UNIVERSITY of CALIFORNIA

SANTA CRUZ

RADIATION FLUENCE TO DOSE CONVERSION

FACTORS FOR SENSORS STUDIED IN

SLAC EXPERIMENT T-506

A thesis submitted in partial satisfaction of the

requirements for the degree of

BACHELOR OF SCIENCE

in

APPLIED PHYSICS

by

Nikolas P. Guillemaud

June 5, 2015

––––––––––––––––––––––– –––––––––––––––––––––––

Professor Bruce Schumm Professor David P. Belanger

Advisor Senior Theses Coordinator

____________________________

Professor Robert Johnson

Chair, Department of Physics

Copyright © by

Nikolas P. Guillemaud

2015

Radiation Fluence to Dose Conversion Factors for Sensors Studied in

SLAC Experiment T-506

By

Nikolas P. Guillemaud

Abstract:

Stanford Linear Accelerator experiment T-506, under the direction of the Santa Cruz

Institute for Particle Physics, aims to evaluate the radiation hardness of sensor materials for

use in the proposed International Linear Collider forward calorimeters. We discuss the

procedure for evaluating sensor resiliency and how to estimate the radiation dose delivered to

the sensor by the SLAC End Station A Test Beam. We perform Monte Carlo computer

simulations to estimate the shower conversion factor , which is the mean value of the

radiation fluence at the sensor, per incident electron, as a function of electron energy.

Analysis of the simulated data produces fluence distribution profiles that decrease radially

from center of the radiated sensor. This is compensated for by rastering the sample across the

electron beam, providing even illumination over 2cm . The rastering is taken in to account

in the calculation of . We observed that the radiation fluence is linearly dependent upon the

incident electron energy.

iv

Contents

Dedication v

Acknowledgements vi

1. Introduction 7

1.1. International Linear Collider and Beamline Calorimeter . . . . . . . . . . . . 7

2. Beamline Calorimeter 10

2.1. BeamCal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2. SLAC T-506 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1. Charge Collection Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.2. Irradiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3. Computer Simulations 16

3.1. Simulation Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2. Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Appendix A 22

References 23

v

To my

Mother and late Father,

Jean and Gerry Guillemaud

Who impressed upon me the values of education, hard work, and determination.

and

My friends and family who encouraged me to chase my lofty goals and overcome

the numerous hurdles along the way.

vi

Acknowledgements

I would like to thank Professor Schumm for being such an approachable and

personable mentor.

Additionally, I would like to thank all of the excellent professors and teachers I

have had the pleasure of learning from on my journey.

7

1. Introduction

1.1. International Linear Collider and Beamline Calorimeter

The proposed International Linear Collider (ILC) would be the culmination of more than two

decades of research and development from an international collaboration of over 300 institutions.

The Santa Cruz Institute for Particle Physics (SCIPP) at the University of California Santa Cruz

(UCSC) has contributed to the project nearly from its start and its members continue to conduct

research towards the development of the ILC.

Exploring the science goals for this particle collider is needed to further our understanding of

the nature of matter and its interactions at the most fundamental level within the Universe. It

would assist in the refinement and possibly the extension of the Standard Model of particle

physics, which attempts to combine three of the four fundamental forces of nature; the

electromagnetic, weak, and strong forces. The Standard Model has made successful predictions

but requires additional development using data obtained at higher energies to unlock new

physics. The scientific value of these complicated and expensive colliders was demonstrated at

the Large Hadron Collider (LHC) in 2012 with the discovery of a boson that exhibited the

characteristics of a Higgs field quantum. The discovery of this Higgs boson invigorated the

particle physics community and accelerated plans for the construction of the ILC (Feder 2013).

