Packages for Monte Carlo simulation of radiation interaction with matter Saint-Petersburg State...

Packages for Monte Carlo simulation of radiation interaction with matter

Saint-Petersburg State UniversitySaint-Petersburg State UniversityDepartment of PhysicsDepartment of PhysicsDivision of Computational PhysicsDivision of Computational Physics

JASS-06

Sergey Ananko

OutlineOutline

ActualityActuality Short description of physical modelShort description of physical model Monte Carlo methodMonte Carlo method Geant4Geant4 FlukaFluka Comparison of packagesComparison of packages ConclusionsConclusions Future plansFuture plans

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ActualityActuality

GeneralGeneral

Nuclear physicsNuclear physics High-energy physicsHigh-energy physics Cosmic raysCosmic rays Neutrino physicsNeutrino physics MedicineMedicine

ParticularParticular

Necessity to have several Necessity to have several ways of the solution of the ways of the solution of the same problemsame problem

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Gamma-raysGamma-rays

Gamma-rays – high-frequency electromagnetic oscillations: Gamma-rays – high-frequency electromagnetic oscillations: and aboveand above

Gamma-particles characteristics:Gamma-particles characteristics:velocity:velocity:

energy:energy:momentum: momentum:

wave length:wave length:

Gamma photons energy range:Gamma photons energy range:

Effects: photoelectrical absorption, Compton effect and pair productionEffects: photoelectrical absorption, Compton effect and pair production

Physics reviewPhysics review

12010 s

scmc 10103

E

cp

serg 2710054.1

E

cm0

MeVEq 10;01.0

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Scattering cross-sectionScattering cross-section

- number of photons - number of photons through unit square per unit of through unit square per unit of timetime - number of scattered - number of scattered photonsphotons

- cross-sectioncross-section

- number of - number of scattered gamma photonsscattered gamma photons

- probability - probability of photons scatteringof photons scattering


0N

N

0N

Ns

dnNdN s 00

dlndw s 0

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0NN

O

X

Y

Z

Photoelectrical effectPhotoelectrical effect

Photoelectrical effect is a process Photoelectrical effect is a process of gamma photon absorption of gamma photon absorption by atom of substanceby atom of substance

- photoelectron energy- photoelectron energy

- photon energy- photon energy - binding energy- binding energy


bqe EEE

eE

qEbE

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Compton effectCompton effect

Compton effect is a process of gamma photon scattering on electron of atomCompton effect is a process of gamma photon scattering on electron of atom

- scattered photon energy - incident photon - scattered photon energy - incident photon energyenergy

- electron rest-energy- electron rest-energy - wave length after interaction - wave length before - wave length after interaction - wave length before

interactioninteraction - Compton electron energy- Compton electron energy

E


cos11'

0

cm

EE

E

cos1' 'EEEe

cm0

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Compton effectCompton effect

- - minimal value of scattered photon energyminimal value of scattered photon energy

- maximum photoelectron energy- maximum photoelectron energy E

cmE

Ee

21 0

cmEE

E

021

'

;0 2;0

E

'E

eE

- gamma-quantum- gamma-quantum scattering anglescattering angle

- Compton electron- Compton electron scattering anglescattering angle


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Pair productionPair production

Pair production is a process of generation electron-positron pair in Pair production is a process of generation electron-positron pair in nucleus or atom field nucleus or atom field


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Total interaction coefficientTotal interaction coefficient

Number of photons lost by the beam:Number of photons lost by the beam: wherewhere

- cross-sections of Compton effect, photo effect, - cross-sections of Compton effect, photo effect, pair productionpair production

- atom number per unit of volume- atom number per unit of volume - flux density- flux density - beam cross-section- beam cross-section

- total interaction cross-section per one - total interaction cross-section per one atom of matteratom of matter

Quantum energy loss per unit of time:Quantum energy loss per unit of time:

ndlSNdN ppfCs 0


Cs f pp

n0N

S

ppfCs

ndlfSENndlfSENndlfSENdE ppppffCsCs 000

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Total interaction coefficientTotal interaction coefficient

n

- linear absorption coefficient- linear absorption coefficient

- mass absorption coefficient- mass absorption coefficient

- matter density - matter density


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mass absorption coefficient for airmass absorption coefficient for air

pp

meVE,

Cs

f

gcm2

ModelModel

Gamma energy range:Gamma energy range:


MeVE 4;2.0

3111 m

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Point-like sourcePoint-like source

Air-filled Air-filled

cubic volume:cubic volume:

Energy and angular distribution of Energy and angular distribution of secondary particlessecondary particles

Detecting planeDetecting plane

Two approachesTwo approaches

Deterministic methodsDeterministic methods

Finite difference methodFinite difference method Finite element methodFinite element method

The Monte Carlo methodThe Monte Carlo method

The Monte Carlo MethodThe Monte Carlo Method

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Model: probability estimationModel: probability estimation

Source – anisotropic point-like Source – anisotropic point-like monoenergetic gamma monoenergetic gamma photon sourcephoton source

Shield – relatively thick Shield – relatively thick spherical shell, spherical shell, only one sort of atomonly one sort of atom

Effects:Effects: Elastic scatteringElastic scattering AbsorptionAbsorption

Effects are characterized by:Effects are characterized by: Cross-sectionCross-section Probability density function for Probability density function for

path lengthpath length


dxe x

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Simulation steps

First step: free path length

Second step: scattering or absorption

Third step: scattering angle

Further steps: repeating

- number of generated trajectories - number of escaped gamma

photonsphotons - scoreEstimated probability of escape:

Variance of the :

