Jan 5, 2016 - Department of Physics, Northern Illinois University, DeKalb, IL 60115, USA; ... Fermi National Accelerator Laboratory, Batavia, IL 60510, USA;.
arXiv:1601.00249v2 [physics.ins-det] 5 Jan 2016
FERMILAB-TM-2617-AD-CD-E
Calibration and GEANT4 simulations of the Phase II Proton Compute Tomography (pCT) Range Stack Detector
January 6, 2016 S. A. Uzunyan, G. Blazey, S. Boi, G. Coutrakon, A. Dyshkant, K. Francis, D. Hedin, E. Johnson, J. Kalnins, V. Zutshi, Department of Physics, Northern Illinois University, DeKalb, IL 60115, USA; R. Ford, J .E. Rauch, P. Rubinov, G. Sellberg , P. Wilson, Fermi National Accelerator Laboratory, Batavia, IL 60510, USA; M. Naimuddin, Delhi University, 110007, India
1
Introduction
Northern Illinois University in collaboration with Fermi National Accelerator Laboratory (FNAL) and Delhi University has been designing and building a proton CT scanner [1] for applications in proton treatment planning. In proton therapy, the current treatment planning systems are based on X-ray CT images that have intrinsic limitations in terms of dose accuracy to tumor volumes and nearby critical structures. Proton CT aims to overcome these limitations by determining more accurate relative proton stopping powers directly as a result of imaging with protons. Fig. 1 shows a schematic proton CT scanner, which consists of eight planes of tracking detectors with two X and two Y coordinate measurements both before and after the patient. In addition, a calorimeter consisting of a stack of thin scintillator tiles, arranged in twelve eight-tile frames, is used to determine the water equivalent path length (WEPL) of each track through the patient. The X-Y coordinates and WEPL are required input for image reconstruction software to find the relative (proton) stopping powers (RSP) value of each voxel in the patient and generate a corresponding 3D image. In this note we describe tests conducted in 2015 at the proton beam at the Central DuPage Hospital in Warrenville, IL, focusing on the range stack calibration procedure and comparisons with the GEANT 4 range stack simulation.
2
The GEANT 4 model
To verify measurements obtained by the scanner at the CDH proton beam the scanner response was simulated using a detailed model based on the GEANT-4 software. Fig. 2 1
Figure 1: Four (X,Y) stations measure the proton trajectory before and after the patient. A stack of 3.2 mm thick scintillator tiles measures the residual energy or range after the patient. shows a spherical water phantom between the tracker planes of the scanner model. The simulated responses of the range stack and tracker stations were analyzed with the same software as for the data.
Figure 2: The GEANT4 visualization of the scanner model used in the simulations.
3
The CDH test beam
Figure 3 shows the NIU scanner mounted on a cart in a treatment room at Central DuPage Hospital. The proton beam enters the upstream tracker planes from the right followed by the downstream tracker planes and finally the range stack. In this note the range stack tiles are labeled from zero (the tile closest to the tracker) to 95. Data were obtained using proton
2
beams of energy in range from 103-225 MeV, equivalent to 8-32 cm proton stopping range in water.
Figure 3: Fully assembled proton CT scanner at CDH Proton center. From right to left, beam enters the upstream tracker planes followed by the downstream tracker planes and finally the range stack. The gap in the middle is the position of the rotation stage for the head phantom in the horizontal plane.
3.1
Data acquisition (DAQ) system and event selection
The DAQ system of the scanner is described in [2]. The range stack data are collected by twelve front-end boards. Each board provides the readout of one eight-tile range stack frame in form of time-stamped records of signal amplitudes in all tiles of the frame. We form the proton candidate event by combining records with close time-stamps. We remove events candidates with duplicated frames (overlapped tracks). We then found the frame with a Bragg peak, or stopping frame, and check that all frames before the stopping frame are also present in the event.
