

10-1

1

10

10 2

0 25 50 75 100

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1

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0 25 50 75 100

10-3

10-2

10-1

1

10

0 25 50 75 100

10-3

10-2

10-1

1

10

0 25 50 75 100

Figure �� Detector response for a repeated Muons track in the TRIAD detector� A �TeV muon track wasrepeatedly simulated in the TRIAD detector� The �gures show comparisons of simulations with fullGEANT� fast GEANT and minimal ionising muons� �A� The mean number of photons hitting eachOM� �B� Distribution of the total number of hitting photons per event� �C� Distribution of relativearrival time of photons� �D� Distribution of relative arrival time of photon�hits�

less robust� The fast GEANT simulation reproduces well the full GEANT simulation� �D� shows thetime residuals for all hits� not weighted with the number of photons� The distributions shows a dipat $t # ��ns� This dip occurs due to the internal recombination of hits during tracking� Photonsarriving within a time window of about �ns are regarded as equal in time and recombined �see appendixC�� As expected the full simulation generates more hits of smaller light intensity compared to thefast simulation� These hits are related to secondaries of small energies� which produce a subsequent hitto a previous direct muon hit� If one applies the dead time of the OMs to the data� the dip disappearsand the distribution agrees well between fast and the full simulation�

�� Cerenkov light from secondary processes

The characteristics of the individual stochastic energy loss process are investigated by the simulationof muon tracks of �xed energy through the NT�� detector� The tracks have a �xed energy andare isotropically generated over the lower hemisphere� The same data�set of tracks is simulated withcertain physical processes switched on or o� for di�erent simulation runs� The geometrical plane forthe simulated vertices has a radius of ��m which is only slightly larger than the NT�� detector� Thetrigger is set to minimum � hit strings and � hit channels� Multiple hits in one OM are integratedif they occur within the dead�time of ��ns and the local coincidence between two OMs is simulated


with a time window of ��ns�

ΣA [PE]

P i(>PE

)

All

0Q

D

MP

B

NCH

P i(>N

CH

)

All

0 Q

D

M

P

B

10-3

10-2

10-1

1

0 200 400 600 800 1000

10-3

10-2

10-1

1

0 20 40 60 80

�A� �B�

Figure �� Amplitude response of the NT�� for isotropic �TeV muons� �A� shows the relative number ofevents Pi�� pe� with the total energy above a threshold� �B� shows the relative number of hitchannels Pi�� NCH� above a threshold� The di�erent simulations are indicated with� � only minimalionising muons� Q with quasi�continuous energy loss� D delta ray production ��Q�� M muon nuclearinteractions ��Q�� P pair production ��Q�� B bremsstrahlung ��Q�� For �All all processes havebeen switched on� Each process except for �� includes the quasi�continuous secondary light ��Q��

Figure �� displays integral distributions of the total number of pe and hit channels NCH for �TeVmuons� Shown are the results for di�erent simulations� minimal ionising muons �� naked muons �Q��full simulation �All�� and the individual discrete processes� bremsstrahlung �B�� delta�ray production�D�� pair production �P� and nuclear interactions �M�� All but �� include also the quasi�continuouslight �Q� of a naked muon� The distributions for each process i are normalised to the number oftriggered events and thus yield the probability of the occurrence of events with a total amplitudePi� pe� above a threshold and a number of hit channels Pi� NCH� above a threshold

Pi� pe� #N�PE

N itrig

Pi� NCH� #N i�CH

N itrig

��

The trigger e�ciencies �i # N itrig�Ngen are given in following table�

Process Full � Q D M P B

i ��

The total number of �� hit OM is not exceeded by naked muons while about ��" of the events with thefull simulation exceed this value� Events with larger amplitudes are dominated by the pair productionprocess and for the largest amplitudes by bremsstrahlung� The contribution by delta rays is relativelyweak� since only delta rays above ��GeV are considered �see section �� Though muon nuclearinteractions have only a rare occurrence� their contribution is still visible� especially for large numbersof hit channels�Figure �� shows how the relative contributions of the di�erent processes summarise up to the totalamplitude response� The comparison has to respect the di�erent trigger e�ciencies and is calculated


Σ A [PE]

PR s

um (

>PE

)

NCH

PR s

um (

>NC

H)

+B+P+M+D+QMin.Ion.

10-3

10-2

10-1

1

0 200 400 600 800 1000

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1

0 200 400 600 800 1000

10-3

10-2

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0 20 40 60 80

Figure �� Contributions of discrete muon energy loss processes �E� �TeV � to the amplitude response of theNT�� detector� Shown is how the processes add up to the total response�

as follows� Each distribution Pi of �gure �� is weighted with its relative trigger e�ciency �i��Fullcompared to the full simulation

Pi PRi # Pi � �i

�Full��

The distribution for naked muons Q is subtracted from B� P � M � D and the distribution for mini�mal ionizing muons � is subtracted for Q� Finally the contributions of the di�erent simulations aresubsequently added to the contribution of minimal ionizing muons in �gure �� giving the summedprobability of the relative contributions PR

sum� It has to be noted� that this calculation is not exactand yields a slightly larger distribution than for the full simulation� This is explained by the fact thatduring the simulation of one process with the other processes switched o� the total energy loss of themuon itself is smaller� Since the cross sections rise for higher energies the probability of the occurrenceof a process is slightly larger if no other processes occur in the same simulation run� The individualsimulations may also involve a slightly di�erent event topology which may be di�erently a�ected bythe trigger condition �� strings� � hit channels��

Not only the amplitude response but also the time response of the detector is di�erently in�uenced bysecondary processes� as shown in �gure �� and �� The majority of hits arriving at later times thanexpected from the model of a naked muon are strongly dominated by bremsstrahlung events� Pairproduction events signi�cantly enlarge the hit probability at the expected time� As discussed in moredetail in section �� late secondary hits are strongly suppressed by the local BAIKAL coincidencecondition� Only secondary cascades with large energy transfer� such as bremsstrahlung events� arelikely to produce enough light for a coincident hit to trigger both OMs�

Figure �� and �� show the time residuals for muons with the energies ��GeV � ��GeV � �TeVand ��TeV simulated in the NT�� detector� Tracks from same data set as in the above simulationhave been tracked through the NT�� detector using only a changed muon energy� The �gure showsthe time distribution of hits in OMs� which are not weighted with the hit amplitude� The plots arenormalised to the total number of events� The �gure does not include the relative trigger e�ciencies�Figure �� shows the corresponding amplitude distributions� Especially from �C� one concludes that


Δt [ns]

P i R

Full

B+Q

P+Q

M+Q

D+Q

Q

10-4

10-3

10-2

10-1

1

-20 0 20 40 60 80 100

Figure �� Contributions of discrete muon energy loss process to the time residuals eq�� of hits in the NT��detector� The distributions are normalized on the number of triggered events for the full simulationof �TeV muons�

Δt [ns]

P i R ⋅ A

[P

E]

FullB+QP+QM+QD+QQ

10-4

10-3

10-2

10-1

1

10

10 2

-20 0 20 40 60 80 100

Figure �� Contributions of discrete muon energy loss process to the time residuals �amplitude weighted� of hitsin the NT�� detector�

�� Cerenkov light from muons ��

Δt [ns]

PR

50 TeV5 TeV500 GeV50 GeV

10-4

10-3

10-2

10-1

1

10

-20 0 20 40 60 80 100

Figure �� Time residuals for muons of di�erent energies in NT�� Shown are the time residuals of each hitnormalised to the trigger e�ciency of �TeV muons�

Δt [ns]

PR ⋅

A

[PE

]

50 TeV

5 TeV

500 GeV

50 GeV

10-2

10-1

1

10

10 2

-20 0 20 40 60 80 100

Figure �� Time residuals �amplitude weighted� for muons of di�erent energies in NT��


(A) ΣA [PE]

P(>P

E)

(B) NCH

P(>N

CH

)

(C) NCH

P(N

CH

)

50 TeV

5 TeV

500 GeV

50 GeV

(D) d [m]

P hit

10-3

10-2

10-1

1

0 200 400 600 800 1000

10-3

10-2

10-1

1

0 200 400 600 800 1000

10-3

10-2

10-1

1

0 20 40 60 80

10-3

10-2

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1

0 20 40 60 80

0

0.02

0.04

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0 20 40 60 800

0.02

0.04

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0 20 40 60 800

0.2

0.4

0.6

0.8

1

1.2

0 20 40 600

0.2

0.4

0.6

0.8

1

1.2

0 20 40 60

Figure �� Amplitude response of the NT�� detector for di�erent energies� �A� the integral distribution ofthe total energy in the detector� �B� the integral distribution of hit channels� �C� the di�erentialdistribution of hit channels� �D� the hit probability as a function of the length d of the �Cerenkov lightpath� The distributions in �A�� B� and �C� are normalised to the number triggered events of eachenergy� The distribution �D� is determined by the individual occurrence of a hit in each OM for alltriggered events�

a measurement of the muon energy is di�cult� especially for low energies ��TeV � unless one usesmore sophisticated methods as described in e�g� ��

�� Pointing accuracy of muons

An interesting aspect for the operation of a neutrino telescope is the pointing accuracy of a detectedmuon track into the initial neutrino direction� Three e�ects provide deviations from the initial directionof the neutrino� The dominant deviation is due to the kinematics of the neutrino nucleon interactionwith an average scattering angle given in eq�� A negligible contribution comes from the de�ection


by the Earth magnetic �eld� A conservative estimate gives

�B�rad� � L � �� Bp�

��

with the muon momentum p� in units GeV�c� A �eld value of ��T gives �B�radm�� p� per

m track length� Typical deviations after a muon traveled its half mean range �see eq�� are of theorder of �� degrees�

In addition� during propagation through water� the muon is a�ected by multiple scattering and recoilinge�ects in secondary processes� This e�ect is treated in detail in the following�

.

L’

Detector (NT36)

μextrapolated track

differential angle

true track

Θintegrated angle deviation

L

ϑ

D.

Figure �� Sketch of a muon track traveling through a detector�

The situation is sketched in �gure �� A muon wobbles along its initial track and eventually changesits direction� Two characteristic quantities determine the pointing accuracy of a muon� The di�eren�tial angle � gives the angle between the initial direction and the direction of the muon after travelinga certain distance L� The deviation D gives the distance between the actual position of the particleand the extrapolated initial track� It allows to calculate the integrated angle + between the initialdirection �L and the averaged direction �L� The two angles play a complementary role for the evaluationof the pointing accuracy� In case of a high energy muon and a small detector �e�g� NT�� the muontravels most of the time outside the detector and thus � limits the pointing accuracy� In case of a largedetector �e�g� KM�� and a low muon energy the angle + becomes more interesting� In general � hasa larger value than +�

The pointing accuracy due to recoiling e�ects and multiple scattering are investigated by the simulationof muons tracks through water� As an example �gure �� shows typical distributions of di�erentialangle �W and the deviation DW for ��GeV muons after traveling ��m�


EntriesMeanRMS

1000 0.3427 0.2403

υW [deg]

entr

y

EntriesMeanRMS

1000 0.1544 0.1050

DW [m]

entr

y

0

20

40

60

80

100

0 1 2 30

20

40

60

80

100

0 0.5 1 1.5

Figure �� Typical distributions of W and DW � Shown is the simulation of muons with ��GeV initial energyafter track�length of ��m�

E [GeV]

υW

[deg

m-1

]

υW = 0.294/E

E [GeV]

DW

[m m

-1]

DW = 0.134/E

10-5

10-4

10-3

10-2

10-1

10 102

103

104

10-5

10-4

10-3

10-2

10-1

10 102

103

104

Figure �� Parametrisation of the mean W and the mean DW versus the energy� The error bars indicate themean deviations of the simulated distributions�

E [GeV]

υW

[deg

m-1

]

E [GeV]

ΘW

[deg

m-1

]

Parameterization

0

0.2

0.4

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0.8

1

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1.4

102

103

104

0

0.2

0.4

0.6

0.8

1

1.2

1.4

102

103

104

Figure �� W and �W after the half mean muon range versus the initial muon energy� Plotted are also datapoints obtained by direct simulations�


25GeV

50GeV

100GeV

300GeV

1TeV

10TeV

L [m]

υW

[deg

m-1

]

L [m] Θ

W [d

eg m

-1]

25GeV

50GeV

100GeV

300GeV

1TeV

10TeV

10-4

10-3

10-2

10-1

1

10

1 10 102

103

104

10-3

10-2

10-1

1

10

1 10 102

103

104

Figure �� W and �W versus the muon track�length for di�erent initial energies�

The integrated angle +W is calculated from the track�length L and the deviation DW via

cos+W #L� � L� � d�

�LL� �� d�

�L��

Muons of di�erent initial energies are simulated and tracked via a distance of ��m� The values �Wand DW per meter track are calculated and plotted versus the average energy of the muon �the muonlooses energy during the ��m track�� Figure �� shows a parameterization versus the energy using

�W #��WE

DW #�DW

E��

In order to calculate the mean values �W and DW for a muon traveling a certain distance one has totake it&s energy loss into account� Using eq�� one gets

�W �r� #

Z r

�

��WE�r�

dr

��

#��Wa

��ln�

a � E�

exp��b � r� � �E� �ab �� a

b

�� b � r�

and similar for WW � The value +W is calculated via eq��

An estimate of the typical pointing accuracy may be achieved using the half mean range R�� of themuon as calculated via eq�� Figure �� shows the result of the calculation� By comparisonwith simulated data one sees that the parameterization yields a good estimate for low energy tracksbut overestimates �W and underestimates +W for large energies� The di�erences occur due to largestochastic �uctuation especially for long track length and high energies� Also the calculation eq��does not take into account a possible scattering of the muon into it&s original direction and uses a verysimple approximation of the muon energy loss� It has to be noted that muons traveling upward mayalso travel through rock before reaching the detector giving rise to larger scattering angles� Figure �� shows the results for �W and +W versus the track�length for muons of di�erent initial energies�


(A) Δt [ns]

P Hit

Single OM

(B) Δt [ns]

P Hit

⋅ A [P

E]

Single OM

(C) Δt [ns]

P Hit

Pair OM

(D) Δt [ns]

P Hit

⋅ A [P

E]

Pair OM

10-5

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1

10

0 50 10010

-410

-310

-210

-11

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10

0 50 10010

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10 2

0 50 100

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10-4

10-3

10-2

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1

10

0 50 10010

-410

-310

-210

-11

10

10 2

0 50 100

Figure �� Time residuals of hits PHit and weighted with the hit amplitudes PHit �A for isotropic �TeV up�goingmuons for the NT�� detector with single and pair OMs� The trigger condition is � hit strings ��The distributions are normalised on the number of triggered events

�� Muon detection in BAIKAL

The capability of detecting and reconstructing muon events depends critically on the sensitivity of thedetector and the signal topology of the registered events� In the BAIKAL approach both quantitiesare strongly in�uenced by the local coincidence condition between two OMs� Figure �� shows timeresiduals �eq�� for isotropically simulated up�going �TeV muons in the NT�� detector� Thedetector is equipped with either single OMs or pairs of OMs switched in a local coincidence at thespace points� The same trigger condition �� hit strings� is applied to both simulations� The tails in thetime residuals are approximately one order of magnitude smaller in case of a local coincidence� Themean amplitude is calculated via

A�t� #PHit�t� �APHit�t�

��

For single OMs one �nds A��ns� � ��pe� A��ns� � ��pe� A��ns� � ��pe� while for pairs �perOM� A��ns� � ��pe� A��ns� � ��pe� A��ns� � ��pe�

The additional presence of noise requires much stronger trigger conditions for single OMs but not forpairs� Therefore the trigger condition for singles is raised to a typical trigger of the DUMAND experiment�but the trigger for singles remains unchanged� The simulated time residuals for ��kHz noise are shownin �gure �� The trigger e�ciency for the single OM trigger condition is only ��" of the pair condi�

�It has to be noted that only noise hits have been simulated into muon events� but no events due to �pure� noise hitshave been generated�


(A) Δt [ns]

P Hit

Single OM

(B) Δt [ns]

P Hit

⋅ A [P

E]

Single OM

(C) Δt [ns]

P Hit

Pair OM

(D) Δt [ns]

P Hit

⋅ A [P

E]

Pair OM

10-5

10-4

10-3

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1

10

0 50 10010

-410

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0 50 100

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1

10

0 50 10010

-410

-310

-210

-11

10

10 2

0 50 100

Figure �� Time residuals of hits PHit and weighted with the hit amplitudes PHit �A under presence of ��kHznoise� The �gure shows the same muon events as �gure �� but uses the trigger condition � hitstrings �� for pair OM and hit neighbouring OMs in strings or two times � hit neighbouringOMs in strings ��T � �� T � �� eq�� for single OMs

tion� Even under the presence of noise the muon events with a local coincidence may be still regardedas almost noise�free �see also �� Without the coincidence condition sophisticated noise reductionalgorithms would be required to enable a good reconstruction�

Figure �� shows the e�ective area for the NT�� NT�� NT�� and NT��detectors� Simulated are isotropic up�going muons without noise� Each diagram shows two graphs�The �rst gives the e�ective area for all events that passed the condition of minimum � hit strings and hit channels� These triggered events are reconstructed with the recoos program� Events� which arereconstructed with a pointing�error better than �� are selected� The second graph shows the e�ectivearea for these events� Though NT�� has a larger geometrical volume than NT�� it hasa smaller e�ective area for small energies� This is due to the fact� that the spacing between channelswas enlarged in �� to a value optimised for NT�� The much smaller detector NT�� does note�ciently trigger muon events of low energies� This e�ect was already discussed in section �� Thee�ective area for NT�� especially for high energies� is slightly underestimated� because only muontracks with a distance to the detector centre smaller than ��m have been simulated� Tracks furtheroutside may also contribute to the e�ective area�

It has to be stressed� that the selection of well reconstructed tracks on basis of the information on thegenerated track does not represent the experimental situation� Since the original track is unknown in

�The detectors NT�� ""�� NT�� ""�� are simulated by removing not installed OMs from the events simulatedwith the NT�� detector�


NT-36 (1993)

E [GeV]

Aef

f [m

2 ]

Trigger 6/3

Reco <50

NT-36 (1994)

E [GeV]A

eff [

m2 ]

Trigger 6/3

Reco <50

NT-72 (1995)

E [GeV]

Aef

f [m

2 ]

Trigger 6/3

Reco <50

E [GeV]

Aef

f [m

2 ]

Trigger 6/3

Reco <50

NT-200

10 2

10 3

102

103

104

105

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10 3

102

103

104

105

10 2

10 3

10 4

102

103

104

105

10 3

10 4

102

103

104

105

Figure �� E�ective area for the NT� �� NT� �� NT�� and NT�� detectors versus theenergy of isotropic up�going muons� The hatched areas indicate the geometrical area of the detectors�

experimental data� quality cuts on the reconstruction results have to be applied� The evaluation andoptimisation of cut criteria depends on the speci�c detector��

��

Experimental Results

The following sections show initial data from the BAIKAL and the DUMAND II experiments� Thediscussion concentrates on atmospheric muons in Baikal and background noise due to ��K in theocean�


The detector NT�� started operation on April ��th �� This section uses the calibrated data takenin the runs d�� and d�� The data �les correspond to a runtime of about h with �� operatingchannels and ��h with � operating channels respectively� The detector con�guration with � operatingchannels will be named NT�� in the following� The data��les contain �� and �� triggeredevents� which are reduced to � �� and �� events after application of a trigger requiring � hitstrings and hit channels�

rGEO [m]

Aef

f [m

2 ]

NT-36

rGEO [m]

Aef

f [m

2 ]

NT-32

0

50

100

150

200

250

300

0 20 40 600

50

100

150

200

250

300

0 20 40 60

Figure �� E�ective area of NT� and NT�� for atmospheric muons versus the radius of the geometricalsimulation plane� The trigger is set to hit strings �always� and �� hit channels�The error bars include an assumed systematic error of �m� and statistical errors�

In order to compare the experimental data with simulated data� atmospheric muons are generatedusing the basiev event generator program �see appendix C�� Atmospheric muon events are generatedfor two depths ��m and ��m with a threshold of �GeV and zenith angles from �� to �� Thecorresponding vertical energy thresholds are set to ��GeV and ��GeV for muons and to ��TeVand ��TeV for the initial proton respectively� The generated muons� which are passed to the Dadadetector simulation� are simulated on a plane� whose radius is varied in di�erent simulation runs from��m to �m� The plane itself is at a distance of ��m to the detector� The radius of the plane on whichthe initial protons are simulated is typically ��m larger� The detector simulation uses spline�functionsfor the the sensitivity of a typical Baikal OM and standard water properties from the standard BaikalMonte Carlo program �see appendix C�� After the detector simulation events are further processed�Hits with an amplitude smaller than ��A��pe� are rejected and noise pulses � A # �pe� are simulated

�� EXPERIMENTAL RESULTS

into the data stream with a rate of ��kHz per OM� A dead time of ��ns is simulated� for each OMand the local coincidence is applied with a coincidence window of ��ns� Events with � hit strings and hit OMs are selected� Events for the NT�� detector are generated by removing hits in the nonoperating channels � and � before the application of the above trigger conditions�Figure �� shows the e�ective area Aeff � calculated via eq�� of the NT�� and NT�� detectorfor atmospheric muons versus the radius rGEO of the simulation plane for three di�erent triggers�Below rGEO # ��m the e�ective area is drastically reduced� For a �� trigger and above values ofrGEO � ��m the e�ective area is roughly constant with a value of about ��m�� Noise pulses� whichoccur in one OM� may prevent the local coincidence to trigger within the dead�time� For a higher��kHz� or a lower ��kHz� simulated noise rate the e�ective area is changed by about ��m�� For athreshold of �� A��pe� in each OM the e�ective area rises by about ��m��

A further data set �nt��gr�� contains atmospheric muons simulated with the standard Baikal MonteCarlo program� After application of the same trigger conditions � �� events remain forNT�� and �� for NT�� The initial muon tracks also were generated with the above basievprogram� ��

�� Hit e�ciency and channel multiplicity

channel No.

P hit

Run 145Exp.DataDada MCBaikal MC

channel No.

P hit

Run 196Exp.DataDada MCBaikal MC

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 150

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 5 10 15

Figure �� Hit probability versus the channel number for a trigger of � hit channels and � hit strings�

The total number of hits in each channel is normalized to the total number of triggered events gives thehit probability Phit for each channel� Figure �� shows Phit for the experimental data in comparisonto the Monte�Carlo result� The alternating orientation of the OMs is clearly visible by a lower hitprobability for down�looking OMs� The di�erences between data and MC are not due to statistical�uctuations� The major contributing error results from the individual quantum e�ciencies of thePMTs and the thresholds individually set in each OM during the experiment� The down�lookingOMs seem to have a lower relative hit probability� A detailed analysis of the absolute hit probabilityshowed� that the down�looking channels give correct values� but the up�looking channels show an

�This time is larger than the nominal value of about ��ns� On the other hand the simulated noise rate is smallerthan the typical rate of ��kHz� Also no additional dead time for the digitisation process is simulated�


increased hit probability� �� Comparing NT�� and NT�� one observes� that for the applied triggerthe topology of the hit probability is only slightly changed with two not operating channels� Thoughthe three strings are arranged in a non�symmetric triangle the Monte Carlo calculations predict almostsymmetric relative hit probabilities between the strings� The di�erences to the experimental dataindicate the maximum attainable level of accuracy in describing the data by MC�calculations�

Exp.Data

Baikal MC

Dada MC

NCH

P(N

CH

)

RUN 145

Exp.Data

Baikal MC

Dada MC

NCH

P(N

CH

)

RUN 196

10-4

10-3

10-2

10-1

0 5 10 1510

-4

10-3

10-2

10-1

0 5 10 15

Figure �� Channel multiplici ty for triggered events in NT� and NT�� A general trigger requiring hit stringsis set� The distributions are normalised on the total number of triggered events� The data for BaikalMonte Carlo includes a simulation of measured ine�ciencies of individual channels � ��

Figure �� shows the distribution of the number of hit channels� The distribution is well describedby the Dada program and the Baikal Monte Carlo within the experimental uncertainties due to OMparameters and water attenuation� A di�erent simulated noise rate also changes the shape slightly�Without simulated noise the simulation yields results above the experimental results� For ��kHz noisethe simulation results are slightly below the experimental data� The Baikal Monte Carlo produces aharder distribution� If this is attributed to incorrectly simulated water properties� a larger light outputfrom physical processes� or more sensitive OMs� one also expects larger signal amplitudes in eachchannel �see chapter �� It has to be noted that a di�erent trigger condition or normalizationalso yields a good agreement of the Baikal MC with the measured multiplicities �� A �t to thedistributions with an Exponential gives a decay constant� which agrees better than ��" between bothsimulations and the experimental data�

�� Signal amplitudes of individual channels

A comparison of the amplitude distributions in each channel between experimental data and simulationresults shows a rough agreement for a part of the channels� e�g� -� in �gure �� but a poor agreementfor most channels� e�g� - in �gure �� The Baikal Monte Carlo generally produces higher signalamplitudes and yields a slightly better agreement for most channels� Several experimental distributionsshow an obvious shift on the x�axis� For instance the distribution for channel - starts approximatelyat �pe instead of �pe� Reasons for this discrepancy may be due to a wrong determined pedestal during


Exp.Data

Dada MC

[PE]

P(PE

)

OM 3Exp.Data

Dada MC

[PE]

P(PE

)

OM 6

10-5

10-4

10-3

10-2

10-1

1

0 50 100 15010

-5

10-4

10-3

10-2

10-1

1

0 50 100 150

Figure �� Amplitude distributions for channel ! and ! of string !�� The distributions are normalised on thenumber of hits in the OM� Each point represents a bin width of pe�

Exp.Data

Dada MC

[PE]

P(PE

)

OM 6Exp.Data

Dada MC

[PE]

P(PE

)

OM 6

10-5

10-4

10-3

10-2

10-1

1

0 50 100 1500

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 20 40

Figure �� Corrected amplitude distribution of channel ! in comparison to simulated data� The distributionsare shown in a logarithmic and a linear plot� Each point represents a bin width of pe�

the calibration procedure �see section �� and a di�erent sensitivity of a speci�c OM compared tothe simulated standard OM�

A simple correction is applied to the data� The horizontal scale is multiplied with a correction factor�� The normalisation is changed according to the changed bin�width� The resulting distribution ismoved horizontally by the shift �� This achieves a good description of the shape and the pedestal of thedistributions for all channels� Though the distributions are independently normalized also the absolute


λ (Dada)

λ (B

aika

l MC

)

ε (Dada)

ε (B

aika

l MC

)0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

0.4 0.6 0.8 1 1.2 1.4-4

-3

-2

-1

0

1

2

3

4

-4 -2 0 2 4

Figure �� Correlation between amplitude corrections between the Baikal and Dada Monte Carlo�

Run �� Dada � Run �� Baikal MC� Run �� Dada �OM � �pe� � �pe� � �pe��

Table �� Results for the correction of signal amplitudes�

vertical values are in good agreement� The result is shown for OM - in �gure �� This correctionwas applied to all channels for run -�� and run -�� in comparison with the Dada results and forrun - �� in comparison with the Baikal Monte Carlo� A good agreement is achieved for each channeland the correction factors are well reproduced between run -�� and -�� They are given in table��

An important aspect to identify probable errors in the simulation programs is the comparison of


corrections between Dada and the Baikal Monte Carlo� Figure �� shows the correlations betweenthe determined correction values� Both programs yield strongly correlated correction factors� Due tohigher signal amplitudes of the Baikal Monte Carlo program the correlation for � is shifted upwards�

For the interpretation of these results it is important to distinguish between � and �� Since the pedestal� is barely a�ected by simulation parameters� it seems to indicate errors during the calibration� Thescale parameter � may be attributed to both� errors in the simulation and in the calibration� This isdiscussed in the following�

The simulation of physical processes in the two programs is realized in completely independent ways�Other than the Dada program� the Baikal Monte Carlo treats individual sensitivities of the OMs�Despite of this� all channels show approximately the same correlation� Large errors in the determinationof the light attenuation may lead to larger or smaller signal amplitudes� but also to di�erent hitmultiplicities ��gure �� which agree in �rst for both programs and the experimental data� Acomparison of the individual hit probabilities� �gure �� shows no correlation to the correction factors�� This contradiction between the well reproduced hit probabilities and multiplicity compared to thepoorly reproduced shapes of the amplitude distributions may indicate that mostly calibration errorsare responsible for the � correction� with an additional contribution due to the individual quantume�ciencies� At least� it is possible to adjust experimental data and Monte�Carlo results on each other�

�� Time characteristics

The time characteristics of signals from atmospheric muons are shown in �gure �� A� shows thetime residuals� eq�� for all hits calculated from the generated tracks� In case of multiple muonsthe residual is calculated for the �rst track in the data �le� Opposite to single muons� which produce asharp peak with a tail due to hits attributed to secondary processes �see �gure �� a shoulder of hitsearlier than expected occurs� These hits are attributed to multiple muon events� The leading muonin a bundle is de�ned as the muon� which produces most hits in the detector� Additional muons mayhit channels earlier than expected from the leading muon� Both Monte Carlo programs show a goodagreement for the central peak and the shoulder at earlier times� but disagree for late hits� A secondcharacteristic quantity is the reduced ��t function� calculated in eq��C�� and shown in �B�� The��t function calculated for the generated tracks corresponds to the maximum reconstruction accuracyachievable via a pure ��t minimisation�

In a comparison with experimental data� the true track parameters are not available� Therefore onehas to use the track parameters of a reconstructed track� Due to the reconstruction method� whichminimises the ��t function assuming symmetric Gaussian errors �see section C�� the resulting timeresiduals become also more Gaussian ��gure �� C�� The reconstructed residuals are in agreementbetween both Monte Carlos and the experimental data� The Dada residuals are peaked slightlystronger� which may be attributed to the di�erent reconstruction program� For large time di�erencesone observes a larger discrepancy between experimental data and both Monte Carlo calculations� �D�shows the reduced ��t calculated from the reconstructed tracks�

The time di�erences measured between two OMs is an additional experimentally accessible quantity�The time di�erences for selected OMs of string -� are plotted in �gure �� for run -�� The measureddistributions are generally met by those simulated� but especially for the �rst OMs in string -� and-� the measured distribution is wider than that simulated� The experimentally observed distributions�though statistically signi�cant� show a shape which is not �at but shows a distinct structure� Thissuggests a systematic time uncertainty� which occurs during signal processing� As shown in �gure��the reconstruction is not strongly a�ected by this discrepancy�

For the interpretation of the discrepancies between the simulation and experimental data one has toconsider additional e�ects such as scattering of light in the water� calibration errors and the time jitter


(A) Δtgen [ns]

NH

it

Dada MC

Baikal MC

(B) χ2gen/NHit

entr

y

Dada MC

Baikal MC

(C) Δtrec [ns]

NH

it

Exp.Data

Dada MC

Baikal MC

(D) χ2rec/NHit

entr

y

Exp.DataDada MC

Baikal MC

10-4

10-3

10-2

10-1

1

-50 -25 0 25 5010

-4

10-3

10-2

10-1

0 5 10

10-2

10-1

0 1

10-4

10-3

10-2

10-1

1

-50 -25 0 25 5010

-5

10-4

10-3

10-2

10-1

0 5 10

10-2

10-1

0 1

Figure �� Time residuals and time�� for atmospheric muons� �A� shows the time residuals for the generatedmuons� �B� shows the reduced time ��values for the generated muons� �C� shows the time residualsfor the reconstructed tracks� �D� shows the reduced time ��values for the reconstructed tracks� Thedistributions are normalized on the number of triggered events �� The experimental data and theBaikal MC data are reconstructed with the the standard Baikal reconstruction ��# the Dada MCdata is reconstructed with the recoos program �see appendix C�� No quality cuts are applied to thedata and the �t results�

of the OMs�

�� Vertical muon intensity

The vertical muon intensity Iv �eq�� can be measured using the experimental counting ratesRTrig� given by

RTrig #J�

Aeff�T rig��

The total �ux J� is de�ned in eq�� and the e�ective area Aeff�T rig is calculated for the angularand energy distribution of atmospheric muons with the same trigger level as the experimental data�


Exp.DataDada MC

Δt [ns]

P Hit

/ 5 n

s

Ch 2 (str 2) - Ch 1 (str 2)

Δt [ns]

P Hit

/ 5 n

s

Ch 3 (str 2) - Ch 1 (str 2)

Δt [ns]

P Hit

/ 5 n

s

Ch 4 (str 2) - Ch 1 (str 2)

Δt [ns]

P Hit

/ 5 n

s

Ch 5 (str 2) - Ch 1 (str 2)

Δt [ns]

P Hit

/ 5 n

s

Ch 6 (str 2) - Ch 1 (str 2)

Δt [ns]

P Hit

/ 5 n

s

Ch 1 (str 3) - Ch 1 (str 2)

0

0.02

0.04

-100 -50 0 50 1000

0.01

0.02

0.03

-50 0 50 100

0

0.01

0.02

-50 0 50 1000

0.005

0.01

0.015

0.02

0.025

-50 0 50 100 150

0

0.005

0.01

0.015

0.02

0 50 100 1500

0.005

0.01

0.015

-100 -50 0 50 100

Figure �� Time di�erences between channels along string !� and between the �rst channels in string !� and!�

Evaluation gives

Iv #RTrig

� Aeff�T rig

Zf�� sin �d� �z �

��K�

��

The integral K� is calculated from the angular distribution of generated tracks� It&s averaged value�� does not change signi�cantly for the two simulated depths ��m and ��

The value for Iv is calculated for both detector con�gurations NT�� run �� NT�� run �� andthe simulation for both depths� Figure �� shows the results for di�erent trigger levels� The resultsare stable and give an averaged value Iv # �� cm��s��sr�� with an estimated error of �"� dueto �uctuations in �gure �� systematic errors in the angular and energy distribution of atmosphericmuons and the determination of Aeff �

Figure �� shows the results in comparison with other experiments and an independent analysis ofthe BAIKAL experiment ��


NCH

Ver

tical

Muo

n In

tens

ity [1

0-6cm

-2s-1

sr-1 ]

Run 145/ MC 1070m

Run 196/ MC 1070m

Run 145/ MC 1170m

Run 196/ MC 1170m

Average

Average (All)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

4 6 8 10 12 14 16

Figure �� Calculation of vertical muon intensity� The calculated values are plotted for di�erent runs and simu�lated depths versus the minimum required hit channels� A general trigger of � hit strings is set� Theresults are averaged�

depth [m]

vert

ical

inte

nsity

[cm

-2s-1

sr-1

]

This Work (BAIKAL NT-36)

BAIKAL NT-36, prelim.