The ILC would be a linear, electron-positron collider based on 1.3 GHz superconducting

radio-frequency accelerating technology and will operate in the energy range from 90 to 500

GeV and eventually 1 TeV (Behnke 2013). This lepton collider will have a distinct advantage

over hadron colliders due to the fact that there will be fewer constituent particles involved. This

will make the analysis of the collisions much simpler. After verifying the results found at the

LHC, it will explore more predictions made by the Standard Model. Specifically it will be used

8

to study Higgs boson reactions with greater precision than the LHC, pair production of EW

bosons, and to explore for new particles (Behnke 2013). As the upgrade cycles proceed, it will be

able to search for the possible constituents of dark matter and, at 1 TeV, further the search for

evidence supporting the theory of supersymmetry beyond the standard model. The ILC will have

the capability to perform these experiments with unprecedented precision (Behnke 2013). A

diagram of the proposed ILC and its subsystems is shown in Fig. 1.

http://www.linearcollider.org/pdf/ILCposterNEW_200702.pdf

Figure 1: Diagram of proposed ILC (Behnke 2013). The primary components are the

e (electron) and e

(positron) sources, the main linear accelerators (linac), and the

central detection area where the beams intersect.

The collision point of the ILC will be instrumented by two detector systems, the International

Large Detector (ILD) and the Silicon Detector (SiD). These detection systems are

complementary and will enable independent verification of experimental results, and will be

swapped (via a rail system) with one another on a periodic basis.

Our interest lies in the development of a calorimeter at the most forward part of the detectors.

The proposed Beamline Calorimieter (BeamCal) (Fig. 2) will provide fast estimation of the beam

9

luminosity and targeting, allowing fine adjustment of the beam. Additionally, it will provide a

veto for “two photon” events in which the electron and positron are only slightly deflected by

one another in their collision (Behnke 2013).

http://www.interactions.org/imagebank/images/SL0078H.jpg

Figure 2: Position of BeamCal within the detector (Behnke 2013). This is a cross

section of the symmetrically designed detector. On the right is the beam pipe

and to the left is the interaction point (IP). Adjacent to the Beamline and

covering the smallest radii relative to the IP, BeamCal will be exposed to large

doses of radiation. The majority of a collision event would be

absorbed/detected by the central region of the SiD (immediately surrounding

the IP) and would consist of the vertex tracker and encasing calorimeters.

BeamCal would contribute to the overall hermiticity of the SiD by “capping”

the ends.

The very forward location of BeamCal will put it in a region of high radiation produced

by the beam collisions. This necessitates that it be constructed with radiation hard

materials. We test prospective sensor materials in intense radiation environments induced

by showers of beam in metal target. The purpose of this thesis is to develop the calibration

of radiation fluence in the induced showers as a function of beam current and energy.

10

2. Beamline Calorimeter

2.1. BeamCal

Of layered design, BeamCal will be a cylindrical electromagnetic sampling calorimeter (Fig.

3.1). It will consist of active detection layers between sections of a passive absorber, most likely

tungsten. The active detection layers are radially-segmented, disk sensor arrays composed of

doped semiconductor materials. The proposed semiconductors for BeamCal sensors include

gallium arsenide, silicon diode, silicon carbide, CVD diamond, and sapphire. The sensors’

segmentation is relatively small 210 100mm which allow for accurate reconstruction of the

particle showers induced by high-energy electrons or positrons.

When an incident electron (or positron) interacts with the passive absorber it induces an

electromagnetic shower (Fig. 3.2). The shower propagates by way of the bremstrahlung and pair

production processes, with the number of particles in the shower growing exponentially until the

average energy per particle is low enough so that they get absorbed with no further radiation or

pair production, and depositing energy throughout the instrument. The detection layers track the

evolution of the shower by sampling the number of charged particles in the showers as a function

of depth and transverse position. The particle enters the active area of the sensor and creates an

observable signal on the electrode. Therefore, the energy and width of the shower can be

reconstructed as a function of position in the BeamCal and compared to those expected for EM

showers of a given energy.

Centered on and immediately surrounding the ILC beampipe, our central challenge for

BeamCal sensors is the requirement of radiation hardness. They must withstand a high fluence of

radiation, up to 100 MRad per year (Behnke 2013), and retain their detection capabilities.