3.2
Units of measurement
The CDH accelerator control system is tuned to operate with proton beams with energies expressed in units of the proton stopping range in water in cm, Rw (cm). One can also express the proton stopping range Rw , and thus the beam energy Ebeam , in density-independent units of g/cm2 : Ebeam (g/cm2) ≡ Rw (g/cm2 ) = Rw (cm) × ρw (g/cm3 ) (1) To obtain the energy Ebeam in MeV we use proton energy-range tables (a.k.a. Janni’s tables) [4]. A fit of the stopping range Rw (g/cm2) as a function of E(MeV ) is shown in Fig. 4(a). We use (1.77) Rw (g/cm2) = 0.0022 × EM eV (2) to convert beam energies between MeV and g/cm2 units. We calculate the proton stopping range in the range stack Rrs (g/cm2 ) using the measured proton stopping position as described in Section 5. We compare the Rrs (g/cm2) with the 3
range calculated from the total energy measured by the range stack using the energy-range dependence in polystyrene shown in Fig. 4(b). Proton Range vs Energy in polystyrene Range, 0.1*(g/cm2)
Range, 0.1*(g/cm2)
Proton Range vs Energy in water 900 χ2 / ndf
800
201.4 / 42
p0
0.02153 ± 0.0001327
p1
-1.773 ± 0.001395
700 600
900 χ2 / ndf
800
p1
-1.78 ± 0.001989
600 500
400
400
300
300
200
200
100
100
102 Proton energy, MeV
10
0.02064 ± 0.0001796
700
500
0
102.3 / 42
p0
102 Proton energy, MeV
10
(a)
(b)
Figure 4: a) The proton stopping range in water Rw (g/cm2) (black dots) versus proton energy (1.77) E(MeV ), as measured in [4]. The fit Rw (g/cm2) = 0.0022 × EM eV conversion function (the red line) is used to find beam energies in MeV that correspond to nominal CDH energies in cm. b) The proton stopping range in polystyrene Rpoly (g/cm2 ) (black dots) versus proton energy E(MeV ).
4
Stack calibration procedure
Energy deposition in each range stack scintillator tile is measured by two SiPMs connected to the tile’s single wavelength shifting (WLS) fiber. After passage of a proton, for each of the two SiPMs the maximum digitized signal, Amax SiP M , is collected by the DAQ system. Thus the max measured energy deposition in each range stack tile, AADC tile , is obtained as a sum of ASiP M signals from SiPMs connected to this tile. This measurement varies from tile to tile even for protons of similar energy due to differences in the SiPM’s properties and the settings of corresponding readout channels. The following four step procedure is applied to calibrate the range stack detector. M1 M2 M1 1) We measure pedestal amplitudes ApdSiP , ApdSiP and amplitudes A1peSiP , tn tn tn 1peSiP M 2 Atn of the first photo-electron (PE) peak for all range stack tiles, tn, by collecting events with no beam. Fig. 5(a) and Fig. 5(b) show these distributions for SiPM1 and SiPM2 of Tile0. The combined SiPM1+SiPM2 no-beam signal in Tile0 is shown in Fig. 5(c). Figure 6 shows calibration signals for all 16 SiPMs of the first range stack frame. From these data the ADC to PE conversion coefficients for each SiPM are calculated as peSiP M M M Ktn = A1peSiP − ApdSiP tn tn peSiP M 0 peSiP M 0 Ratios of PE conversion coefficients Ktn /Kt0 of the first and second SiPM in each tile to the conversion coefficient in the first SiPM in Tile0 are shown in Fig. 7(a) and Fig. 7(b). Most sensors have a response within 10% of one another.