BAIKAL NT-14

DUMAND I

Higashi

Davitaev

Vavilov

Fyodorov

Bugaev-Naumov

10-9

10-8

10-7

10-6

10-5

10-4

10-3

0 1000 2000 3000 4000 5000 6000

Figure �� Vertical muon intensity as measured by the NT� experiment in comparison with other underwaterexperiments �� adapted from �� The solid line corresponds to the parameterization byBugaev et�al��


�� Ocean background

After the installation of the �rst string of DUMAND II in December �� the counting rate of ��operating OMs� �� JOM and one EOM have been measured until the string controller failed due to awater leak� The sampled counting rates approximately cover a real time of �� hours �see �gure ��The measured counting rates are shown and their characteristics are analysed in �� The EOM showsa high but decreasing counting rate due to the previous exposure to intense sun�light and the recentswitch on of the power�supply� Therefore it will not be regarded in the following discussions�

OM

Rat

e [k

Hz]

Measured rateCorrected rate

0

20

40

60

80

100

120

140

0 5 10 15 20 25

Figure �� Measured and corrected count rates during the December � DUMAND II deployment�

The JOMs were operated with high voltage approximately ��V below the nominal value� Becauseof the smaller gain and thus reduced detection e�ciency for �pe signals� the measured ��K countingrate is reduced� In order to obtain the true rate of ��K signals a correction has to be applied to themeasured counting rates� The following approach involves large uncertainties� and results have to beregarded with caution*No laboratory measurements of the dark noise rate of the OMs and its �pe detection e�ciency areavailable for the lowered HV� The noise rate N� is only known for the nominal high voltage� Thereduction of the detection e�ciency �� was measured for a ��V reduced HV� The detection e�ciencyat the nominal operating voltage � is typically ��"� The measured values for �� are between �" and��"� The detection e�ciency is expected to decrease more strongly for a further lowered HV and isthus assumed to �� The dark noise rate is expected to decrease even more and is thusassumed �noise�� The �rst step is to subtract the dark noise rate of each PMT from the measured rate R� in the ocean�The rate )R� corrected for the dark noise� is assumed

)Ri � R��i �N��i � �� i� �In the next step the rates )Ri have to be corrected for the reduced detection e�ciencies and thethe detection e�ciency at the nominal operational voltage� The true rate of ��K signals Rcor isapproximated by

Rcor�i #)Ri

� � �� i� �

�� Ocean background ��

Figure �� shows the results of the correction� Typical ��K rates are of the order of ��kHz� Theerrors�bars depend mainly on the systematic errors of the above assumptions� It has to be noted� thatno dead time correction is applied�

Theoretical expectations are calculated according to the method described in section �� and appendixC�� using the wavelength dependent parameterization eq�� by J�Learned for the calculation of thelight attenuation� ��K decays in a spherical shell with the radius r around an OM contribute to thetotal counting rate Itot with the rate R�r�dr� The total rate is given by Itot # I�� with the integralcount rate I�d� de�ned as

I�d� #

Z d

�R�r�dr ��

The simulation results for I�d� are shown in �gure �� for di�erent attenuation lengths and the productof the collection e�ciency and peak quantum e�ciency � # ��

d [m]

I(d)

[kH

z]

X0 = 60m

X0 = 50m

X0 = 40m

X0 = 30m

X0 = 25m

X0 = 20m

0

20

40

60

80

100

120

140

160

0 50 100 150 200 250 300 350

Figure �� Integrated ��K count�rate I�d� for di�erent attenuation lengths X�� Simulated is a JOM using apeak quantum e�ciency times collection e�ciency � ��

X� �m� �� kHz� �� Itot��pe�kHz� �� Itot��pe�kHz� �� Itot��pe�kHz� �� Itot��pe�kHz� ��

Table �� Fit results for I�d� and simulated total ��K rates ��

A simple function

R�r� # � � r� � � � exp�� r

X�

��


X0 [m]

I tot [

kHz]

Itot [kHz] = -1.27933

+ 1.75508*X0

+ 0.016177*X02

κ = 0.15

κ

I tot [

kHz]

Itot [kHz] = 0.288487 + 632.911*κ

X0 = 40m

0

20

40

60

80

100

120

140

160

180

200

0 20 40 600

20

40

60

80

100

120

140

160

0 0.1 0.2

�A� �B�

Figure �� Total ��K signal rate as a function of the attenuation length X� �A� and as a function of the quantumtimes collection e�ciency of the photo�cathode � �B�� The values are �tted with Polynomials of �stand �nd order�

with the two parameters �� and the attenuation length X� is assumed for a parameterization�Evaluation of eq�� yields

I�d� #� � � �X�

��X�

� � �� d� � �X�� X� � � � d� � exp�� d

X��

��

The total rate is given by

Itot # � � � ��X�

�

��

The function I�d� is �tted to the simulated rates in �gure �� Table �� gives the results for the �tparameters as well as the calculated total signal rate Itot above � � � � �pe� The parameterization doesnot give an accurate description of the shape but yields good values for Itot� The attenuation lengthstrongly a�ects the total counting rate� It is important to note� that especially for large attenuationlengths the dominant contribution to the signal rate is due to decays far from the OM� For X� # ��mthe region ��m from the OM still contributes more than �kHz to the total rate� This is di�erent forlarger signals� About ��" of signals larger �pe originate from a distance closer than �m to the OM�Figure �� shows the dependence of the total ��K signal rate from the sensitivity of the cathode�B� and the attenuation length �A�� The dependence on the attenuation is �tted with a second orderPolynomial� The dependence on � is linear�

A comparison with the experimental rates of typically ��kHz gives a typical value of � # �� forX� # ��m and � # �� for X� # ��m� Hamamatsu published a value for the peak quantum e�ciencyof ��" �� This corresponds to a collection e�ciency of �" and ��" averaged over the cathodearea�The ��K counting rate is measured with high accuracy in a neutrino telescope under permanentoperation� The attenuation length can be well measured for a known cathode sensitivity� Howeverfor an OM with good energy resolution� capable of discriminating �pe and more pe� it is possible toestimate both� the attenuation and the cathode sensitivity� As mentioned above� the counting rate

�� Ocean background ��

Itot,1PE [kHz]

I tot,2

PE [k

Hz]

0.12

0.15

0.18

20m

30m40m 50m 60m

X0

κ

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 25 50 75 100 125 150 175 200

Figure �� Counting rate for ��K signals above a threshold of pe �Itot��pe� and above �pe �Itot��pe� for di�erentvalues the attenuation length X� and collection times quantum e�ciency �� Points of constant � areconnected with solid lines� points of constant X� with dashed lines�

above �pe originates mainly from distances �m and is only marginally a�ected by the attenuation�see table �� The two measured values of �Itot��pe� and �Itot��pe� de�ne a point in a two dimensionalspace�� which corresponds to certain values of the attenuation length X� and cathode sensitivity ��This is shown in �gure �� Background to this measurement comes from the dark noise of the OM and random coincident signalsof two independent ��K decays� The second can be calculated from the dead�time of the OM and theabsolute �pe counting rate� In case of the dark noise the situation is more complicated and requires agood calibration of the single and multi�pe dark noise rate of the OM� The thermal emission of photo�electrons from the cathode contributes only to the �pe rate and depends only on the temperature�E�ects� such as decays of ��K in the glass of the pressure housing and the PMT� provide a constantrate of additional dark noise pulses� which have often multi�pe amplitudes� A third contribution ofpulses with �pe and multi�pe energies is connected to the ionization of residual gas in the PMT byphotoelectrons �after�pulses�� This rate depends on the rate of all other signals�This measurement may yield an accuracy of the order of �m for the absolute value of the attenuationlength X�� For a telescope under permanent operation this method is extremely sensitive for smallrelative changes of the water transparency� This can be thus monitored online with high accuracy�Using additional information� e�g� from Laser calibrations� improves the accuracy of the absolutemeasurement�As an application for ocean and environmental science a system consisting out of a single OM can bedesigned to operate remotely and to measure continuously changes of the water transparency� TheEOM is capable of separating �pe� �pe and higher pe signals �see �gures B��B�� Unfortunatelydue to the previous exposure to sun light� the operating EOM of December �� still showed too highcount rates during the short time of detector operation�

�The �K rates � � �� are still of the order of ��Hz above �pe and ��Hz above �pe� These rates can be usedindependently or alternatively to check the results�

�� SUMMARY AND CONCLUSIONS

Summary and Conclusions

Damit ist dann die Br�ucke vom Mikrokosmos zum Makrokosmos geschlagen� Angesichts ihrergewaltigen Spannweite und angesichts der Winzigkeit unserer menschlichen Ma#st�abe im Ver�gleich dazu emp�ndet man einen An�ug von Unwirklichkeit�

Ch�Spiering in ��

This work investigates fundamental aspects for the design and operation of deep underwater water�Cerenkov detectors� which aim at the detection of muons induced by cosmic neutrinos� It thus coversmethodical� hardware and software issues� Focus is put on the BAIKAL and the DUMAND experiments�but results may be applied to similar experiments like AMANDA � NESTOR or next generation detectors�

Two main technical developments have been achieved during this work�First is the design� construction and calibration of an optical sensor� the European Optical Module�EOM�� for the DUMAND II experiment�Secondly a new detector simulation program� Dada � based on the GEANT detector simulation

library was written� This program is embedded in a general modular frame for the analysis of neutrinotelescope data� the SiEGMuND software�

Following items are discussed�

A review of the production mechanisms of high energy cosmic neutrinos and a discussion ofcandidate objects for possible neutrino sources is given� A methodical discussion of the detectionmethods shows� that next generation experiments may detect a large variety of sources and thusopen a new observational window to the universe� The prototype experiments currently underconstruction will improve upper limits on neutrino �uxes by two orders of magnitude� Theexperimental detection of a few neutrino sources and the measurement of di�use extra�galacticneutrinos from the cores of active galaxies is already possible at this stage� Additional aspectssuch as the search for atmospheric neutrino oscillations or the annihilation of super�symmetricdark matter particles in the sun may lead to results signi�cant to elementary particle physicsand cosmology�

Current stage experiments� especially BAIKAL and DUMAND II � are discussed with emphasis puton the general design� calibration and signal processing� It is found� that the optical propertiesof deep water� especially light attenuation� strongly determine the mean visual range of opticalsensors and thus the detection capability and design of neutrino telescopes�

The European Optical Module �EOM� is designed as a self�contained optical sensor for faintlight embedded in a glass pressure housing� It is equipped with the large area photomultiplierPhilips XP�� a fast read�out for the charge integration of photomultiplier signals and aremote computer system for the survey of the module parameters and communication to anexternal host� The photomultiplier is constructed according to a new technology and providesadvanced characteristics for the time and energy resolution�

The EOM was designed during this work and �� modules have been produced� The integrationof the new type photomultiplier required measurements of characteristic parameters and thedevelopment of a special charge integrating circuit DMQT� Measurements and simulationsshow� that a linear charge to time conversion sliding over to a logarithmic dependency yieldsthe best performance for the EOM� The properties of the produced EOMs are investigated andcalibrated� covering mainly sensitivity and characteristics of the time and amplitude response�It is found� that the calibration of time and amplitude characteristics is mostly described by twoanalytical functions� which are �tted to the data from test measurements�

��

Secondary particles from neutrino interactions� mainly muons� electrons and hadrons� lead tothe emission of �Cerenkov light� which is measured by optical sensors� The propagation of theseparticles involves several di�erent physical energy loss mechanisms and leads to the production offurther secondary particles along a muon�track� an electro�magnetic or a hadronic cascade� Thesesecondary processes are simulated with the GEANT library and visualised� The characteristicsof �Cerenkov light from muons and cascades are analysed and parameterized� A transformationmethod� which allows the calculation of the angular distribution of the �Cerenkov light fromcascades from the angular distribution of tracks in the cascade� is developed� The simulationof cascades shows� that the approximation of a point�like source of light gives only a roughdescription of the arrival times of photons at the optical sensors in a detector�

The application of the GEANT library to a deep underwater �Cerenkov detector involves a largeamount of required CPU time due to low tracking thresholds � ��keV and an extremely largedetector volume� Parameterizations for the �Cerenkov light from muons and cascades are imple�mented in the Dada program� This drastically improves the execution speed and enables a massproduction of muon events�

Simulations of muons in the BAIKAL NT�� detector are presented� Secondary processes oc�curing during muon propagation a�ect the amplitude and arrival time of registered �Cerenkovsignals as well the number of hit optical sensors� The results of the simulations show� that thedominant process producing larger signal amplitudes and hit multiplicities is connected to pairproduction and bremsstrahlung� These two processes also dominate the di�erences of the arrivaltime distributions of detected light signals in comparison to distributions expected from minimalionising muons� Light due to pair�production mainly increases the signal amplitudes at the meanexpected arrival time� A tail of signals arriving at later times than expected is almost entirelyconnected to bremsstrahlung events� The simulations with muons of di�erent energies indicatethat a separation of muons with energies above typically �TeV is possible via an analysis ofthe hit multiplicities� An improved topological analysis of the track kinematics� signal ampli�tudes and hit multiplicities should give better results� The e�ective area for several stages of theBAIKAL experiment is calculated versus the energy of single isotropic muons�

The maximum achievable angular resolution of a neutrino telescope is not only limited by thereconstruction accuracy but also by the pointing�accuracy of the neutrino induced muon� Thisaccuracy is mostly limited by the deviation of the muon direction from the initial neutrinodirection due to the interaction� Additional recoiling e�ects due to secondary processes a�ectthe muon direction� The recoiling e�ects are found to produce scattering angles in the order of�� to �� depending on the muon energy and the covered distance of the muon�

Though the usage of two optical sensors in a local time coincidence reduces the e�ective detectorarea for triggered muon events� a less stringent detector trigger condition may be used� whichagain enlarges the e�ective area� The simulations show� that the time signature of registered�Cerenkov signals is strongly improved for a local coincidence� especially under the presence of ahigh noise rate� This allows the usage of a more simple and less robust reconstruction method�

A comparison of simulated atmospheric muons to experimental data from the BAIKAL NT�� detector shows an overall good agreement� Discrepancies for the hit e�ciencies� individual signalamplitudes and response times may be accounted to the neglection of individual optical sensorproperties in the simulation and calibration errors of the data� The application of a plausi�ble correction to the amplitudes in the experimental data or simulated data gives an excellentagreement�

�� SUMMARY AND CONCLUSIONS

The BAIKAL NT�� detector �� achieves an e�ective area for atmospheric muons of approx�imately ��m� for �� and ��m� for � operating channels� The vertical muon intensity at adepth of ��m is measured to � �� cm�� s�� sr��

Apart of �Cerenkov light from cosmic rays also ambient sources of light like bioluminescenceand natural radioactivity are detected in deep underwater �Cerenkov detectors� Monitoring andanalysis of these light signals may provides important information on these processes such asstudies on the populations of light emitting species and the long�term variations of these sources�

A general method to calculate signal rates for uniformly distributed faint sources of light isderived� It is used for the calculation of expected signal rates due decays of ��K� the dominantradioactive isotope in the ocean� as a function of the light attenuation and the sensitivity of theoptical sensor�

A comparison of experimentally measured counting rates in DUMAND is presented and gives anindirect measurement of the sensitivity of the involved optical sensors� Using an optical sensorwith a good amplitude resolution allows to measure both the optical attenuation length and thesensitivity of the optical sensor by the comparison of signal counting rates of certain amplitudes�This method is extremely sensitive to changes of the attenuation and the sensitivity� It providesthus an in�situ method for on�line monitoring� Already a single optical sensor provides a self�contained detector� which may be autonomously installed at remote underwater locations tomeasure variations of the water transparency�

��

A Additional calculations

A�� Transformation from a track to a �Cerenkov light distribution

The purpose of the following calculation is the transformation from a given angular track�length distri�bution dl�d� into the resulting angular �Cerenkov light distribution dn�d�� The angular track lengthdistribution is calculated during the tracking of an initial particle and its secondaries� dl�d� is de�nedas the distribution of the length of track pieces li with a directional angle � to the direction of the initialparticle �de�ned as �z��axis� �see eq�� The idea is to summarize all fractions of �Cerenkov cones�which contribute to a photon �ux into the direction � over all angles �� The geometry is sketchedin �gure A�� For each direction � of a track in a shower� the �Cerenkov cone is divided in fractionsds� which point into di�erent directions �� The angular distribution of �Cerenkov photons emitted intodirection � is

dn

d�#

Z

�d� � n� � dl

d�

Z �max��

�min��d� � �

S� ds��

d��A��

n� is the number of �Cerenkov photons per unit track�length� S is the total length of the rim andds�d� is the fraction of the rim of the �Cerenkov cone� which points into the zenithal direction �� It isproportional to the number of photons emitted into this direction� The integration boundaries �max

and �min depend on the possible directions of the �Cerenkov light in respect of ��

Figure A�� shows the geometry used to calculate ds�� for two angles �� The length of the outerneck F is normalised to F � �� Thus one �nds

S # � � � cos+c with +c � �Cerenkov angle�A��

and�

S� ds��

d�#

�

� d0d�

��A��

In order to calculate 0�� a triangle is drawn into �gure A�� The cosine�law gives

cos0 #b� � c� � a�

�bc��A��

From the �gure one obtains

c # cos+c � tan� � b # sin+c � a #

qd� � v� �

and

d # sin� � v # ju� wj � u # cos� � w #cos+c

cos��

Evaluating the above gives

cos0 #cot +c

sin��

cos�

cos+c� cos�

��A��

Tracks with � # � emit �Cerenkov light only into the direction � # +c� For this case eq��A�� divergesexcept for � # +c� If the �Cerenkov cone does not hit the �z��axis �� +c� � � +c�� the angles�min� �max are given by

�min # j��+cj ��max # ��+c �

�A��

Except for � � �+c��

�max # � � ��+c �

�� A ADDITIONAL CALCULATIONS

li

li

c

(z) (z)

c

(B)

(C) (D)

(A)

(z)

(z)