11

1. Prof. Schumm 2. http://www-cdf.fnal.gov/~group/WORK/DISS_PAGE/EM_SHOWER.gif

Figure 3: (1.) Example of an electromagnetic calorimeter. This calorimeter is constructed of

tungsten and silicon. Note that the transverse depth of the passive absorber sections

correspond to multiples of radiation length RadL .

(2.) Electromagnetic shower. At high energies, brehmstrahlung and pair production are the

dominant processes. One radiation length RadL is roughly the average distance the charged

particle will travel before interacting.

2.2. SLAC T-506

As part of the Forward Calorimeter (FCAL) collaboration, SCIPP and Dr. Bruce Schumm’s

research group aim to test various types of sensors for radiation hardness. In cooperation with the

Stanford Linear Accelerator (SLAC), radiation damage studies are performed on candidate

sensors which simulate the radiation exposure that BeamCal is anticipated to encounter. This

experiment is referred to as SLAC T-506. Under the direction of Dr. Schumm, the T-506

experiment is carried out in five stages consisting of two main procedures, the characterization

12

and irradiation of the sensor samples. The samples are characterized before irradiation to

establish baseline performance. Characterization includes measurement of the current,

capacitance, and charge collected in response to a penetrating β particle, as a function of sensor

bias voltage. They are then irradiated at SLAC and characterized again to assess radiation

damage. For selected sensors, annealing studies are done, in which the sensors are performance

tested a final time to observe any recovery of performance after heating.

2.2.1. Charge Collection Efficiency

The sensors’ charge collection efficiency is measured using an in-house apparatus located at

SCIPP (Fig.4). The apparatus uses a source placed in line such that the emitted particles pass

through the sensor and in to the aperture 2 7x mm of the scintillator behind it. The size of the

scintillator aperture requires that the sensor be uniformly irradiated over 21cm area. Thus, the

sensor must be rastered through the beamline during irradiation. Looking for temporal

coincidences between scintillator and sensor signals allows for the discrimination of particle

signatures from the source against those from thermal excitations or cosmic rays. The

amplified signals from the sensor and scintillator are fed through a field programmable gate array

(FPGA), and in to a computer for analysis.

13

Image Courtesy of Prof. Schumm

Figure 4: Charge collection efficiency apparatus. The source is placed in the holder and

charged particles (electrons) pass through the sensor sample and in to the aperture of the

scintillator. The signals are then fed in to the field programmable gate array and in to the

computer for analysis.

By counting sensor signals above a variable voltage threshold that coincide temporally

between the sensor and scintillator, and above a certain voltage, it is possible to ascertain the

sensors’ efficiency for collecting charge released by the passage of particles for this radiation

source. Thus, for any given setting of the threshold, the signal efficiency is given by

1 miss

trig

NN

, (1)

where miss trig coinN N N and trig PMT noiseN N N . Note that coinN is the number of events

counted by the silicon and the PMT in coincidence, noiseN is the number of events counted by the

PMT in a run without β sources, and PMTN is the number of events counted by the PMT with the

source. After converting signal voltage to detected charge via a calibration function, the mean

14

charge collection efficiency is determined by finding the charge threshold for which the signal is

50% .

2.2.2. Irradiation

The irradiation process is conducted at the SLAC test beam facility End Station A (Fig.5).

Mauro Pivi SLAC, ESTB 2011 Workshop

Figure 5: Location of sensor irradiation at SLAC. Note that LINAC is an acronym for linear

accelerator.

This location is where electrons, diverted from the Linac Coherent Light Source (LCLS), meet

the experimental sensor irradiation setup (Fig. 6).

Inside an insulated container, maintained at close to 0 C to avoid annealing, the sensor is

positioned between tungsten radiators and attached to a motor. The thickness of the tungsten is

chosen to be approximately six times the average radiation length of an electron in order to

maximize the fluence at the sensor. Fluence is defined as the total particle radiation incident on

the sensor per unit area. The motor moves the sensor perpendicularly across the beam in a

rastering pattern, ensuring even illumination on a 21cm area. Once the sensor irradiation has

taken place, the integrated dose rate must be estimated.

15

Images Courtesy of Prof. Schumm

Figure 6: (1.) Graphical representation of sensor irradiation setup.