4
BID= 30, Tile = 0:: Channel 16 Entries 54775 Mean 120.2 RMS 13.13
6
5
×10
3
h2fit_bid30_tile0_cnl0
Events/bin
Events/bin
3
7
BID= 30, Tile = 0:: Channels (0,16) Entries 54775 Mean 117.6 RMS 12.26
6
= 102.84 ADC = 120.971 ADC
h2fit_bid30_tile0
Entries 54784 Mean 237.8 RMS 20.58
2.5
= 102.794 ADC
4
= 119.91 ADC
PE/ADC = 18.1311
3
3
2
5 4
×10
h2fit_bid30_tile0_cnl16
Events/bin
BID= 30, Tile = 0:: Channel 0 ×10
= 205 ADC = 223 ADC
1.5
PE/ADC = 17.1159
PE/ADC = 18.0055
3 1 2
2 0.5
1
0
1
80
100
120
140
160
180 ADC counts
0
80
100
120
140
(a)
160
180 ADC counts
(b)
0
180
200
220
240
260
280
300
320 340 ADC counts
(c)
Figure 5: Measured Tile0 signal amplitudes : a) pedestal and the first photo-electron (PE) peak in the SiPM1 of Tile 0 in events with no beam. b) pedestal and the first photo-electron (PE) peak in the SiPM2 of Tile 0 in events with no beam. c) SiPM1+SiPM2 combined. pe 2) The proton energy deposition in each tile Etn in PE units is obtained via pe M1 peSiP M 1 M2 peSiP M 2 M1 M2 Etn = (AsSiP − ApdSiP )/Ktn + (AsSiP − ApdSiP )/Ktn . tn tn tn tn
Fig. 8(a) and Fig. 8(b) show the PE signals of SiPM1 and SiPM2 in Tile0, Fig. 8(c) shows the combined SiPM1+SiPM2 signal, Ape t0 , in Tile0. clbExp 3) We measure signals Etn of all range stack tiles in the region far away from the Bragg peak. We conducted two calibration runs at an energy of 32 cm (225 MeV). For the second run, the assembled scanner was turned 180 degrees to expose the back tiles to the beam first. The “front” run is used to calibrate the first front 48 tiles of the stack, while the “back” run clbT rue is used to calibrate the 48 back tiles. We assume that the “true” Etn amplitudes of the tile signals follow energy profiles calculated from proton energy-range tables for polystyrene (the material used for the range stack tiles). Figure 9(a) shows the tabulated proton dE/dx dependence. Fig. 9(b) and Fig. 9(c) show energy profiles calculated for protons entering the range stack with energies of 30.6 cm in the “front” run and 31.4 cm in the “back” run (corrections to the nominal CDH accelerator energy were applied to account for material in the tracker which is only present in the “front” run configuration and material in the CDH beam transport line, as discussed in Section 5.3). clbExp clbT rue All “true” Etn , tn = 0, 95 amplitudes are normalized to the signal Et0 of the Tile0 in the “front” run. That is, we take the observed energy in Tile0 as to be correct. The comparison of signals observed in Tile0 in runs of different energies and expected signals obtained by integration of the tabulated proton dE/dx dependence are shown in Fig. 10. The expected signals are normalized to the mean Tile0 data signal in the 32 cm run. The measured and calculated amplitudes are in good agreement, however the data signals are about 5% higher at low proton energies. E clbT rue clb 4) We extract normalization coefficients Ktn ≡ EtnclbExp and use them in all data runs to tn
correct the observed signals in the range stack tiles. Figures 11(a) and (b) show the corrected energy deposition profiles (the mean number of photoelectrons from about 10000 protons per tile as function of tile number) for 200 MeV protons. Corrected energy profiles for different beam energies are shown in Fig. 12 through Fig. 14. Slight variations are attributed to 5
5
7
BID= 30, Tile = 1:: Channel 1 Entries 54775 Mean 117.6 RMS 12.26
6
×10
3
h2fit_bid30_tile0_cnl16
9
BID= 30, Tile = 1:: Channel 17 ×10