α

Θ

Ψ

α

Ψ

ϑ

ϑ

ΨΨ

d

u

cb

ds

w

v

a

bc

b

a

c

a c

d

w

v

u

b

ds

S

S S

S

dsds a

F

F

Θ

Figure A�� Geometry used for the calculation of the e�ective �Cerenkov light distribution �A�� Geometry for a�Cerenkov cone in forward direction� �B�� Geometry for a �Cerenkov cone distinct from the �z� axis��C� and �D�� The triangle used in the calculation projected onto the plane of the �Cerenkov cone�Directions as in �A� and �B��

For a calculation with discrete values ni one has to replace

dn

d� ni

$�i#

ni �K

with the total number of bins K� The calculation may be sketched as follows� The initial distributionforms a histogram with discrete values li� �i� For each value i� �i the angles �min� �max are calculated�Derived from the binning of the target histogram dni�d�i the angles 0l and 0k are calculated from theupper and lower borders of each histogram bin �i within �min� �max� The integrand from eq��A��is given by

�

S

�$s��

$�

i#

0l �0k

� li �

A� Timing and amplitude for minimal ionizing tracks ��

For a point like light source the photon �ux per unit area on a sphere dn�d( is given by

dn

d(#

�

r�� dn

d� d�cos��A��

with the radius r and the azimuthal angle �� Due to azimuthal symmetry one gets

dn

d(#

�

� r� � sin� �dn

d��A��

A�� Timing and amplitude for minimal ionizing tracks

For a given locatation of an optical sensor��

OM and the track parameters �the vertex �V �this can beany point on the trajetory� and the momentum vector �p� it is possible to calculate the time of a hitand the amplitude of the �Cerenkov signal� The geometry is sketched in �gure A��

c

Muon

V

V

R=

-

OM

OM

c

R

θ

R0

Muon

dd 0

θ

αa

b

c

d

L

(z)

(x)

(y)

d

Λ

A� B�

Figure A�� Geometry for a minimal ionizing track� �A� Expected time� �B� Photon �ux calculation�

Time of Hit

Using the distance �R ��

OM ��V between the vertex �V and the OM one gets the angle �

cos� #�p � �Rj�pj � j�Rj ��A��


The perpendicular distance of closest aproach d� is given by

d� # R � sin� # d � sin+c ��A��

The time of hit� relative to the time t� �at the vertex� is given by

t� t� #�

cvac� �a� d � n� # �

cvac� �L� c� #

�

cvac� �a� b� c� ��A��

with the index of refraction n and the speed of light cvac� One �nds the identities

a� b # L � c #d

cos+c� b � b # d � cos+c � d #

R � sin�sin+c

� L # R � cos� �

Photon �ux

The resulting photon density �� hitting the OM is

�� #��d� �N�

Atot��A��

��d� represents the photon attenuation �see section �� N� is the number of photons emitted fromthe part of track� which hits the OM� Atot is the area which is populated by these photons �see also�gure ��B�� Therfore

N� # 1 � n��A��

with n� the number of photons generated per unit tracklength �n� � �� m�� and

1 #� �R�

sin+c�A��

with R� the area of the OM� The area Atot is given by

Atot # � � d sin+c � �R� ��A��

Evaluation of eq��A�� gives

��d� #��d� � n�

� � d � sin�+c��A��

If the length � of a �Cerenkov radiating track is shorter than 1 the photon �ux eq��A�� has to bemultiplied with a relative tracklength L given by

L #�

1#� � sin+c

� �R��A��

For non relativistic �� the �Cerenkov photon yield becomes smaller �eq��

L #� � sin+c

� �R��sin+c

sin+�c

��A��

with +�c the �Cerenkov angle for � # � and +c calculated from eq��

Amplitude

The mean amplitude m of an optical module is calculated from the photon �ux and with projectedsensor area AOM �� and its sensitivity �

m�d� # ��d� � AOM�� A��

A� Time and amplitude for spherical and plane waves ��

In case of a photocathode the amplitude is measured in units pe! � becomes the quantum e�ciencytimes the collection e�ciency �� The projected area of the OM is

AOM � � R�� A��

�� is the relative angular e�ciency of the OM� depending on the angle � between the incident lightand the orientation of the OM� The angle � is given by

cos � # �� d � �ezd

#

��dz�d for up�looking OM�dz�d for down�looking OM

��A��

� � �R� � �ez de�nes the orientation of the OM in detector coordinates� �� for up�looking and �� fordown�looking OM�

If the length � of the �Cerenkov radiating track is shorter than 1 the amplitude depends on the positionof the photons hitting onto the surface of the sensor� The average amplitude may be approximated by�see eq��A��

m � �� AOM � � � L ��A��

A�� Time and amplitude for spherical and plane waves

α

1α

d

1

2α

d

N

D

(B)(A)

2R

1R

φβ

αD

Figure A�� Geometry for a spherical �A� and a plane wave �B��

The spherical geometry is an important case for point�like sources of light �see �gure A�� A��The time of arrival at each optical module OMi is given by

ti #j�Rij � ncvac

�A��

relative to the initial time at the vertex� The time di�erence between two OMs is given by

$t #D � ncvac

��A��


withD # j�R�j � j�R�j ��A��

To express the distance D via the two polar angles �� one may use the sine�law

R� # d � sin�sin�

R� # d � sin��sin�

�A��

Evaluating the angles �� in �� and �� gives

D # d � sin�� sin��sin��

# d � � � cos ��

�sin

��

sin�� A��

The plane wave ��gure A�� B�� is the special case of a spherical wave� when the light source is locatedat in�nite distance or �� # �� # �� Using the normal vector �N of the plane one gets

$t #�N � �dd

� n

cvac# cos� � n

d � cvac ��A��

The photon �ux �� for a point�source at the distance r and the angle � is given by

��r� �� #�

r�� r� � I�� A��

��r� is the attenuation and I�� the relative angular intensity of the light emission�R�� I�� sin� d�

is normalised to �� One may de�ne the relative track�length L representing the relative number ofminimal ionising tracks producing the same amount of light at the distance r �see appendix A��

L #� � � sin�+c

n� � r � ��

��A��

A�� The cumulative Poisson probability

Several calculations require the space integration of a function P � which gives the probability to producea signal above an amplitude A� Assuming a Poisson�like probability for a signal with a mean amplitude m the cumulative Poisson probability to produce a signal above the amplitude A is

P m� A� #Xi�A

mi � e� m

i# G� m�A� ��A��

with the Incomplete Gamma�function G� The Incomplete Gamma�function is de�ned by

G� m�A� � �

'�A�

Z m

�e�t � tA�� dt �A �� A��

with the gamma function

'�A� #

Z

�tA�� e�t � dt

��

��

B EOM test and calibration measurements

During the construction phase of the EOMs a larger sample� of Philips XP� �� PMTs have been tested�Table B�� gives a summary of the measured PMTs� Serial numbers below � have been produced inEindhoven �Netherlands�� the rest in Brive �France��

Number Remarks

- �� EOM delivered ��- �� EOM delivered ��- � EOM delivered �� JULIA OM�- � EOM delivered �� lost Dec�� JULIA OM�- �� PMT accidently damaged during assembly� �JULIA OM�- �� EOM delivered �� EOM prototype Jan��- �� EOM delivered �� lost Aug��- �� EOM delivered �� year operation in Lake Baikal� ��- �� EOM delivered ��- � EOM delivered ��- �� EOM delivered �� lost Sep��- �� EOM delivered ��

Table B�� List of measured photomultipliers XP� ��

B�� Point sensitivity

The relative sensitivity of �� photomultipliers has been measured with a blue LED directly attached tothe surface� The measurement was done for �� measurement points� spread in a grid� approximately�� distant from each other� Each measurement point represents the same cathode area� In orderto achieve this� two zenith angles �x� �y� which represent a Cartesian grid on the spherical PMTsurface� were de�ned� Each point was measured twice with opposite directions in respect to themagnetic �eld� Both measurements are combined by calculation of the average and di�erence values�No measurements were done with zenith angles larger than �� The LED was adjusted to a highintensity � ��pe� for which the PMT still works linearly� Energy distributions have been measuredwith a charge sensitive ADC �LeCroy ��A�� The mean of the energy distribution minus the pedestalof the ADC is proportional to the sensitivity� The sensitivity of the central point ��x # �y # �� wasnormalised to �� Several control measurements of the ADC pedestal and the sensitivity of the centralreference point are done in order to check the stability of the measurement�

Figures B�� and B�� show the result of the measurements� plotted as contour levels of the relativesensitivity� Di�erent shades correspond to a change of ��"� The exact location of each measure pointis indicated by a �� Since no measurement has been done for a zenith angle larger than �� thecorresponding sensitivity is set to to �� Earlier measurements showed that the sensitive area extendsto more than ��

Except for PMT - �� all photomultipliers show a high sensitivity up to �x�y # �� which is usuallyuniform� Good are -�� -�� and - �� Two photomultiplier �- �� - �� show a ��" decreasedsensitivity on one side� These PMTs also show a weak dependency on the earth magnetic �eld in theorder of � ��" visible by the di�erence of the two measurements at each point�

�Three additional testet PMTs are not considered in this discussion� $�� did not �t into the glass housing� $�showed a too high noise rate and a ghost peak at high pe energies� $� had larger insensitive cathode areas�

�� B EOM TEST AND CALIBRATION MEASUREMENTS

-100

-75

-50

-25

0

25

50

75

100

-100 -75 -50 -25 0 25 50 75 100

θx [deg]

θy

[deg

]

11

-100

-75

-50

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0

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θx [deg] θ

y [d

eg]

12

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-100 -75 -50 -25 0 25 50 75 100

16

θx [deg]

θy

[deg

]

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-100 -75 -50 -25 0 25 50 75 100

19

θx [deg]

θy

[deg

]

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0

25

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100

-100 -75 -50 -25 0 25 50 75 100

22

θx [deg]

θy

[deg

]

-100

-75

-50

-25

0

25

50

75

100

-100 -75 -50 -25 0 25 50 75 100

27

θx [deg]

θy

[deg

]

Figure B�� Relative sensitivity for point illumination�

B� Point sensitivity ��

-100

-75

-50

-25

0

25

50

75

100

-100 -75 -50 -25 0 25 50 75 100

33

θx [deg]

θy

[deg

]

-100

-75

-50

-25

0

25

50

75

100

-100 -75 -50 -25 0 25 50 75 100

35

θx [deg] θ

y [d

eg]

-100

-75

-50

-25

0

25

50

75

100

-100 -75 -50 -25 0 25 50 75 100

44

θx [deg]

θy

[deg

]

-100

-75

-50

-25

0

25

50

75

100

-100 -75 -50 -25 0 25 50 75 100

46

θx [deg]

θy

[deg

]

-100

-75

-50

-25

0

25

50

75

100

-100 -75 -50 -25 0 25 50 75 100

52

θx [deg]

θy

[deg

]

-100

-75

-50

-25

0

25

50

75

100

-100 -75 -50 -25 0 25 50 75 100

53

θx [deg]

θy

[deg

]

Figure B�� Relative sensitivity for point illumination�


Some PMTs show a dip at certain points �e�g� -�� -�� -�� and -�� It was discovered after themeasurement� that these points agree with the small contact stripes� which supply the cathode withthe high voltage�If one summarises the relative sensitivities over all points

S #

��Xi��

Si

��B��

one gets a characteristic quantity for the e�ective sensitive cathode area relative to the absolute sen�sitivity of the centre point� The results are summarised in the table B��

- ��

S�"� ��

Table B�� E�ective sensitive cathode area� relative to the absolute sensitivity of the cathode centre�

In a separate measurement the LED was switched to a low intensity and distributions of the integratedcharge have been measured for di�erent zenith angles� Examination of the position of the �pe peakyields an estimation of the stability of the gain for di�erent zenith angles� The position of this peakwas found to be constant except for PMT -�� and -�� which show a shift of about ��" for certainzenith angles�

B�� Amplitude and time response

Figure B�� shows energy distributions of EOM -�� for di�erent light intensities� The relative heightof the contributions from di�erent photoelectrons changes according to a Poisson distribution� Theamplitude function� eq�� is �tted to the distributions� It shows a good description of the linear�but gives only a rough estimate of the logarithmic region of the read�out� The �t parameter nlog is notconstant for very high intensities�

EOM No� x� �� c� c� nlog xlog $E�E �FWHM�- �ns� �ns� �ns� �ns� �PE� �ns� �"�

��

Table B�� Results of the EOM energy calibration with the �amplitude function�

B� Amplitude and time response ��

IDEntriesMeanRMS

19021 40050

228.1 234.4

630.0 / 234P1 1.191 0.1041E-01P2 189.3 1.015P3 43.16 0.2521P4 26.84 1.106P5 0.1788E+06 1393.P6 3.894 0.6298E-01

Q-T [ns]

entr

y IDEntriesMeanRMS

19020 40060

509.4 304.6

522.9 / 273P1 2.614 0.1555E-01P2 191.4 1.163P3 48.29 0.4095P4 32.47 1.339P5 0.1936E+06 1039.P6 3.056 0.2988E-01

Q-T [ns]

entr

y

IDEntriesMeanRMS

19024 40056

583.1 308.9

546.9 / 272P1 3.120 0.1775E-01P2 187.6 1.227P3 47.20 0.4406P4 34.83 1.443P5 0.1936E+06 1019.P6 3.042 0.2741E-01

Q-T [ns]

entr

y IDEntriesMeanRMS

19022 40039

656.4 306.9

660.3 / 275P1 3.585 0.2278E-01P2 190.0 1.499P3 49.54 0.6049P4 32.77 1.789P5 0.1941E+06 1010.P6 2.888 0.2713E-01

Q-T [ns]

entr

y

IDEntriesMeanRMS

19023 40022

796.4 290.6

857.3 / 275P1 4.611 0.3121E-01P2 192.4 2.069P3 50.29 0.9021P4 35.91 2.709P5 0.1936E+06 980.8P6 2.658 0.3091E-01

Q-T [ns]

entr

y IDEntriesMeanRMS

19025 40014

849.5 280.0

1117. / 274P1 5.071 0.4185E-01P2 197.3 3.007P3 54.05 1.380P4 32.85 3.925P5 0.1920E+06 966.2P6 2.506 0.3782E-01

Q-T [ns]

entr

y

0

200

400

600

500 10000

100

200

300

500 1000

0

100

200

300

500 10000

100

200

300

500 1000

0

100

200

300

400

500 10000

100

200

300

400

500 1000

Figure B�� Amplitude response of OM !�� for increasing light intensities� The �amplitude�function eq�� is �tted to the data� The �t parameters P�� P� P�� P�� P�� P� correspond to �m� c�� c�� anormalisation and nlog �

In order to achieve a calibration of the energy scale� this procedure has been performed for each OM�Table B�� shows the results of this calibration� Previously reported results in �� table �� require acorrection factor �� for all constants except for nlog� In addition some �t results have been improved�The �ts to OMs -�� -� and -�� show only a poor convergence� Therefore the results for these OMshave to be applied with care� Due to a weakness of the produced circuit boards the energy resolutionis less good than for the naked PMT�

Figure B�� shows time distributions for pulses of a certain energy� These distributions are �tted withthe timing function� eq�� yielding characteristic time constants� Fit results for all EOMs aregiven in table B��

�These OMs show a much better �t if one introduces the additional constant c� � �� of eq��


EntriesMeanRMS

7758 487.1 81.30

289.1 / 87P1 70.93P2 12.09P3 411.3P4 5193.

PE=0.6±0.3

transit time [0.1ns]

Ent

ry /

0.5n

s EntriesMeanRMS

10717 456.5 61.56

432.0 / 85P1 39.81P2 11.30P3 408.9P4 7525.

PE=1.2±0.3


Ent

ry /

0.5n

s

EntriesMeanRMS

12446 429.5 34.82

166.9 / 79P1 24.07P2 10.33P3 403.4P4 9544.

PE=2.3±0.4


Ent

ry /

0.5n

s EntriesMeanRMS

9233 413.7 21.06

61.32 / 53P1 15.32P2 8.939P3 397.9P4 7671.

PE=4±0.5


Ent

ry /

0.5n

s

EntriesMeanRMS

4636 407.1 16.54

39.62 / 35P1 12.56P2 8.312P3 394.6P4 3988.