(2.) Actual experimental setup for sensor irradiation at SLAC.

In order to estimate the dose rate, a parameter called the shower conversion factor must

first be determined. The shower conversion factor gives the mean fluence of particles e at the

sensor, per 2cm and per incident electron, as a function of the incoming beam electron energy.

For example an 10 delivers 210nCcm

at the sensor per 1nC delivered on the target. The

dose rate is then calculated as

2

2

160 10 0.15 10 2.43

1

nC nC Rad kRadDose Rate Hz

nCpulse cm s

cm

, (2)

16

where 10Hz is the typical frequency of the beam, 0.15nC is the typical charge delivered per

pulse, and 21601 /RadnC cm is the standard fluence to Rad conversion factor for electrons and

positrons. This calculation is done to estimate the total dose delivered to the sensor for a given

period of time and anticipate the required beam time for upcoming experiments. For example, at

the dose rate of 2.43s

kRad it would take approximately 11.5 hours of beam time to expose the

sensor to 100 MRad. In Section 3 we discuss the simulations performed to estimate the shower

conversion factor .

3. Computer Simulations

At SCIPP, we have performed Monte Carlo computer simulations to estimate the shower

conversion factor . These simulations provide a mean value for the radiation fluence at the

sensor, per incident electron, as a function of electron energy. The factor is also dependent

upon the geometry of the experimental setup.

The simulations were performed with GEANT 3.21, a Fortran program developed by CERN

that simulates the passage of subatomic particles through matter. This program, running on

SLAC servers, recreates the sensor irradiation configuration (Fig. 6.2) and simulates a beam of

particles passing through that experimental model.

3.1. Simulation Procedure

First, we edited the simulated geometry to mimic the experimental setup seen in Figs. 6(1) &

6(2) and summarized in Table 1. We set the thickness of each element as follows: pre-radiator

0.7cm , post-radiator 1.43cm , sensor 0.03cm . The program places each element of the setup by

17

its center point. With the simulated beam originating from the origin and traveling in the positive

Z direction, the pre-radiator was arbitrarily placed at 1.65Z cm , this put the back face of the

pre-radiator at precisely 2.0Z cm . The post-radiator was placed at 43.01Z cm and the sensor

at 44.28Z cm . Each element was modeled as 210 10x cm square.

Table 1: Geometry of experimental setup used in simulations.

The positioning of each layer was then verified using the interactive visualization routine within

GEANT (Fig. 6).

Figure 6: Simulated experimental configuration with updated geometry. The beam enters

from the origin on the right side and travels in the positive Z direction. The beam electrons

interact with the pre-radiator and produce electrons (red) and positrons (green) which then

travel through the post-radiator and sensor on the left side. Note that, due to the large

quantity, photon paths have been excluded from the visualization.

Layer Thickness (cm) Position (cm)

(on center from origin)

Tungsten pre-radiator 0.7 1.65

Tungsten post-radiator 1.43 43.01

Sensor 0.03 44.28

18

Next, we chose the number of incident particles to be 2000 , set their desired energy in GeV,

and executed the simulation. We then manipulated the results of the beam simulation to provide

the “fluence profile”. This is an expression for the mean fluence as a function of position on the

detector relative to the “center point”, the position the beam would strike if the tungsten radiator

were not present. The program rad.kumac creates the simulated fluence profile and organizes it

in to radial bins as a function of distance from the center point. With the fluence profile modeled

in that way, we then used that fluence profile to run the raster program. This program calculates

the fluence distribution over a 21cm area averaged over the full rastering scan that results from

moving the detector in 0.1cm steps in the two transverse dimensions across the beam. The

resulting average fluence is calculated for an array of points on the face of the sensor. Note that

due to symmetry, this needs to be done only in the 1st quadrant of the sensor. This rastering

program thus simulates the rastering done by the motor in the actual experiment. The result is the

average fluence as a function of position in the x-y plane. These simulations were run for

electron energies of 3 , 5 , 7 , 9 , 11, and 15GeV .

