Guillemaud Thesis

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
2015

Radiation Fluence to Dose Conversion Factors for Sensors Studied in
SLAC Experiment T-506
By
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 2
cm . 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  2
10 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 2
1cm 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
N
N
   , (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 2
1cm 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 2
cm and per incident electron, as a function of the incoming beam electron energy.
For example an 10  delivers 210nC
cm
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 kRad
Dose 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   2160
1 /Rad
nC 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 2.43
s
kRad it would take approximately 11.5hours 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 2
10 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 2
1cm 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.

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