PE=5.6±0.7


Ent

ry /

0.5n

s EntriesMeanRMS

663 405.8 19.56

18.69 / 23P1 11.98P2 7.822P3 392.7P4 577.4

PE=10±2.1


Ent

ry /

0.5n

s

0

200

400

600

200 400 600 8000

250

500

750

1000

200 400 600 800

0

500

1000

1500

200 400 600 8000

500

1000

1500

200 400 600 800

0

250

500

750

1000

200 400 600 8000

50

100

150

200 400 600 800

Figure B�� Transit time distributions for OM !�� The �timing�function eq�� is �tted to the data� The�t parameters P�� P� P�� P� correspond to � �� t� and a normalisation�

OM a�� a� b� b� c�� c� d� d� e� e� f� f��ns� �ns� �ns� �ns� �ns� �ns� �ns� �ns� �ns� �ns� �ns� �ns�

��

Table B�� Fitted parameters of the time response measurements� The values are averaged over the measuredzenith angles� OM �� was measured in full illumination with a fast laser�

B� Dark noise measurements ��

B�� Dark noise measurements

(A) pulse width [ns]

cou

nt r

ate

/1ns

[Hz]

HV = 1270 V

HV = 1320 V

HV = 1390 V

(B) pulse width [ns]

cou

nt r

ate

/1ns

[Hz]

TH = 130 mV

TH = 90 mV

(C) pulse width [ns]

cou

nt r

ate

/1ns

[Hz]

TH = 130 mV

TH = 180 mV

0

100

200

300

400

500

600

0 100 200 300 400

050

100150200250300350

0 200 400

050

100150200250300350

0 200 400

Figure B�� Dark noise for di�erent high voltage and thresholds measured with OM ! �� A� shows the energydistribution for three di�erent high voltages� �B� and �C� show the in�uences of a small and a largevalue of the high threshold in comparison with a moderate choice�

A major demand of the calibration procedure is the adjustment of the internal operational parameters�namely the high voltage of the small PMT and the two thresholds of the fast circuit� This can beexcellently performed using the energy distributions and counting rates of dark noise pulses� This isdemonstrated in �gure B�� The �gures show the energy distributions of dark noise pulses� which aremostly �pe signals due to thermionic emission at the photocathode� The sharp peak at ��ns is anartefact of the read�out and corresponds to the minimal conversion time� due to small signals �� pe��e�g� noise of the small PMT��A� shows the energy distribution for three di�erent high voltages� The thresholds have been adjustedin such a way� that the total counting rate stays constant� For a large high voltage ��V � the�pe peak becomes visible at large conversion times �� ns�� showing a shoulder on the left edge�� ns�� For a small high voltage ��V �� the peak �� ns� becomes non�Gaussian and theenergy resolution decreases due to non�linearities of the fast circuit and too short integration times� Agood choice combining a small conversion time together with a good energy resolution is seen for theHV ��V ! the shoulder at the left edge of the �pe peak is still visible�The high threshold has to be adjusted in such a way� that noise smaller �pe is e�ciently discriminatedbut signals of �pe� which have a small pulse�amplitude �in mV � are not rejected� �B� shows a moderatechoice of ��mV and a smaller value ��mV � The smaller threshold gives no improved e�ciency for�pe signals but signi�cantly rises the counting rate of small pulses� �C� shows that an enlargementof the threshold to ��mV does not yield a better rejection of small pulses but leads to a loss of �pepulses� The low threshold is generally set to a small value� typically ��mV to ��mV �Each OM has to be adjusted individually �see �� As an example �gure B�� shows the energydistribution of dark noise pulses in a linear and a double logarithmic plot after this adjustment� Apeak for �pe and �pe signals is clearly visible� The rate of dark noise pulses extends to high pulse�


pulse width [ns]

cou

nt r

ate

/1ns

[Hz]

pulse width [ns]

cou

nt r

ate

/1ns

[Hz]

0

200

400

600

800

1000

0 200 40010

-1

1

10

10 2

10 3

102

103

Figure B�� Dark noise distribution of OM!�� in a linear and double logarithmic plot�

energies� Several mechanisms can be identi�ed� which are responsible for these large signals� The mostdominant are due to �Cerenkov light produced by ��K decays in the glass of the PMT� after�pulses dueto ionisation of residual gas in the PMT and cosmic rays� which hit the PMT during the calibrationmeasurement� ��The integral counting rates have been measured with their energy distribution for the individual PMTsand the OMs� During the �nal test of the EOMs� the temperature has been too high to apply usefulnumbers for deep ocean temperatures� The counting rates range between �kHz to ��kHz for roomtemperature and decrease down to few kHz for ��C� For higher temperatures ��C the ratesstrongly increases up to ��kHz � ��kHz�

��

C Software details

C�� The Dada program

C�� Geometry de�nition� data structures and initialisation

The initialisation phase follows the general structure of GEANT� ��

Initialisation of ZEBRA� GEANT� HBOOK and HIGZ via standard calls�

Initialisation and parsing of the database� GEANT� uses the FFREAD package to read necessaryinformation from a format�free database� Archive data required by the Dada program are storedin the same �le� called Dadabase ��

De�nition of the particle data structures� These are standard particles of GEANT with theextension of � &s� charmed mesons and the Z�W� bosons��

De�nition of materials according to their chemical composition� Materials included in the Dad�abase are ocean�water� fresh�water� basalt for the ocean ground and some additional materials�glass� air and vacuum��

De�nition of tracking media� A tracking medium is a material with kinetic energy cuts and a listof allowed GEANT�mechanisms� ��

De�nition of the detector geometry� This is a complex hierarchic data structure� which is de�scribed below�

De�nition and initialisation of� histograms� the random generator� data streams � � � ��

Calculation of cross section and energy loss tables� This is done by GEANT� using the previouslyde�ned data structures� ��

Several sets of standard con�gurations for known detector geometries and tracking parameters arede�ned in the Dadabase� They may be independently selected� Implemented detector geometriescover various con�gurations of DUMANDand BAIKAL as well as other geometries� Most importantsets of tracking parameters are TEXA and TFAS� which implement the full tracking down to the�Cerenkov threshold and the fast�tracking� ��

Following data streams are �optionally� opened�

The output �le for event output�

A �le for the input of the initial kinematics of events�

A Dadabase �le� e�g� dada�steer

A HBOOK��le for histograms� which are �lled during tracking� dada�rz�

A postscript �le for graphical output� dada�ps�

An additional �le for the output of special data �requires re�compilation��

The de�nition of a detector geometry is done according to a �xed hierarchy of embedded detectorvolumes� Each detection volumes is encapsulated by a volume of higher hierarchy and surroundsvolumes of lower hierarchic order� Each volume is �lled with a tracking medium�

�� C SOFTWARE DETAILS

Up to �� strings may be de�ned� Each string represents a cylindrical volume and a certain con�gura�tion of optical modules� The con�guration of OMs is de�ned by the data structure string�type� whichis assigned to each string� A string�type de�nes orientation� positions in the string and types of OMs�Up to �� di�erent string�types with each up to �� OMs may be de�ned� The typical radius of a stringvolume is ��m� Each OM represents a spherical OM�volume of lower hierarchy with a typical radius of�m� The OMs are not necessarily positioned in the centre of the OM�spheres because of a non uniformcathode sensitivity�

The string volumes are positioned into a larger cylindrical volume which is of the order of two times thelight�attenuation length larger than the detector itself� This volume is designed to de�ne the e�ectivesensitive detector volume� The absolute positions of OMs are mirrored into a separate data structure�independent of the GEANT geometries�� This structure is used for the detection of �Cerenkov hitsand may be changed during tracking� The detector volume is again enclosed by a larger cylinder whichis typically �� attenuation lengths larger� This cylinder is located in the centre of a large box withtypically �km long sides� which de�nes the total simulation space and encloses all other volumes� Ifthe outer volumes overlap with the ocean�lake bottom� they are divided into two volumes of di�erentmaterials �e�g�rock and water��

The tracking parameters for each volume may be individually adjusted� which allows to select anaccurate tracking close to OMs and a tracking with higher thresholds further outside� Each volumemay be declared passive to increase the speed of the tracking procedure� In passive volumes secondaryparticles are stored only in a temporary GEANT stack and tracking is abandoned for particles� thatdo not point into the detector�

Six di�erent optical modules may be used and simulated with di�erent levels of accuracy� The BOM�EOM and JOM may be simulated with detailed routines� a standard ��PMT� � �PMT and theAMANDA OM are only rudimentarily implemented�

C�� Fast tracking

The fast tracking mode allows to bypass the standard GEANT tracking and to calculate the resulting�Cerenkov light according to a parameterization� During initialisation a fast�tracking type is assignedto each GEANT particle� Default is the full tracking with GEANT for all particles� Within certainenergy ranges particles may be declared to be treated as a muon� electro�magnetic cascade or a hadroniccascade� For each of these three types several parameterizations are implemented� Each secondaryparticle� e�g� a bremsstrahlung photon� is tested if a fast tracking type is assigned to this particleand if its energy falls into the corresponding range� In this case the further tracking is not passed toGEANT� but done via the fast tracking mode and the �Cerenkov light is simulated according to theselected parameterization� Parameterizations� are deduced in section �� for cascades and in �� formuons� Cascades are simulated including their longitudinal evolution� The implementation of fastmuons is done as follows� Energy losses smaller ��GeV are assumed to occur continuously along themuon trajectory and the amount of �Cerenkov light from the muon is enlarged �see section �� Themuon is tracked by GEANT with tracking thresholds enlarged to ��GeV �

C�� Signal generation

Generation and attenuation of �Cerenkovlight� During the execution of a tracking step thesimulation loops� over all OMs and checks for �Cerenkov hits�

�Other implemented parameterizations cover the treatment of muons as a minimal ionising tracks and the point�likesimulation of cascades for parameterizations of Belyaev and Hauptman��

�This loop is only executed� if the energy is above the �Cerenkov threshold% if the particle has left the active detectorvolume the direction has to point into the detector and if the current track length is above a minimal cut �e�g�� mm��

C� The Dada program ��

c

(z)

(y)

θ

(x)

r

2

r1λ

2

λ

1

λs

OM

Figure C�� Geometry for the evaluation of a �Cerenkov hit�

The geometry is shown in �gure C�� The current track piece is de�ned by the length s� the start point�r�� the end point �r� and its direction 2p # �p�p� In order to minimise the computing time during theevaluation of a possible �Cerenkov hit and the length of the hitting track � several tests are performedin sequential order� If one check fails the generation of �Cerenkov light is abandoned

�� Is the angle between 2p and �OM � �r� smaller ��3

�� Is the point �r� before ��3

�� Is the point �r� behind ��3

If these conditions are ful�lled a hit has happened and the length � is interpolated� The relative lengthL is calculated via eq��A�� for fast cascades via eq��A�� and the angle between the �Cerenkovwave�front and the OM�axis �H �eq��A�� are calculated and stored together with a reference to thehitting track in a stack� The time of the hit tH is calculated from the centre of the hitting track piece� via eq��A�� A value proportional to the time spread $H is assumed using

$H # �� cvac ��C��

If two hits in one OM originate from the same track and occur within the time window tw �typically�ns�� the values for the length are added L # L� � L�� the angles �H � the distance d� and the timestH are averaged� weighted with L� e�g�

�H #�H� � L� � �H� � L�

L� � L��C��

The new time spread $H is calculated via

$H # min

�tw �

$H� � L� �$H� � L�L� � L� �min�jtH � tH�j � jtH � tH�j�

��C��

After the tracking is �nished� the photon �ux �� is calculated for each hit with eq��A�� Hits occuringin one OM at the same time are recombined analogous to the above method eq��C�� C�� exceptthat values are weighted with �� instead of L� The attenuation is calculated according to the Learned


parametrisations eq�� except for Baikal water� The attenuation here is calculated according to aspline parametrisation� which was extracted from the standard BAIKAL Monte Carlo ��

All tracks are numerated in a straight order �� Hits from secondary tracks� which are onlystored temporarily in a GEANT stack� receive the negative number of the initial track� During re�combination of the reference to the hitting track emphasis is put on the track with the lowest positivenumber� Only if both combined tracks have a negative number the least negative value is kept� Afterthis procedure the stack contains no hits occuring at the same time at the same OM�

Simulation of Optical Modules� The simulation of OMs generates the amplitude in units of peeq��A�� and the response time� The simulation of the response time t involves time deviations dueto the initial spread of the arrival time of photons $H and due to the time accuracy of the OM $OM �The response time is calculated without the �xed transit�time of an OM� The time deviation due to$H is simulated according to an Exponential distribution �E

t # tH �$H

npe� ��E � �� $OM ��C��

with npe the number of photoelectrons�

The simulation of OMs may be done with � levels� of accuracy�

�� No PMT but only the number of photons hitting the OM is simulated�

�� The number of photoelectrons are simulated according to Poisson distribution� No time andamplitude response is simulated for the PMT �$OM # ��

�� In addition to � time�deviations and the amplitude�response are simulated according to Gaussiandistributions�

�� Detailed simulation for BOM� EOM and JOM according to standard parameterisations�

The parameters necessary for � to � are taken from the Dadabase� the simulation level � is implementedvia special routines regarding details of the OMs� The routine for the JOM was kindly providedby A�Okada �� and contains only minor modi�cations� The angular sensitivity is simulated viaS # �� cos �H with an absolute peak quantum e�ciency times collection e�ciency � # ��and a geometrical area of ��m�� The sensitivity of the EOM is simulated according to eq�� assuming � # �� and the area ��m�� The amplitudes are simulated according to the amplitude�function eq�� with an energy resolution of �"� The calculation of the time deviations usesthe timing�function eq�� with the parameters derived in �� The routines to simulate thesensitivity and the amplitude of the BOM were taken from the Baikal Monte Carlo program �� Theprogram uses a spline parametrisation for the angular sensitivity� The absolute quantum e�ciency isalready included in in the parametrisation of the light attenuation of Baikal�water� The time jitter forthe BOM may be simulated according to � functional dependencies using the Exponential distribution

�A �th level� which respects the properties of individual OMs� is under consideration�

C� Event generation ��

�E and the Gaussian distribution �G

�� $OM # �E � ��pnpe

� �G � ��

�� $OM # �E � ��npe

��

�� $OM # �E � ��npe

� �G ��

��pnpe

��

�� $OM # �E �max

B��

��

npe

�CA� �G � ��

�C��

All units are ns� The second simulation requires an additional Gaussian jitter of �ns after the localcoincidence of two OMs in Baikal is calculated�

The �nal amplitudes and times are written to the data �le� No local coincidence is performed withinthe Dada program� but may be applied later using the de� utility �appendix C��

Noise generation� It is possible to simulate noise or to sample additional noise hits into an eventeither within the Dada program or during later data processing using the de� program �appendix C��Signals are simulated uniformly distributed in the time window � of the event �typically ��s�� Theprobability P of a hit is P # � �R� with the total noise rate R� Two di�erent choices for the amplitudesof these signals are possible� The �rst generates �pe signals� second choice allows to generate theamplitudes according to a potential law�

C�� Internal event generation

Besides the possibility to read the initial event kinematics from a data �le� three alternate methodsare included in Dada �

�� Initial kinematics� vertex and particle type may be interactively provided� The same track maybe simulated several times�

�� An internal generator muoi allows to generate isotropic muons� The functionality is a subset ofthe muo� generator �see appendix C��

�� Simulation without initial kinematics in order to simulate only noise events�

C�� Event generation

The event generator program basiev simulates atmospheric muons� The program code was developedfor the Baksan experiment at the INR Moscow by Boziev et�al� �� The program generates protoninduced hadronic cascades in the top of the atmosphere and simulates resulting muons at sea level�The muons are transported to the depth of an underwater experiment using the mean energy loss� Itwas extracted from the standard Baikal Monte Carlo as a stand�alone program� Several parameterscan be adjusted� such as the minimum muon energy at the detector site� or the distance of muons tothe detector �from where tracking is taken over by Dada �� The program yields good results comparedto experimental data and other air shower programs� ��


The general purpose generator muo� generates single particle trajectories� The particle may be anyGEANT�particle� whose energy is simulated either according to a logarithmic� potential or constantenergy distribution within a certain energy range� The vertex is simulated either on a plane at a certaindistance from the detector or within a surrounding volume� The second is useful for the generation ofshowers inside the detector� the �rst for the generation of muon tracks passing through the detector�Directions may be simulated isotropically or within certain ranges �e�g� simulation of muons from thelower hemisphere��

A third event generator program nue� is under development� Its purpose is to simulate chargedcurrent and neutral current neutrino ��e� �� and �� interactions with nucleons or electrons close tothe detector� using the Pythia program� Particle tracks can be also generated with the built ingenerators of the Dada program �appendix C��

C�� Triggering� event selection and reconstruction

During the �rst step of data analysis it may be desirable to apply triggers or to recon�gure the data�The following discussion uses the term channel instead of OM� This expresses that �lter conditionsare equivalent for individual OMs and several OMs forming a local coincidence� The term OM isonly used if explicitly required� In case of the BAIKAL experiment a pair of OMs forms a channel� incase of DUMAND II one OM is equivalent to one channel�The de� program intends to implement hardware�speci�c features as well as a possible recon�gurationof the data�� Most important items are�

Implementation of a local coincidence condition between OMs �e�g� OM�pairs in BAIKAL �� Co�incident hits are detected and non coincidence hits are deleted�

Implementation of the dead time of channels� If multiple hits in one channel are detected tooccur within a speci�ed time�window �dead�time�� the second hit is deleted and the amplitudeadded to the �rst�

Simulation of noise hits into the data stream�

Simulation of an additional time�jitter� e�g� to handle time uncertainties due to digitisation�

Simulation of the e�ciency of channels� Hits may be removed from the data stream accordingto a random number�

Hits in certain channels may be deleted� This allows to apply MC�data� simulated for a fulldetector� to experimental data with certain modules switched o� during a speci�c run period�

Removal of hits with amplitudes smaller than a certain threshold�

Removal of detector elements �strings and channels� from the data stream� Smaller detectors areoften a subset of a larger detector �E�g� NT�� is a subset of NT�� This allowsto simulate data for a larger detector� Data subsets may be extracted and applied to smallerdetectors�

The second program� so�� provides trigger conditions� which may be applied to the data�stream andcombined in AND or OR conditions� Possible triggers are�

A minimum number of total hits� a minimum number of hit channels or a minimum number ofpe in the event�

Implementation of the T�trigger eq�� which allows to require a minimum number of neigh�bouring hit channels in several strings�

C� Data processing ��

Several special trigger conditions such as� minimum number of hits in a certain string� minimumnumber of pe in a certain channel � � � �

The trigger logic� to select all events which ful�ll a trigger condition� may be inverted� to select thoseevents� which do not pass�

The reconstruction of events is the most important step during data analysis� The reconstructionusually involves the minimisation of a �� function or uses a more sophisticated likelihood method�The �� function for the muon track reconstruction may be written as sum of three contributionscorresponding to the response times ��t and amplitudes ��a and the probability of non hit channels ��p