3.2. Simulation Results

The average shower conversion factor , as function of position in the x-y plane, for each of

the six electron energies are listed in Table 2 (Appendix A). Figure 7 depicts the symmetric

fluence profile for as a function of position along the y-axis, at each of those six energies.

Only the highest average value for , at each energy, is used for the stated sample sensor

exposures rates.

19

Figure 7: Cross sections of the symmetric, three dimensional fluence distributions for the

shower conversion factor for each of the six simulated electron beam energies.

Figure 8 shows the relation between electron energy and radiation fluence which is observed to

be nearly linear. This relation is well approximated by the equation

2.7515 3.1625electronE , (3)

where is the shower conversion factor and the electron energy is in GeV.

20

Figure 8: Shower conversion factor as a function of beam electron energy.

2.3. Conclusion

Examining the data in Table 2 (Appendix A), we observe fluence distribution profiles that

are consistent with expectation. The fluences are highest in the middle of the sample, 0,0

in x-y plane, and consistently decrease for points extending radially from the center. The least

amount of fluence is observed farthest from the center of the sample. This makes sense because

the center of the sample has the most radiation exposure as the sample is rastered through the

electron beam. We observed that the radiation fluence is linearly dependent upon the incident

21

electron energy as shown in Fig. 8. These shower conversion factors will be used to estimate the

sensor radiation exposures in an upcoming run of T-506 this Summer.

22

Appendix A:

Table 2: Mean fluence (α) as a function of beam energy ( 3 , 5 , 7 , 9 , 11, and 15GeV ) and

position in the x-y plane.

x-pos

(cm)

y-pos

(cm)

3GeV

(nC/cm2)

5GeV

(nC/cm2)

7GeV

(nC/cm2)

9GeV

(nC/cm2)

11GeV

(nC/cm2)

15GeV

(nC/cm2)

x-pos

(cm)

y-pos

(cm)

3GeV

(nC/cm2)

5GeV

(nC/cm2)

7GeV

(nC/cm2)

9GeV

(nC/cm2)

11GeV

(nC/cm2)

15GeV

(nC/cm2)

0.0 0.0 5.06 10.37 16.06 21.94 27.33 37.84 0.5 0.6 1.96 3.53 5.09 6.49 7.91 10.53

0.0 0.1 5.00 10.26 15.89 21.74 27.11 37.6 0.5 0.7 1.59 2.72 3.82 4.73 5.71 7.43

0.0 0.2 4.83 9.91 15.35 21.01 26.24 36.41 0.5 0.8 1.27 2.10 2.92 3.50 4.23 5.43

0.0 0.3 4.49 9.27 14.32 19.65 24.55 33.99 0.5 0.9 1.02 1.66 2.25 2.67 3.22 4.07

0.0 0.4 4.00 8.24 12.72 17.37 21.84 30.29 0.5 1.0 0.83 1.32 1.77 2.08 2.51 3.12

0.0 0.5 3.41 6.79 10.32 13.87 17.34 23.91 0.6 0.0 2.77 5.13 7.56 9.79 11.98 16.08