Relative error

The Monte Carlo Method

iix 1ln1

1;1.01.0;01;0

i

N

z

n

2

2

2 11

N

nNns

Ns

NsVar

i iiii

Nn

nN

s

NsVar i

is

NnsNs i 1is

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Variance reductionVariance reduction

Brute-force approachBrute-force approach TruncationTruncation Population control:Population control: SplittingSplitting Russian rouletteRussian roulette Probability modificationProbability modification Pseudodeterministic methodsPseudodeterministic methods


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Geometry descriptionGeometry description

Combinatorial objectCombinatorial object Surface-sense objectSurface-sense object


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Monte Carlo packagesMonte Carlo packages

Main components:Main components: Data base of cross-sections Data base of cross-sections

and other parametersand other parameters Theoretical baseTheoretical base Random number generatorRandom number generator Tool for geometry descriptionTool for geometry description

Main aspirations:Main aspirations: Extended range of abilityExtended range of ability FlexibilityFlexibility

Examples:Examples:

MNCP, Fluka, Geant, Geant4, Vulcanu, PYTHIA, ARIADNE MNCP, Fluka, Geant, Geant4, Vulcanu, PYTHIA, ARIADNE and so onand so on


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Geant4: statusGeant4: status

Geant4 is a detector description and simulation Geant4 is a detector description and simulation tooltool

Application areas:Application areas:High-energy physics, nuclear experiment, medical, accelerator and space High-energy physics, nuclear experiment, medical, accelerator and space

physics studiesphysics studies

History:History:1974 – GEANT first version1974 – GEANT first version1982 – the appearance of GEANT31982 – the appearance of GEANT31998 December – first release of GEANT41998 December – first release of GEANT4

Geant4 is a free softwareGeant4 is a free softwareIt can be downloaded from It can be downloaded from URL: URL: http://geant4.cern.ch

Operating systems: Operating systems: Unix, Linux, WindowsUnix, Linux, Windows

GEANT4GEANT4

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Main featuresMain features

GEANT4 is written in C++GEANT4 is written in C++

GEANT4 is based on an object-oriented technologyGEANT4 is based on an object-oriented technology

Experiment stages:Experiment stages: Detector descriptionDetector description Source descriptionSource description Physics descriptionPhysics description Detector reaction descriptionDetector reaction description

GEANT4GEANT4

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Fluka: statusFluka: status

Fluka is a general purpose tool for calculations of particle transport and interactions with matter, covering an extended range of Fluka is a general purpose tool for calculations of particle transport and interactions with matter, covering an extended range of applications spanning from proton and electron accelerator shielding to target design, calorimetry, activation, dosimetry, applications spanning from proton and electron accelerator shielding to target design, calorimetry, activation, dosimetry, detector design, Accelerator Driven Systems, cosmic rays, neutrino physics, radiotherapy etc. detector design, Accelerator Driven Systems, cosmic rays, neutrino physics, radiotherapy etc.

Fluka is distributed under the licence as a tar fileFluka is distributed under the licence as a tar file

It can be downloaded from its web-site: It can be downloaded from its web-site:

www.fluka.org

Supported platforms:Supported platforms: - Hewlett-Packard 9000 Series 700/800 running HP-UX - Hewlett-Packard 9000 Series 700/800 running HP-UX - Sun running SunOS - Sun running SunOS - Intel PCs running LINUX: - Intel PCs running LINUX: - RedHat 7.3 - RedHat 7.3 - RedHat 9.0 - RedHat 9.0 - Scientific Linux 4.1 `- Scientific Linux 4.1 ` - Fedora Core- Fedora Core

FlukaFluka

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History: History: First generation – the Fluka of the 70thFirst generation – the Fluka of the 70thSecond generation – the Fluka of the 80thSecond generation – the Fluka of the 80thThird generation – the Fluka of todayThird generation – the Fluka of today

Main featuresMain features

Fluka is written in FortranFluka is written in Fortran

Package consists of compiled libraries, user routing in source form, Package consists of compiled libraries, user routing in source form, INCLUDE files, various unformatted and formatted data INCLUDE files, various unformatted and formatted data andand aa numbernumber ofof scriptsscripts forfor compiling,compiling, linkinglinking andand runningrunning thethe programprogram..

Structure of input file: particle source, geometry, transport options, Structure of input file: particle source, geometry, transport options, detectorsdetectors

Example: source (kind of particle, energy, location in space, distribution)Example: source (kind of particle, energy, location in space, distribution)

BEAM 50.E+00 PROTONBEAM 50.E+00 PROTONBEAMPOS 0.0 0.0 -50.0BEAMPOS 0.0 0.0 -50.0

FlukaFluka

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Comparison: main featuresComparison: main features

photoelectric effect:photoelectric effect:Compton effect:Compton effect:

multiple scattering:multiple scattering:

Geant4Geant4 FlukaFluka

keV1keV1 keV1

keV1keV1keV10keV1keV10

pair production:pair production:

keV105 - recommended - recommended value for threshold value for threshold for Flukafor Fluka

threshold energythreshold energy

ConclusionConclusion

Both Fluka and Geant4 provide with ability Both Fluka and Geant4 provide with ability of simulation particles transport in a very of simulation particles transport in a very extended energy range.extended energy range.

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Future plansFuture plans

To receive results from FlukaTo receive results from Fluka To process themTo process them To compare them with Geant4To compare them with Geant4 To parallel both Fluka and Geant4To parallel both Fluka and Geant4

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Thank you for attentionThank you for attention

Packages for Monte Carlo simulation of radiation interaction with matter Saint-Petersburg State...

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