�� # ��t �Wa � ��a �Wp � ��p�C��

#NhXi��

�ttheo�i � ti��

��t�i� Wa �

NhXi��

�atheo�i � ai��

��a�i� Wp �

NXi�Nh��

Ph�i��

ti� ai are the response times and amplitudes of the hit channels �� Nh�� t�i and �t�i are thecorresponding deviations� ttheo�i� and atheo�i� are the expected response times and amplitudes e�g�for a reconstructed muon track� Ph�i� is the probability of the occurrence of a hit in the not hitchannel i� The contribution ��t has the largest signi�cance determining the track reconstruction� Theamplitude accuracy is strongly limited due to additional light from secondary cascades� Therefore thecontributions ��a are ��p are weighted with factors Wa and Wp or completely neglected �Wp # Wp # ��The �t of a muon track involves � free parameters� � for the geometrical track parameters and one forthe time� It thus requires at least � hit channels� ��

The presence of noise signi�cantly complicates the �tting procedure and requires sophisticated noisereduction methods� e�g� causality criteria� during the �tting procedure� in order exclude suspected noisehits from the calculation of the ��

After the calibration of BAIKAL events� they are �tted with a standard BAIKAL reconstruction programassuming a single muon track� For each �t result several quality criteria� such as an investigation ofthe covariance matrix� are applied and a quality value is assigned to the result� �� The recoos program� by O�Streicher� provides a fast �t program for the reconstructions of single muons�Together with the �lter programmu� a large variety of quality criteria may be applied to a data streamto identify mis�reconstructed tracks and especially reject down�going �fake� muons� ��

C�� Data processing

Usually the user has to deal with various di�erent� mostly incompatible� data formats� The data�format used for the SiEGMuND software is based on a line�oriented ASCII�format introduced forthe DUMAND II experiment in �� A second format is a binary format used at Zeuthen for theBAIKAL experiment �� Within the development of the rdmc library �� the initial ASCII�formatwas extended considering following requirements�

Full downward compatibility with the DUMANDASCII�format and logical compatibility with theBAIKAL binary format�

One general format for all analysis steps� Possible pipelining of data streams on UNIX platforms�

Possible user speci�c extensions� especially for data analysis purposes�

Independence on the speci�c detector�


The rdmc library provides format independent I�O routines and memory data�structures� A userapplication program written on basis of rdmc may access any data�format known to rdmc via formatindependent calls� The library provides automatic decompression of gzip&ed data��les� Changes informats require no change of the application program� The program cpfeil converts data �les betweendi�erent formats and provides further data manipulation options� ��

Name Description Referencerdmc I�O library and memory data structures for data �les �� cpfeil File handling and format conversion program ��dada Detector response Monte Carlo �GEANT� program ��C��de� Hardware simulation and data�manipulation program C��so� Trigger and event selection program C��ge� Filter program for generator speci�c information ��

recoos Fast muon reconstruction program �� mu� Reconstruction �lters �� rtt Display program �X��Postscript� ��

basiev Generator for atmospheric muons �bundles� �� muo� Generator for generic tracks C�� nue� Generator for neutrino nucleon�electron interactions �Pythia� ��nt MC�data histograming program ��calib Baikal speci�c calibration of raw data ��danton Data histograming program ��

Table C�� Summary of SiEGMuND programs� ��

Table C�� shows an overview on the most important SiEGMuND programs� The programs fortriggering� data �ltering and reconstruction� so�� de�� mu� and recoos are described in appendix C��The event generator programs are described in appendix C��

The rtt program implements a small ��dimensional event display� It shows the detector� hits and ifavailable the reconstructed and generated tracks� It is possible to rotate and to zoom the picture aswell as to print verbose information on the event� ��

Two programs �nt and danton generate HBOOK��les with standard histograms and n�tuplesfor further analysis with PAW��

The calib program reads raw data��les from BAIKAL and performs a calibration according to a smalldatabase� It writes calibrated events to a �le� readable by rdmc� ��

C�� Calculation of ��K rates

The expected counting rate of signals due to decays of ��K are calculated via a Monte Carlo integrationof eq�� Besides the three spatial coordinates� which are simulated spherically within an inner andan outer radius� the type of decay and its energy is randomised �see section ��

If a resulting electron is above the �Cerenkov threshold the number of �Cerenkov photons n� is simulatedwith a constant distribution between � and �� photons for Compton electrons and via the �notnormalised� probability function

��n�� #

�� ln�n�� for n� �� ln�n�� for �� n� ��

�C��

for ��electrons� These assumptions are supported by detailed simulations of the ��K decay and theresulting �Cerenkov photons �� After the simulation of the decay� the mean number of photo�electrons

C Calculation of ��K rates ��

m for a PMT� which is hit by the non isotropic �Cerenkov cone in the distance d� is calculated via

m�d� #��d� � FOM�eff � � � n�� (�d� �� ROM ��

��C��

with the attenuation ��d� �eq�� the radius of the OM ROM � the collection times the quantume�ciency of the photo�cathode � and the solid angle ( # sr for the emission of the photons� Thee�ective area FOM�eff of the OM is simulated according to the geometrical cathode area and theangular sensitivity parameterized for the JOM� EOM� BOM and the AMANDA OM� to a speci�c OMtype� Finally the hit probability is calculated via eq�� A volume integration and multiplicationwith the decay rate yields the noise rate�

�� D THE BAIKAL AND THE DUMANDCOLLABORATION

D The BAIKAL and the DUMAND collaboration

The Baikal Collaboration �

I�A� Belolaptikov� � L�B� Bezrukov�� B�A� Borisovets�� N�M� Budnev�� A�G� Chensky��I�A� Danilchenko�� Zh��A�M� Djilkibaev�� V�I� Dobrynin�� G�V� Domogatsky�� L�A� Donskykh��A�A� Doroshenko�� S�V� Fialkovsky�� A� Gaponenko�� A�A� Garus�� O�A� Gress�� T�A� Gress��

H� Heukenkamp�� A� Karle� A�M� Klabukov�� A�I� Klimov�� S�I� Klimushin�� A�P� Koshechkin��J� Krabi� V�F� Kulepov�� L�A� Kuzmichov�� B�K� Lubsandorzhiev�� M�B� Milenin�� T� Mikolajski�R�R� Mirgazov�� N�I� Moseiko�� S�A� Nikiforov�� E�A� Osipova�� A�I� Pan�lov�� Yu�V� Parfenov��A�A� Pavlov�� D�P� Petukhov�� K�A� Pocheikin�� P�G� Pokhil�� P�A� Pokolev�� M�I� Rosanov��

V�Yu� Rubzov�� S�I� Sinegovsky�� I�A� Sokalski�� Ch� Spiering� O� Streicher� B�A� Tarashansky��T� Thon� I�I� Tro�menko�� Ch� Wiebusch� R� Wischnewski

�Institute for Nuclear Research� Russian Acad� of Science� Moscow� Russia�Irkutsk State University� Irkutsk� Russia�Moscow State University� Moscow� Russia

�Nizhni Novgorod State Technical University� Nizhni Novgorod� Russia�St� Petersburg State Marine Technical University� St�Petersburg� Russia

�Kurchatov Institute� Moscow� Russia�Joint Institute for Nuclear Research� Dubna� Russia

DESY � Institute for High Energy Physics� Zeuthen� Germany� now at University of Wisconsin

��

The DUMAND Collaboration �

W� Anderson�� T� Aoki�� H�G� Berns�� J� Bolesta�� P�C� Bosetti�� H� Bradner�� U� Camerini��V� Chaloupka�� R�J� Clark�� H�J� Crawford�� S�T� Dye�� I� Flores�� M� Fukawa� J� George��P�W� Gorham�� P�K�F� Grieder�� W� Grogan�� H� Hanada�� J�M� Hauptman�� T� Hayashino��E� Hazen�� M� Jaworski�� A� Kibayashi�� T� Kitamura�� S� Kondo�� P� Koske�� C� Kuo��J�G� Learned�� J�J� Lord�� R� March�� T� Matsumoto�� S� Matsuno�� K� Mauritz�� M� Mignard��P� Minkowski�� R� Mitiguy�� K� Mitsui�� T� Narita�� D� Nicklaus�� D�J� O&Connor�� Y� Ohashi��A� Okada�� S� Olsen�� V�Z� Peterson�� A� Roberts�� M�D� Rosen�� G� Shapiro�� V�J� Stenger��A� Suzuki�� R�C�Svoboda�� T� Takayama�� D� Takemori�� S� Tanaka�� E� Torrente�� S� Uehara�C�H� Wiebusch�� R�J� Wilkes�� G� Wilkins�� A� Yamaguchi�� K�K� Young��

�� RWTH�Aachen University of Technology� Germany!�� University of Bern� Switzerland!�� Boston University� Massachusetts� USA!�� University of California� Berkley� USA!�� University of Hawaii� Manoa� USA! � Hirosaki U�� Japan!�� Iowa State University� Ames� USA!�� KEK �National High Energy Physics Lab�� Japan!�� University of Kiel� Germany!�� Kinki University� Japan!�� Louisiana State University� Baton Rouge� USA!�� Scripps Institution of Oceanography� USA!�� Tohoku University� Sendai� Japan!�� Institute of Cosmic Ray Research� University of Tokyo� Japan!�� Vijlen Institute for Physics� Vijlen� Netherlands!� � University of Washington� Seattle� USA!�� University of Wisconsin� Madison� USA�

REFERENCES a

References

�� Alexander et�al� Contributions to �� by the DUMAND II Collaboration

Update on the status of DUMAND �Optical Module for DUMAND II � Japanese Version�An Optical Sensor for DUMAND II � European Version�Trigger strategies an processing for DUMAND �On the Detection of UHE Cascade Showers with DUMAND II �The DUMAND II Digitiser�Acoustical Detection of Cascades in DUMAND �Estimate of Downgoing Atmospheric Muon Background Events in DUMAND II �Capabilities of the DUMAND II Phase I ��string Array�Acoustical Locating System for DUMAND II �Atmospheric Neutrino Oscillations with DUMAND �

�� van Aller et�al� A smart ��cm Diameter Photomultiplier� Helvetia Physica Acta� ��

�� Contributions to �� by the AMANDA Collaboration

Status and Capabilities of AMANDA ��Measurements of the Absorption Length of the Ice at the South Pole in the Wavelength Interval ��nm to��nm�Indirect Evidence for Long Absorption Lengths in Antarctic Ice�The Design of a Neutrino Telescope Using Natural Deep Ice as a Particle Detector�A system to Search for Supernova Bursts with the AMANDA Detector�

�� Atsuno et�al� Single photon light detector for deep ocean applications� NIM� A��!�� Sep� ��

�� Babson et�al� Cosmic!ray muons in deep ocean� Phys�Rev�D� ��!�� Dec� ��

�� S�Barwick Transparency of Antarctic Ice� First Results �in ��

F�Halzen AMANDA� Antarctic Muon And Neutrino Detector Array �in ��

�� I�Belolaptikov and Ch�Spiering Optimisation of NT�� with respect to Neutrino Detection� Baikal�Note��

� � Belolaptikov et�al� Track Reconstruction and Background Rejection for the Baikal Neutrino Telescope� �in��

�� Belolaptikov et�al�Results from the Baikal Underwater Telescope �rd Conf�onTrends in Astroparticle Physics� Stockholm�September �� Nucl�Phys�B �Proc�Suppl�� Status of the Lake Baikal Neutrino Detector� Proceedings of the �th Int�Conference on High EnergyPhysics� Dallas� August ��

�� Belolaptikov et�al� The BAIKAL Underwater Telescope � Status and Results� Proc� of the Int�Conf�on HighEnergy Cosmic Rays� RIKEN� Tokyo� ��

�� Belolaptikov et�al� Contributions to �� by the BAIKAL Collaboration�

The Lake BAIKAL Neutrino Project� Status Report�Analysis of Muon Events Recorded with the NT�� Detector in Lake Baikal�Search for Magnetic Monopoles with the Baikal Neutrino Telescope�Separation of Upward going Muons with the Baikal Underwater Telescope�Response of the NT�� to a Distant Point�Like Light Source�Variations of Water Parameters at the Site of the Baikal Experiment and their E�ect on Detector Perfor�mance�A Sonar Triangulation System for Position Monitoring of the Baikal Underwater Array�

�� A�A�Belyaev� I�P�Ivanenko and V�V�Markov"Cerenkov Radiation from showers developing in saline water� �in ��

"Cerenkov Radiation from electron�photon showers developing in water� �in��

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�� V�S�Beresinsky High Energy Cosmic Neutrinos of Acceleration and Non!Acceleration Origin� INFN� GranSasso� INR� Moscow� January �� LNGS � ��

�� V�S�Beresinsky Dark Matter and High Energy Neutrinos� �in ��

�� V�S�Bersinsky On astrophysical Solution to the Solar Neutrino Problem� Preprint LNGS�� June��

Gallex!Collaboration� Implications of the Gallex determination of the solar neutrino #ux Phys�Lett�B ��

N�Hata Solar Neutrinos� Hint for Neutrino Mass� Preprint University Pennsylvania UPR��T�

D�R�O�Morrisson Brief review of theory and experiments on the Solar Neutrino Problem� Preprint CERN�PPE�� Nov��

A�Y�Smirnov The Solar neutrino Problem� Neither Astrophysics nor Oscillations$ International Workshopon� %Solar neutrino problem� Astrophysics or Oscillations Gran Sasso� Feb��

�� U�Berson Entwicklung und Test eines optischen Moduls zum Nachweis schwacher Lichtquellen in Wasser�"Cerenkov�Detektoren� Diploma thesis� RWTH Aachen� Feb� ��

�� Berson et�al� Messungen zu den optischen Eigenschaften des Gels� Julia internal report� Juli ��

�� Bezrukov et�al� Search for superheavy magnetic monopoles in deep!underwater experiments at Lake BaikalYad�Fiz�� July ��

�� Bezrukov et�al� The Optical Module of the Baikal Neutrino Telescope NT�� in ��

�� Bezrukov et�al� The Electronic system of the BAIKAL Neutrino telescope NT�� Izvest�Acad�Nauk� Fiz�� No�� in Russ��

�� Bionta et�al� Observation of a Neutrino Burst in Coinidence with Supernova �� a in the Large MagelanicCloud� Phys�Rev�Lett�� !�� April ��

Hirata et�al� Observation of a Neutrino Burst from the Supernova SN�� A� Phys�Rev�Lett�� !��April ��

Alexeyev et�al� Detection of the Neutrino signal from SN�� A in the LMC using the Baksan UndergroundScintillation Telescope� Phys�Lett�B � �� April ��

�� Bird et�al� Evidence for Correlated Changes in the Spectrum and Composition of Cosmic Rays at ExtremelyHigh Energies Phys Rev�Lett��

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�� T�Bolln Untersuchungen an neuartigen� hochemp�ndlichen gro&#�achigen Photomultipliern f�ur den Einsatzin der Tiefsee� Diploma thesis� University Kiel� Juli ��

�� P�C�Bosetti JULIA �in ��

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Webster et�al� Mechanical stimulation of bioluminescence in the deep Paci�c Ocean� Deep�Sea Research�� !��

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� � Burrows et�al� The future of supernova neutrino detection� Phys�Rev�D �� May ��

Y�Suzuki Kamikande Results on Solar Neutrinos and a Supernova Search� Preprint ICRR�Report��May ��

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d REFERENCES

�� J�G�Learned Attenuation of "Cerenkov photons in the ocean� HDC Memo �� Hawaii Dumand Center�April ��

�� J�G�Learned Attenuation functions�phomiz� phocas� Private communication ��

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�� J�G�LearnedDUMAND II System Description� DIR�� May ��DUMAND II Speci�cations� DIR�� May ��

�� C�Ley Berechnungen �uber den Nachweis hochenergetischer Neutrinos mit dem DUMAND Detektor�Diploma thesis� RWTH Aachen� May ��

�� C�Ley Untersuchungen zur Rekonstruktion des radiativen D��Zerfalls im H��Experiment� PITHA �� Phd thesis� RWTH Aachen Nov ��

�� C�Ley and C�H�Wiebusch� The shape of EOM pulse�height distributions� Dumand Internal Report� ��Jan� ��

�� Lohmann et�al� Energy loss of muons in the energy range �!�� GeV� CERN � ��

�� E�Lorenz High energy gamma astronomy above ��GeV �in ��

�� Lubsandorzhiev et�al�The optical sensor for the lake Baikal project �in ��QUASAR�� The optical sensor of the Lake Baikal Neutrino Telescope �in ��

�� K�Mannheim High energy neutrinos from extragalactic jets� Ast�Part�Phys� in press� ��

�� M�A�Markov On high energy neutrino physics� Proc�Int�Conf�on High Energy Physics� Rochester� ��

�� T�Matsumoto and S�Matsuno� private communication� ��

�� T�Mikolajski Methodische Untersuchungen und Entwicklung eines Kalibrationssystems f�ur das Neutrinote�leskop NT�� im Baikalsee� Dissertation�DESY�IfH Zeuthen� December ��

�� K�Mitsui Muon energy!loss distributions and its application to muon energy determination� Phys�Rev�D��!��May ��

�� S�Miyake Emperical Formula for Range Spectrum of Cosmic Ray � Mesons at Sea Level� J�Phys�Soc Japan��

�� P�Mohrmann Untersuchung von Wechselwirkungen mit hoher Energiedeposition in einem Unterwasser!Neutrino!Teleskop� Diploma thesis� DESY IfH!Zeuthen� Okt��

�� M�Mori Upward going muons in Kamiokande� �in ��

�� D�J�Nicklaus Three String DUMANDTriggers University of Wisconsin� August ��

�� A�Okada A Monte Carlo Study of the DUMAND II Array� ICRR�Report�� March ��

�� A�Okada Sensitivity of DUMAND II to AGN Neutrinos �in �� and ICRR�Report�� June ��

�� A�Okada Simulation of JOM Signal Generation and Muon Reconstruction � Dumand Internal Report�DIR�� August ��Private comunication� ��

�� A�Okada On the Atmospheric Muon Energy Spectrum in the Deep Ocean and its Parametrisation� ICRR�Report�� ISSN �� June ��

�� E�Osipova� private communication�

�� R�D�Peccei The Physics of Neutrinos� Preprint DESY �� April ��

�� A�A�Petrukhin and V�V�Shestakov The in#uence of nuclear and atomic form factors on the muonbremsstrahlung cross section� Can�J�Phys��

REFERENCES e

�� F�A�Raupach Point!Like Sources of High Energy Cosmic Rays Inaugural dissertation� RWTH Aachen��

Berger et�al� A search for high energy neutrinos from SN �� A� the Crab� Hercules X�� and Cygnus X��with the Fr(ejus detector� Z�Phys�C� � � ��

�� L�K�Resvanis NESTOR� A Neutrino Particle Astrophysics Underwater Laboratory for the Mediteranian��in ��

L�K�Resvanis NESTOR� A neutrino particle astrophysics underwater laboratory for the Mediteranean� �in��

�� W�Rhode Untersuchungen der Energiespektren hochenergetischer Muonen im Fr)ejusdetektor� Dissertation�WUB�DIS �� Wuppertal Oktober ��

�� I�L�Rozental Interaction of Cosmic Muons of High Energy Sov�Phys�Usp� ��

� �� R�C�Smith and K�Baker Optical properties of clearest natural waters �� nm�� Appl�Opt��No��Jan ��

� �� P�Sommers Neutrino #uxes from Compact Sources in the Galaxy �in ��

� � Ch�Spiering and P�Mohrmann Dependence of the muon visual range in water on the attenuation lengthand the PMT diameter� Baikal�Note ��

� �� V�J�Stenger Optimizing Deep Underwater Neutrino Detectors� Proc�of nd NESTOR Int� Workshop�Pylos�Greece� Oct��

� �� R�Svoboda Characteristics of the December �� Monster Bu�er Data� DUMAND Internal Report ��

� �� T�Stanev Astrophysical Sources of High Energy Neutrinos� Nucl�Phys�B �Poc�Suppl�� A �� NorthHolland ��

� �� Stecker et al� High!Energy Neutrinos from Active Galactic Nuclei Phys�Rev�Lett� �� !�� May ��Erratum �� !��

� �� O�Streicher Nachweis von Myonen aus Wechselwirkungen atmosph�arischer Neutrinos in Unterwasser!Neutrino!Teleskopen� Diploma thesis� DESY IfH!Zeuthen� Okt��

� � A�P�Szabo and R�J�Protheroe Implications of particle acceleration in active galactic nuclei for cosmic raysand high energy neutrino astronomy� Preprint ADT�AT�� acc�f�pub� in Ast�Part�Phys University Ade�laide� ��

� �� K�O�Thielheim Fundamental processes relevant for cosmic particle dynamics in compact objects ! pulsarsas cosmic accelerators� �in ��

J�E�Gunn and J�P�Ostriker Acceleration of High!Energy Cosmic Rays by Pulsars� Phys�Rev�Lett��

�� R�Tomski �Uber Messungen schwacher Lichtquellen in der Tiefsee Diploma thesis� RWTH Aachen� Feb��

�� C�H�Wiebusch Zum Nachweis schwacher Lichtquellen im Ozean mit Hilfe eines neuartigen gro&#�achigenPhotomultipliers� Diploma thesis� PITHA �� RWTH Aachen� Dec��

�� Wiebusch et�al� Plane�wave Measurements with an EOM Dumand Internal Report� �� June ��

�� C�H�Wiebusch and G�Wurm Report to the DUMANDmeeting� Hawaii� July ��

�� R�Wischnewski The Lake Baikal Telescope NT�� A �rst Deep Underwater Multistring Array� PreprintDESY �� ISSN �� March �� also in ��

�� R�Wischnewski Private communication�

�� J�R�V�Zaneveld Optical Properties of the Keahole!DUMAND �Site� �in ��

H�Bradner and G�Blackminton Measurements of uncolliminated Light transmission Distance �in ��

f REFERENCES

Proposals� proceedings and text books

�� BAIKAL WWW�server http��www�ifh�de�baikal�baikalhome�html�

�� DUMANDWWW�serverhttp��www�phys�hawaii�edu�dmnd�dumand�html�http��web�phys�washington�edu�local web�dumand�aaa dumand home�html�

�� AMANDA WWW�server http��dilbert�lbl�gov�www�amanda�html�

�� KM�� WWW�serverhttp��dilbert�lbl�gov��http��web�phys�washington�edu�local web�km��aaa readme�html�

�� The Baikal Collaboration� The Baikal Neutrino Telescope NT!�� Project Description BAIKAL��Nov��

�� A�Roberts� editor� DUMANDProceedings of the �� DUMANDSummer Workshops at Honolulu� Fermilab��

�� A�Roberts and G�Wilkins editors� DUMANDProceedings of the �� DUMAND Summer Workshops atHonolulu� Scipps Institute of Oceanography San Diego� ��

�� J�G�Learned� editor� DUMAND �� Summer Workshops at Khabarovsk and Lake Baikal� August !�� University Hawaii�

�� A�Roberts� editor� DUMANDSignal processing Workshop� University of Hawaii� February ��

�� V�J�Stenger� editor� DUMAND ! �� Proceedings of the �� International DUMANDSymposium Vol�� *� July � ! Aug�� University Hawaii�

�� A�Roberts� editor� DUMANDSignal processing Workshop� University of Hawaii� Feb��

�� DUMAND Collaboration� DUMAND� Proposal to Construct a Deep!Ocean Laboratory for the Study ofHigh!Energy Neutrino Astrophysics� Cosmic Rays and Neutrino Interactions� The International DUMANDCollaboration� Okt��

�� A�Roberts� editor� Proceedings of the �� DUMAND Workshops on ��Ocean Engineering and Deployment�Signal Processing� University of Hawaii� Jan��Mar��

�� DUMAND Collaboration� DUMAND II � Proposal to Construct a Deep!Ocean Laboratory for thestudy of High!Energy Neutrino Astrophysics and Particle Physics� HDC�� DUMAND Collaboration�University Hawaii� Aug��

�� K�K�Young and R�J�Wilkes� editors� Proceedings of the DUMAND �� Trigger Workshop University ofWashington Seattle� July ��

�� S�Tanaka and A�Yamaguchi� editors� Proceedings of the DUMAND �� Optical Module Workshop�Tohoku University Sendai Japan� Oktober ��

�� DUMAND Collaboration� DUMAND II � Supplementary Proposal to Complete Construction of a Deep!Ocean Laboratory for the study of High!Energy Neutrino Astrophysics and Particle Physics� UniversityHawaii� Aug��

�� P�C�Bosetti� editor� Proceedings for the second conference on Trends in Astroparticle�Physics� ISBN�� Teubner� ��

�� P�K�F�Grieder� editor� Cosmic Rays � � Proceedings of the ��th European Cosmic Ray Symposium�Nucl�Phys�B �Proc�Suppl�� A�B� May ��

�� Proceedings of the �rd International Cosmic Ray Conference� Calgary� July ��

�� L�K�Resvanis� editor Proceedings of the �rd NESTOR Int� Workshop� Pylos� Greece� Oct� ��

�� TAUP �� Nucl�Phys�B �Proc�Suppl�� May ��

REFERENCES g

�� Neutrino Astrophysics Technology Workshop� JPL� Pasadena USA� March ��

KM� meeting � Saclay France� June ��

Astroparticle�Physics in the next millenium� Snowmass USA� August ��

High Energy Neutrino Astrophysics� Irkutsk Russia� October ��

�� Proceedings of the �th International Cosmic Ray Conference� Rome� ��

�� J�N�Bahcall Neutrino Astrophysics� Cambridge University Press� ��

�� M�Fukugita and A�Suzuki� editors� Physics and Astrophysics of Neutrinos� Springer� ISBN ��Tokyo� ��

�� T�K�Gaisser Cosmic Rays and Particle Physics� Cambridge University Press� ��

�� F�Halzen and Alan D�Martin� Quarks and Leptons� Wiley * Sons� ��

�� S�Hayakawa Cosmic Ray Physics� Wiley ��

�� N�G�Jerlov Marine Optics ISBN �� Elsevier� ��N�G�Jerlov and E�S�Nielsen� editors� Optical Aspects of Oceanography ISBN �� AcademicPress� ��

�� W�J�Kaufman III� Universe� �rd�ed� ISBN ��

�� W�R�Leo Techniques for Nuclear and Particle Physics Experiments� Springer� ��

�� M�S�Longair High energy astrophysics� Cambridge University Press� ��

�� D�H�Perkins Introduction to High Energy Physics� Addison!Wesley� ��

�� E�Seibold and W�H�Berger� The Sea Floor ! An Introduction to Marine Geology� Springer�

H�J�R�osler and H�Lange� Geochemische Tabellen� Ferdinand Enke Verlag Stuttgart�

James Kennett Marine Geology�

�� S�L�Shapiro and S�L�Teukolsky Black Holes� White Dwarfs and Neutron Stars Wiley� ISBN ��

�� Ch�Spiering Auf der Suche nach der Urkraft� ISBN �� Leipzig ��

�� V�J�Stenger� J�G�Learned� S�Pakvasa� X�Tata� Editors� Workshop on High Energy Neutrino AstrophysicsProceedings� ISBN � �� World Scienti�c ��

�� C�Sutton� Spaceship Neutrino� Cambridge University Press� ��

Technical Books� Tables and Manuals

�� Particle Data Group� Review of Particle Properties ! August �� Phys�Rev�D �� ISSN ��

Particle Data Group� Particle Physics Booklet ! July �� from Phys�Rev�D ��

�� Photomultiplier handbooks�

Photomultiplier tubes � principles * applications� Philips photonics� ��Data Handbook Photomultipliers Philips Components� ��Photomultiplier Handbook � Theory� Design Application RCA�

�� Several manuals and data sheetsVitrovex � Glass Instrument Housings for Deep ocean use� * Private comunication� Nautilus Marine serviceGmbH� Germany�Glass Flotation spheres� Benthos� Inc� USA� Semicosil �� SilGel �� Wacker�Chemie GmbH� Germany�

�� I�Belolaptikov and E�Osipova Baikal Monte Carlo� Program description� In preparation�

�� U�Berson and C�H�Wiebusch The European Optical Module for DUMAND II � A technical description�Dumand Internal Report� �� September ��

h LIST OF FIGURES

�� F�Bei&el und V�Commichau� A fast Charge to Time Converter V�� Internal Report HD�� IIIB�III�Phys�Inst�RWTH Aachen� Feb��

�� V�Commichau� FADC unit Version V�B� Internal report III�Phys�Inst�RWTH Aachen� Feb�� H�K�Trieu� Entwicklung eines Bit Transientenrecorders �FADC� mit �� MHz Abtastrate zur Unter�suchung von Driftkammersignalen� Diploma thesis� PITHA �� RWTH�Aachen� March ��

�� J�Krabi and R�Wischnewski� Short description of MC� and Data�Formats used for Reconstruction andHigher level analysis software� Internal note� Zeuthen� Okt��

�� D�J�Nicklaus DUMANDArchived Data Format Description� Dumand Internal Report� DIR�� Uni�versity of Wisconsin� Aug��

Private comunication�

�� O�Streicher and C�H�Wiebusch RDMC �� Installation and user's guide� DESY IfH Zeuthen� Mai ��

�� O�Streicher and C�H�Wiebusch merz �� Installation and user's guide� DESY IfH Zeuthen� June ��

�� O�Streicher and C�H�Wiebusch calib �� Installation and user's guide� DESY IfH Zeuthen� March ��

�� O�Streicher recoos Installation and user's guide� DESY IfH Zeuthen� in preparation�

�� O�Streicher rtt Installation and user's guide� DESY IfH Zeuthen� in preparation�

�� C�H�Wiebusch Dada Installation and user's guide� DESY IfH Zeuthen� in preparation�

�� Wiebusch et�al� gen � event generators for neutrino telescopes� Installation and user's guide� DESY IfHZeuthen� in preparation�

�� FFREAD� Format Free Input Processing� CERN Program library Q��

�� GEANT� Detector Description and Simulation Tool� CERN Program library� W �� Version ��

�� HBOOK� Statistical Analysis and Histogramming� CERN Program library Y��

�� HIGZ� High Level Interface to Graphics and Zebra� CERN Program library Q��

�� P�Horowitz and W�Hill� The Art of Electronics� Cambridge University Press� ��

�� PAW� Physics Analysis Workstation� CERN Program library Q�� Oct��

�� W�H�Press� B�P�Flannery� S�A�Teukolsky� W�T�Vetterling� Numerical Recipes � The art of scienti�ccomputing Cambridge University Press� ��

�� T�Sj�ostrand Pythia �� and Jetset �� Physics and Manual� Theory division� CERN� May ��

�� M�G�Sobel A practical guide to the Unix system� �rd ed�� ISBN ��

�� Helmut Kopka� LATEX� Eine Einf�uhrung� Addison�Wesley� ��

Helmut Kopka� LATEX� Erweiterungsm�oglichkeiten� Addison�Wesley� ��

List of Figures

�� Principle of a DUMAND � type detector� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Principle of an %astrophysical beam dump � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Accretion onto a neutron star � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Neutron star in a young supernova remnant � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� X�ray binary systems as high energy neutrino sources � � � � � � � � � � � � � � � � � � � � � � � � �� Principle of a muon and neutrino telescope� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Signal and background #uxes for neutrino telescopes � � � � � � � � � � � � � � � � � � � � � � � � � �� E�ective area and volume for underground muon telescopes� � � � � � � � � � � � � � � � � � � � � � �� Total event rates from AGN according to several models � � � � � � � � � � � � � � � � � � � � � � � �� Luminosity and detectability of cosmic neutrino source candidates versus distance � � � � � � � � �� Geometry of the "Cerenkov cone � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �

LIST OF FIGURES i

�� Stochastic character of muon energy loss � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Typical muon tracks � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Typical electromagnetic cascades � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Transversal spread of electromagnetic and hadronic cascades � � � � � � � � � � � � � � � � � � � � �� Light attenuation for lake Baikal and clearest natural water � � � � � � � � � � � � � � � � � � � � � �� Parameterization of the e�ective photon #ux versus distance� � � � � � � � � � � � � � � � � � � � � �� Ocean noise measured by DUMAND �Dec�� BAIKAL location of the experiment � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� BAIKAL NT�� NT�� and NT�� detectors � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� DUMAND location of the experiment � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� The DUMAND II detector � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� DUMAND II schematic overview � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Number of photoelectrons versus distance � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Hit e+ciency versus distance � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Mean visual range � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� EOM sketch � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� EOM schematic diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� The %smart PMT Philips XP�� Typical charge distributions of the %smart PMT � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Pulse structure of the %smart PMT � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Scintillator decay and integration time for the %smart PMT � � � � � � � � � � � � � � � � � � � � �� DMQT block and timing diagram � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� DMQT linearity � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� EOM electronic circuits boards � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� EOM mechanical assembly � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� EOM relative angular sensitivity �full illumination� � � � � � � � � � � � � � � � � � � � � � � � � � � �� The %amplitude function � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� EOM energy and transit time distributions for two di�erent zenith angles � � � � � � � � � � � � � �� EOM response time characteristics � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� SiEGMuND program modules and their relationship � � � � � � � � � � � � � � � � � � � � � � � � � �� Dada execution #ow during the simulation of one event � � � � � � � � � � � � � � � � � � � � � � � �� GEANT cross sections for %River!water and standard tracking parameters � � � � � � � � � � � � �� Track and "Cerenkov distributions for ��GeV electron!cascades � � � � � � � � � � � � � � � � � � � �� Relative e�ective "Cerenkov light distribution for low energy electrons � � � � � � � � � � � � � � � �� Fit to a longitudinal track and angular "Cerenkov distribution ��TeV e�� Fit to a longitudinal track and angular "Cerenkov distribution ��TeV �� Longitudinal cascade �t parameter versus energy � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Angular �t parameter for electrons versus energy � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Angular �t parameter for hadrons versus energy � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Comparison of the full GEANT and fast cascade simulations � � � � � � � � � � � � � � � � � � � � �� Integrated track length for electromagnetic and hadronic cascades � � � � � � � � � � � � � � � � � �� Comparison of the e�ective angular "Cerenkov light distribution � � � � � � � � � � � � � � � � � � � �� Low energy secondary tracks accompanying a muon track � � � � � � � � � � � � � � � � � � � � � � �� Track and "Cerenkov distributions for ��GeV muons including quasi continuous secondaries� � � �� Additional track�length due to quasi�continuous secondaries � � � � � � � � � � � � � � � � � � � � � �� Detector response for a speci�c muon track � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Amplitude response of the NT�� for isotropic �TeV muons � � � � � � � � � � � � � � � � � � � � � �� Contributions of the discrete muon energy loss to the amplitude response of the NT�� detector �� Contributions of discrete muon energy loss process to the time residuals of hits in the NT��

detector � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Contributions of discrete muon energy loss process to the time residuals �amplitude weighted� of

hits in the NT�� detector � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Time residuals for muons of di�erent energies in NT�� Time residuals �amplitude weighted� for muons of di�erent energies in NT�� Amplitude response of the NT�� detector for di�erent energies � � � � � � � � � � � � � � � � � � ��

j LIST OF TABLES

�� Sketch of a muon track traveling through a detector � � � � � � � � � � � � � � � � � � � � � � � � � �� Typical distributions of W and DW � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Parametrisation of W and DW versus the energy � � � � � � � � � � � � � � � � � � � � � � � � � � �� W and �W after the half mean muon range � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� W and �W versus the muon track�length � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Time residuals of hits and amplitudes for pair and single OM � � � � � � � � � � � � � � � � � � � � �� Time residuals of hits and amplitudes for pair and single OM �with noise� � � � � � � � � � � � � � �� E�ective area for BAIKAL detectors versus the muon energy � � � � � � � � � � � � � � � � � � � � � �� E�ective area of NT�� and NT�� for atmospheric muons � � � � � � � � � � � � � � � � � � � � � � �� Hit probability versus the channel number � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Channel multiplicity for triggered events � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Typical experimental amplitude distributions � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Corrected amplitude distribution � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Correlation between amplitude corrections between the Baikal and Dada Monte Carlo � � � � � � �� Time residuals and time�� for atmospheric muons � � � � � � � � � � � � � � � � � � � � � � � � � � �� Time di�erences between channels along a string � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Calculation of the vertical muon intensity � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Vertical muon intensity in comparison to other underwater experiments � � � � � � � � � � � � � � �� Count rates during the December �� DUMAND II deployment � � � � � � � � � � � � � � � � � � � � �� Integrated ��K count�rate � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Total ��K signal rate as a function of the attenuation and quantum times collection e+ciency of

the cathode � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Counting rate for ��K signals above pe and �pe � � � � � � � � � � � � � � � � � � � � � � � � � � � ��A� � Geometry for the calculation of the e�ective "Cerenkov light distribution � � � � � � � � � � � � � � ��A� Geometry for a minimal ionizing track � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��A� � Geometry for a spherical and a plane wave � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��B�� Relative sensitivity for point illumination �A� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��B�� Relative sensitivity for point illumination �B� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��B�� Amplitude response of OM �� for increasing light intensities � � � � � � � � � � � � � � � � � � � � ��B�� Transit time distributions for OM �� B�� Dark noise for di�erent high voltages and thresholds � � � � � � � � � � � � � � � � � � � � � � � � � ��B�� Dark noise distribution of OM�� C�� Geometry for the evaluation of a "Cerenkov hit � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