0.0 0.6 2.77 5.13 7.56 9.79 11.98 16.08 0.6 0.1 2.74 5.08 7.49 9.69 11.85 15.9

0.0 0.7 2.19 3.83 5.48 6.89 8.34 10.97 0.6 0.2 2.64 4.90 7.22 9.35 11.43 15.34

0.0 0.8 1.70 2.88 4.04 4.90 5.95 7.71 0.6 0.3 2.47 4.60 6.75 8.74 10.69 14.32

0.0 0.9 1.34 2.21 3.02 3.60 4.37 5.55 0.6 0.4 2.24 4.14 6.04 7.79 9.54 12.74

0.0 1.0 1.06 1.71 2.29 2.71 3.29 4.12 0.6 0.5 1.96 3.53 5.09 6.49 7.91 10.53

0.1 0.0 5.00 10.26 15.89 21.74 27.11 37.6 0.6 0.6 1.66 2.86 4.09 5.05 6.17 8.06

0.1 0.1 4.93 10.15 15.74 21.50 26.88 37.23 0.6 0.7 1.37 2.28 3.20 3.88 4.70 6.06

0.1 0.2 4.76 9.81 15.20 20.78 26.02 36.06 0.6 0.8 1.12 1.82 2.51 2.98 3.61 4.59

0.1 0.3 4.44 9.17 14.17 19.49 24.37 33.8 0.6 0.9 0.91 1.47 1.98 2.34 2.82 3.54

0.1 0.4 3.95 8.15 12.61 17.19 21.66 30.01 0.6 1.0 0.75 1.18 1.59 1.85 2.24 2.77

0.1 0.5 3.37 6.71 10.21 13.75 17.21 23.8 0.7 0.0 2.19 3.83 5.48 6.89 8.34 10.97

0.1 0.6 2.74 5.08 7.49 9.69 11.85 15.9 0.7 0.1 2.17 3.79 5.43 6.81 8.24 10.83

0.1 0.7 2.17 3.79 5.43 6.81 8.24 10.83 0.7 0.2 2.09 3.65 5.23 6.57 7.93 10.43

0.1 0.8 1.68 2.85 4.01 4.85 5.87 7.62 0.7 0.3 1.97 3.43 4.89 6.14 7.41 9.72

0.1 0.9 1.32 2.18 3.00 3.57 4.32 5.49 0.7 0.4 1.79 3.11 4.42 5.52 6.66 8.7

0.1 1.0 1.05 1.69 2.28 2.68 3.25 4.07 0.7 0.5 1.59 2.72 3.82 4.73 5.71 7.43

0.2 0.0 4.83 9.91 15.35 21.01 26.24 36.41 0.7 0.6 1.37 2.28 3.20 3.88 4.70 6.06

0.2 0.1 4.76 9.81 15.20 20.78 26.02 36.06 0.7 0.7 1.15 1.89 2.61 3.11 3.77 4.82

0.2 0.2 4.59 9.49 14.68 20.08 25.20 34.95 0.7 0.8 0.97 1.55 2.12 2.49 3.01 3.8

0.2 0.3 4.28 8.87 13.69 18.85 23.61 32.78 0.7 0.9 0.80 1.27 1.71 2.00 2.42 3.02

0.2 0.4 3.81 7.88 12.19 16.63 20.99 29.12 0.7 1.0 0.67 1.05 1.40 1.62 1.95 2.41

0.2 0.5 3.25 6.48 9.87 13.30 16.67 23.08 0.8 0.0 1.70 2.88 4.04 4.90 5.95 7.71

0.2 0.6 2.64 4.90 7.22 9.35 11.43 15.34 0.8 0.1 1.68 2.85 4.01 4.85 5.87 7.62

0.2 0.7 2.09 3.65 5.23 6.57 7.93 10.43 0.8 0.2 1.62 2.74 3.86 4.68 5.65 7.34

0.2 0.8 1.62 2.74 3.86 4.68 5.65 7.34 0.8 0.3 1.53 2.58 3.63 4.39 5.30 6.87

0.2 0.9 1.28 2.10 2.89 3.45 4.17 5.3 0.8 0.4 1.41 2.37 3.31 3.99 4.82 6.21

0.2 1.0 1.02 1.64 2.20 2.60 3.15 3.95 0.8 0.5 1.27 2.10 2.92 3.50 4.23 5.43

0.3 0.0 4.49 9.27 14.32 19.65 24.55 33.99 0.8 0.6 1.12 1.82 2.51 2.98 3.61 4.59

0.3 0.1 4.44 9.17 14.17 19.49 24.37 33.8 0.8 0.7 0.97 1.55 2.12 2.49 3.01 3.8