List of Tables

�� Parameters of various underwater detectors � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Comparison of the JOM TOT� the linear EOM QT and the logarithmic JOM QT read�out � � � �� EOM geometrical transit time di�erences � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� EOM transit time jitter � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� EOM transit time slewing � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Fit results for longitudinal cascade parameterizations � � � � � � � � � � � � � � � � � � � � � � � � � �� Fit results for angular cascade parameterizations � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Results for the correction of signal amplitudes � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �� Fit results for I�d� and total ��K rates � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��B�� List of measured photomultipliers XP�� B�� EOM e�ective sensitive cathode area � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��B�� EOM amplitude calibration � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��B�� EOM �tted parameters of the time response � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��C�� Summary of SiEGMuND programs � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � ��

GLOSSARY k

Glossary

ADC Analog Digital ConverterAGN Active Galactic NucleiAMANDA Antarctic Muon and Neutrino Detector ArrayBAND BAIKAL AMANDA NESTOR DUMAND

BOM Baikal Optical Module And Neutrino Detector ArrayCAMAC Camps Attacks Man At ComputerCM Calibration Module for DUMAND

CEM Central Electronic Module for BAIKALDAC Digital Analog ConverterDada Digitisation And Detector Analysis � detector simulation program �GEANT�DMQT DuMand Q�T � fast circuit of the EOMDUMAND Deep Underwater Muon And Neutrino DetectionEOM European Optical ModuleFWHM Full Width Half MaximumGEANT Detector description and simulation package from CERNHEPTAGON Epoxiframe �� arms� for the BAIKAL detectorJB Junction Box for DUMAND

JBEM Junction Box Environmental Module for DUMAND

JOM Japanese Optical ModuleJULIA Joint Underwater Laboratory and Institute for Astro�Particle�PhysicsMDF Minimum Detectable FluxOCTAGON DUMAND II � full detectorOM Optical ModuleQT Charge �Q� to Time conversionPE PhotoelectronPMT Photomultiplier TubeRCU Remote Control UnitRDMC ReaD Monte Carlo Data � SiEGMuND I�O librarySC String Controller for DUMAND

SM System Module for BAIKALSEM String Electronic Module for BAIKALSiEGMuND Simulation of Events with GEANT for Muon and Neutrino Detectors�SVJASKA Hierarchical unit of the BAIKAL detectorTOT Time Over ThresholdTRIAD DUMAND II � stage � �� strings�UHE Ultra High EnergyVHE Very High Energy

l INDEX

Index

AccelerationAccretion� �Fermi� �Magnetic �elds� �Pulsars� �

AGN� ��Di�use neutrino #ux� �� EGRET observation� ��Generic model� ��Jets� ��Neutrino event rates in DUMAND II � ��Neutrino production� �

AMANDA � �� !�� Amplitude function� ��!�� Angular resolution� ��

OCTAGON � �TRIAD � �NT�� NT��

Atmospheric muons� �� !��Amplitude Calibration� ��!��Bundles� �Multiplicity� �NT�� channel e+ciency� ��!��NT�� channel multiplicity� ��NT�� measurement� ��!�� NT�� signal amplitudes� ��!��NT�� signal time residuals� ��NT�� time di�erences between channels� ��!

��Simulation� ��!��Vertical intensity� �� !��

Attenuation� see Light attenuation

BAIKAL � � !�� Calibration� ��!�� !��Central Electronic Module �CEM�� Channel� ��Digitisation� ��E�ective area� see E�ective areaGeneral Description� � !��Monopole�trigger� ��Monte Carlo �standard�� !�� Next stage� ��NT�� NT�� !�� !�� !�� NT�� NT�� !��NT�� !�� NT� � ��OM� see BOMShore�station� ��Signal processing� ��!��

Site properties� �� String Electronic Module �SEM�� Svjaska� ��System Module �SM�� Trigger� ��

Beam dump �astrophysical�� Bioluminescence� ��!��

Characteristics� ��Intensity distribution� ��Production� ��

Black hole� �Blazar� ��BOM� �� !��

Fast readout� ��Read�out� ��Simulation� ��!�� !��

CascadeAngular "Cerenkov light distribution� �! �� !

�� !��Angular track�length distribution� �� !

��Belyaev parameterization� ��Calculation of "Cerenkovlight� �! �� Critical energy� �Electromagnetic� �� !��Hadronic� �� !�� !��Hadronic interaction length� ��Hauptman parameterization� ��Integrated track�length� ��!��Longitudinal track�length distribution� �! �Non point�like� ��!�� Radiation length� �Simulation� �� ! �� !��

"Cerenkovlight� �� !�� Angle� �� Cascades� �!�� !��Hit amplitude� �� !�� !��

� !��Hit e+ciency� �� !��Hit multiplicity� � !�� Hit probability� �!�� !�� !��Low energy electrons� ��!�� Minimal ionizing tracks� ��!��Muons� ��!�� Photon #ux� �� !� � ��Plane wave� ��!��Reduced �� function� ��Spherical wave� ��!��Threshold� �� Time of arrival� �� !��Time residual� �� !�� !��

INDEX m

Transformation from a track distribution� ��!��

Chemoluminescence� see BioluminescenceCosmic rays

Acceleration� �Origin� � �Primary spectrum� �

Cowan� Clyde� �

Dada � � !�� !�� !�� Comparison to Baikal Monte Carlo� ��!��Comparison to experimental results� ��!��Data structures� ��!��Digitisation� �Execution and tracking� ��! �� !��Fast tracking� �� !�� !�� General Description� ��! �Initialization� ��!��Internal event generation� ��Noise generation� ��Signal generation� ��!��Simulation of "Cerenkov light� ��!��Simulation of OMs� ��!��

DMQT� �� !��Circuit Description� ��!��Design� ��!��Thresholds� ��!��

DUMAND � �!� � �DUMAND I �SPS�� DUMAND II � �� !� � �� DUMAND II � CM� ��DUMAND II � Calibration� �� !��DUMAND II � General description� ��!��DUMAND II � JB� �� DUMAND II � JBEM� ��DUMAND II � SC� �� DUMAND II � Signal processing� ��!��DUMAND II � Triggering� ��!� � ��OCTAGON � �� TRIAD � �� Noise rate ��K�� !��OM� see EOM� JOMPrinciple� �Shore station� ��Site properties� ��

Eddington luminosity� �E�ective area� ��!� � ��

AMANDA � ��DUMAND I � �NESTOR � �� OCTAGON � �� TRIAD � �� KM�� NT�� !�� NT�� !��

NT�� !�� E�ective volume� ��!� EOM� �� !�� !��

After�pulses� ��Amplitude response� see Amplitude function�

�� !�� !��Calibration� � � ��!�� Dark noise� �� !�� Energy resolution� �� Environmental science application� ��Fast readout� see DMQTGeneral description� ��!��High voltage adjustment� ��!�� In situ operation� �� Mechanical design� ��!� RCU� �� !��Sensitivity �full illumination�� !��Sensitivity �point illumination�� !��Simulation� ��Smartness� � !��Threshold adjustment� ��!�� Time jitter� �� !�� Time resolution� ��!�� !�� Time response� see Timing functionTime slewing� ��!�� Transit time di�erence� �� !��

FFREAD� ��

Gamma absorption� �Gamma gamma interaction� �Gamma neutrino ratio� �GEANT� �� ! �� Glashow resonance� ��

Hamamatsu R�� HBOOK� �� HIGZ� ��

IMB� � �Incomplete Gamma function� ��

JOM� �� Calibration� �� Fast readout� �� !��General description� ��In situ operation� �� Simulation� ��

JULIA � � !��Data transmission� ��OM� ��

��K� ��!��Abundance and decay� ��Characteristics of "Cerenkov light� ��!�� Count�rate calculation� �� !�� !

��

n INDEX

Count�rate measurement� �� !�� Count�rate versus attenuation length� ��Count�rate versus distance� ��Count�rate versus OM sensitivity� ��Measurement of OM sensitivity and attenuation

length� ��!�� Rejection trigger� ��Signal characteristic� ��

Kamiokande� � �KM��

Light attenuation� �!��Absorption� �Coe+cient� �Length� �Parameterization� ��Scattering� �Scattering function� �

Luciferase� ��

Magnetic monopoles� ��Mean visual range� ��!��Muon

Angular "Cerenkov light distribution� ��Atmospheric� see Atmospheric muonsCalculation of "Cerenkov light� ��!��De#ection from Earth magnetic �eld� ��Fake� ��Minimal ionizing� �� !�� !��Multiple scattering� ��!��Naked� �� !��Pointing accuracy� �� !�� Range� �� Recoiling� ��!��Secondary processes� � �� !�� Simulated tracks� �� Standard model� �Upward�going� ��

Muon energy loss� �!�� ! Bremsstrahlung� �� !��Catastrophic energy loss� �� !��Crossections for secondary processes� Delta ray production� �� !��Ionisation� �Nuclear Interaction� �� Pair production� �� !��Quasi continuous energy loss� ��!�� !��

Muon telescope� ��

NESTOR � � !��Neutralino� �!�Neutrino

Astrophysics� � �Atmospheric� �� Atmospheric neutrino anomaly� Cosmological origin� �

Interaction� �� !�Oscillations� � Prompt� Standard model� �!

Neutrino production� �!�� AGN� ��Beam dump� �!�Dark matter� �!�� Meson decay� �Neutralino annihilation� �!�Point sources� �R�parity violation� �Ratio �� UHE� �VHE� �

Neutrino sourceDetectability� �� Guaranteed sources� �Hidden source� �Standard source� ��

Neutrino source candidate�C�� C�� Cen A �NGC �� Crab� �� Cyg X�� Cyg X�� Galactic Centre �SGR A�� Galactic plane� Geminga� �� Her X�� LMC X�� M�� Andromeda�� M �� Mk �� Mk �� NGC �� SN�� A� �� SS �� Sun� Vela� ��

Neutrino telescopeAngular resolution� see Angular resolutionBackground� ��Design� ��!��E�ective area� see E�ective areaMinimum detectable #ux �MDF�� Principle� �� !� Signature of events� ��!�� !�

Neutron star� ��

OMPair versus single� �!�� !��

OM readoutLogarithmic versus linear� ��!��TOT versus QT� ��!��

INDEX o

Pauli� Wolfgang� �Paw� � ��Philips XP�� !�� !��

Cathode sensitivity� ��!��Properties� see EOMPulse structure� ��Scintillator decay� ��

Photoelectrons �pe�� Power�law index� �Pulsar� �

Quasar� ��Quasar��

R�parity� �Radioactivity �natural�� see ��KReines� Fred� �

SiEGMuND � �Data format� �� !��Data processing� �� ! � ��!��Detector simulation� see DadaEvent generation� � � ��!��General description and overview� ��!��I�O� see rdmc� �! Reconstruction� see recoos� ��

SiEGMuND Program modules� ��!�� Dadabase� �� basiev� �� calib� ��cpfeil� ��danton� ��deff � ��!�� fint� ��geff � ��muff � �� muo�� nue�� rdmc� �� !��recoos� �� rtt� � ��soff � ��!��Dada � see Dada

Simulation� see SiEGMuNDSmart PMT� see EOM� SmartnessSN�� A� neutrino detection� Solar Neutrino Problem� Spacing of Optical Modules� ��Spectral index� �Super�symmetry� �Supernova� � ��Supernova remnant� ��

Time residual� see "Cerenkovlight� Time residualTiming function� ��

WIMPS� �

X�ray binary� �

ZEBRA� ��

Acknowledgement

This work would not have been realized without the help and support of various people and institutions�I thank Prof�Dr�G�Fl�ugge and Prof�Dr�Ch�Berger for taking over the responsibility for this thesis andfor giving me the chance to continue this exciting branch of physics at Aachen�I am indebted to Dr�Christian Spiering� who not only supervised this work� but also spent large e�ortsgetting me through all di�culties and has last but not least been an excellent teacher and friend�Also thank you� my ino�cial co�advisor and friend Dr�Christoph Ley� for quite a lot*The electronic team around Dr�V�Commichau� especially C�Camps� has continuously supported me�Their help went far beyond the scope of electronics� I thank also all other members of the III� Physikalis�che Institut� RWTH Aachen�Special thanks goes to to Ol4e Streicher for his smart ideas during our SiEGMuND project and to mycompanion during the EOM development Ulrich Berson�Spasibo to the whole BAIKAL collaboration� namely Igor Belolaptikov� Alexander A�Doroshenko�Dr�Bayarto K�Lubsandorzhiev� Dr�Elonora Ossipova and Dr�Igor Sokalski� Prof�Dr�G�V�Domogatzkymade it possible for me to join this excellent team of physicists� Special thanks also to the greatZeuthen team� Stephan Hundertmark� Dr�Albrecht Karle� Dr�Jaanus Krabi� Dr�Thomas Mikolajski�Dirk Pandel� Ol4e Streicher� Dr�Thorsten Thon� Dr�Ralf Wischnewski�Prof�Peter C�Bosetti introduced me to this �eld of physics� He is responsible for the initial idea of thisthesis and strongly enriched it at various stages� His group� the Aachen DUMAND� gang was a vitalplatform�A big mahalo goes to the DUMAND� collaboration� especially to Prof�Dr�P�K�F�Grieder� Prof�Dr�JohnG�Learned� Prof�P�Minkowsky and Dr�A�Okada�I thank all contributors to the EOM�project� I personally thank Prof�P�Koske for his engagement inthis project and his support for my work at Kiel and Hawaii� The people involved in this project arelisted in details in �� Especially I want to mention F�Bei5el� Eduard Hermens� Dr�Michael Rietz�Gerhard Wurm from RWTH Aachen� Thomas Bolln� Dr�Urban Keussen� Dr�J�urgen Rathlev fromUniversity Kiel� Dr�Lars Thollander from University Stockholm� S�O�Flyckt from Philips PhotonicsBrive� Dr�Shigenobu Matsuno and Marc Mignard from University Hawaii� I thank also my house�mateVolker Pichinot for his friendship and patience during the long time at Kiel�I thank all proof�readers� especially Dr�Christoph Ley� Dr�Christian Spiering� Dr�Reiner Schulte� Dr�RalfWischnewski�I wish to thank all my friends and my family especially Jutta� Stephanie and my parents�This work was supported by the Claussen Stiftung im Stifterverband f�ur die Deutsche Wissenschaft�Projekt�Nr��TS ��

I dedicate this work to the memory of my dear friend Dr�Andreas Kaser� who died due to a suddenleukemia on � April �� He was strongly involved in the evaluation of eq�� and eq��A�� andaccompanied me during the time of scienti�c education with help and good fellowship�

Lebenslauf

Pers�onliche Daten

Name WiebuschVornamen Christopher� Henrik� Viktor

Geboren �� Juni �� in Bonn

Ausbildungsweg

�� St�Andreas Grundschule in Bonn�Bad Godesberg

�� Besuch des P�adagogiums Godesberg� Abitur

Okt� �� Beginn des Studiums der Physik an der RWTH Aachen

April �� Diplom Vorpr�ufung in Physik

M�arz �� Abschlu5des Diploms in Physik

M�arz �� Beginn der PromotionsarbeitF�orderung durch ein Stipendium der ,Claussen Stiftung&im Stifterverband f�ur die Deutsche Wissenschaft

Dez�� Promotionspr�ufung in Physik

The Detection of Faint Light in Deep Underwater Neutrino Telescopes

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