0.3 0.2 4.28 8.87 13.69 18.85 23.61 32.78 0.8 0.8 0.83 1.30 1.77 2.07 2.49 3.11

0.3 0.3 3.98 8.30 12.79 17.67 22.12 30.65 0.8 0.9 0.70 1.09 1.46 1.70 2.06 2.54

0.3 0.4 3.56 7.38 11.38 15.64 19.71 27.39 0.8 1.0 0.59 0.91 1.22 1.41 1.70 2.08

0.3 0.5 3.04 6.08 9.22 12.48 15.61 21.55 0.9 0.0 1.34 2.21 3.02 3.60 4.37 5.55

0.3 0.6 2.47 4.60 6.75 8.74 10.69 14.32 0.9 0.1 1.34 2.18 3.00 3.57 4.32 5.49

0.3 0.7 1.97 3.43 4.89 6.14 7.41 9.72 0.9 0.2 1.32 2.10 2.89 3.45 4.17 5.3

0.3 0.8 1.53 2.58 3.63 4.39 5.30 6.87 0.9 0.3 1.28 1.99 2.73 3.25 3.92 4.99

0.3 0.9 1.21 1.99 2.73 3.25 3.92 4.99 0.9 0.4 1.21 1.84 2.52 2.98 3.60 4.56

0.3 1.0 0.97 1.55 2.09 2.46 2.98 3.74 0.9 0.5 1.12 1.66 2.25 2.67 3.22 4.07

0.4 0.0 4.00 8.24 12.72 17.37 21.84 30.29 0.9 0.6 1.02 1.47 1.98 2.34 2.82 3.54

0.4 0.1 3.95 8.15 12.61 17.19 21.66 30.01 0.9 0.7 0.91 1.27 1.71 2.00 2.42 3.02

0.4 0.2 3.81 7.88 12.19 16.63 20.99 29.12 0.9 0.8 0.80 1.09 1.46 1.70 2.06 2.54

0.4 0.3 3.56 7.38 11.38 15.64 19.71 27.39 0.9 0.9 0.70 0.93 1.24 1.43 1.73 2.14

0.4 0.4 3.18 6.57 10.18 13.84 17.58 24.43 0.9 1.0 0.60 0.79 1.05 1.21 1.45 1.79

0.4 0.5 2.73 5.43 8.26 11.10 13.99 19.38 1.0 0.0 0.52 1.71 2.29 2.71 3.29 4.12

0.4 0.6 2.24 4.14 6.04 7.79 9.54 12.74 1.0 0.1 1.06 1.69 2.28 2.68 3.25 4.07

0.4 0.7 1.79 3.11 4.42 5.52 6.66 8.7 1.0 0.2 1.05 1.64 2.20 2.60 3.15 3.95

0.4 0.8 1.41 2.37 3.31 3.99 4.82 6.21 1.0 0.3 1.02 1.55 2.09 2.46 2.98 3.74

0.4 0.9 1.12 1.84 2.52 2.98 3.60 4.56 1.0 0.4 0.97 1.45 1.95 2.28 2.76 3.45

0.4 1.0 0.90 1.45 1.95 2.28 2.76 3.45 1.0 0.5 0.90 1.32 1.77 2.08 2.51 3.12

0.5 0.0 3.41 6.79 10.32 13.87 17.34 23.91 1.0 0.6 0.83 1.18 1.59 1.85 2.24 2.77

0.5 0.1 3.37 6.71 10.21 13.75 17.21 23.8 1.0 0.7 0.75 1.05 1.40 1.62 1.95 2.41

0.5 0.2 3.25 6.48 9.87 13.30 16.67 23.08 1.0 0.8 0.67 0.91 1.22 1.41 1.70 2.08

0.5 0.3 3.04 6.08 9.22 12.48 15.61 21.55 1.0 0.9 0.59 0.79 1.05 1.21 1.45 1.79

0.5 0.4 2.73 5.43 8.26 11.10 13.99 19.38 1.0 1.0 0.52 0.68 0.91 1.04 1.25 1.53

0.5 0.5 2.36 4.55 6.79 8.97 11.26 15.44

23

References:

1. Behnke, Ties. “The Linear Collider Technical Design Report – Volume 1-4.”

http://www.linearcollider.org/ILC/Publications/Technical-Design-Report 6/12/2013

2. Feder, Toni. “Invigorated and unified, US particle-physics community considers

future directions”, Physics Today, October 2013.