3
h2fit_bid30_tile1_cnl1
Entries 54768 Mean 113 RMS 10.09
8
Events/bin
BID= 30, Tile = 0:: Channel 16 Entries 54775 Mean 120.2 RMS 13.13
×10
3
h2fit_bid30_tile0_cnl0
Events/bin
Events/bin
3
Events/bin
BID= 30, Tile = 0:: Channel 0 ×10 6
h2fit_bid30_tile1_cnl17
Entries 54768 Mean 118.3 RMS 12.79
7 6
7 5
4
= 102.84 ADC
4
= 120.971 ADC
= 119.91 ADC
PE/ADC = 18.1311
3
5
6
= 102.794 ADC
= 101.784 ADC
= 103.964 ADC
= 117.05 ADC
5
PE/ADC = 17.1159
= 123.659 ADC
4
PE/ADC = 15.2661
PE/ADC = 19.6951
4
3
3
3
2
2
2 2
80
100
120
140
160
0
180 ADC counts
80
BID= 30, Tile = 2:: Channel 2 ×10
100
120
140
160
0
180 ADC counts
80
BID= 30, Tile = 2:: Channel 18 ×10
3
h2fit_bid30_tile2_cnl2
Entries 53565 Mean 114.9 RMS 11.14
Events/bin
Events/bin
3
10
1
1 120
140
160
0
180 ADC counts
80
BID= 30, Tile = 3:: Channel 3 3
Entries 53565 Mean 113.7 RMS 11.97
9
100
×10
h2fit_bid30_tile2_cnl18
Events/bin
0
1
8
100
120
140
160
180 ADC counts
BID= 30, Tile = 3:: Channel 19 ×10
3
h2fit_bid30_tile3_cnl3
6
Entries 54778 Mean 120.2 RMS 12.74
5
Events/bin
1
h2fit_bid30_tile3_cnl19
Entries 54778 Mean 118.5 RMS 13.49
6
5
8 7 = 105.081 ADC
6
4
= 102.78 ADC
6
= 122.451 ADC
= 121.203 ADC
5
PE/ADC = 17.3698
4
= 104.807 ADC
= 103.7 ADC
= 123.872 ADC
PE/ADC = 18.4234
= 123.669 ADC
PE/ADC = 19.0649
3
PE/ADC = 19.9687
3
4
4
2
3 2
2
0
0
2
1
1
0
0
1 120
140
160
180 ADC counts
80
BID= 30, Tile = 4:: Channel 4 ×10
140
160
180 ADC counts
80
BID= 30, Tile = 4:: Channel 20 Entries 54776 Mean 117.8 RMS 8.875
6
120
×10
3
h2fit_bid30_tile4_cnl4
Events/bin
Events/bin
3
100
120
140
160
180 ADC counts
80
BID= 30, Tile = 5:: Channel 5 ×10
3
h2fit_bid30_tile4_cnl20
Entries 54776 Mean 116.4 RMS 12.01
7
100
100
120
140
160
180 ADC counts
BID= 30, Tile = 5:: Channel 21 ×10
3
h2fit_bid30_tile5_cnl5
Entries 54777 Mean 113.9 RMS 11.74
9 8
Events/bin
100
Events/bin
80
h2fit_bid30_tile5_cnl21
Entries 54777 Mean 111.1 RMS 8.417
8 7
6 7
5 5
= 114.204 ADC
4
= 103.132 ADC
= 123.758 ADC
6 = 102.991 ADC
6
= 120.536 ADC
4
PE/ADC = 9.55459
5
PE/ADC = 17.4045
3
PE/ADC = 19.3804
= 112.784 ADC PE/ADC = 10.2202
4
4
3
3 3
2
2
2
2 1
100
120
140
160
0
180 ADC counts
80
BID= 30, Tile = 6:: Channel 6
100
120
140
160
100
120
140
160
140
80
Entries 54780 Mean 113.6 RMS 10.73
180
100
120
140
160
180 ADC counts
BID= 30, Tile = 7:: Channel 23 h2fit_bid30_tile7_cnl7
Entries 1232 Mean 118.3 RMS 12.71
120
0
180 ADC counts
BID= 30, Tile = 7:: Channel 7 h2fit_bid30_tile6_cnl22
Events/bin
Events/bin
Entries 1232 Mean 120.7 RMS 12.99
120
1
80
BID= 30, Tile = 6:: Channel 22 h2fit_bid30_tile6_cnl6
140
0
180 ADC counts
Events/bin
80
1
160
h2fit_bid30_tile7_cnl23
160
Events/bin
1
0
= 102.564 ADC
5
= 122.371 ADC
Entries 54780 Mean 118.1 RMS 13.21
140 120
100
140
100 = 103.11 ADC
80
= 121.165 ADC
= 102.85 ADC = 120.349 ADC
80
PE/ADC = 18.0555
60
60 40
20
20
= 104.242 ADC
100
= 116.906 ADC
100
PE/ADC = 17.4982
40
= 101.704 ADC
120
PE/ADC = 15.2019
80
= 123.471 ADC
80
PE/ADC = 19.2292
60
60 40 40 20
20 0
80
100
120
140
160
180 ADC counts
0
80
100
120
140
160
0
180 ADC counts
80
100
120
140
160
180 ADC counts
0
80
100
120
140
160
180 ADC counts
Figure 6: No beam signals used for PE calibration for the first eight tiles of the range stack.
6
PE(tN)/PE(t0)
PE(tN)/PE(t0)
2 1.8 1.6
2 1.8 1.6
1.4
1.4
1.2
1.2
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0 0
10
20
30
40
50
60
70
0 0
80 90 Tile number
10
20
30
40
50
60
70
80 90 Tile number
(a)
(b) hfill
Figure 7: a) The ratio of PE conversion coefficients K peSiP M 0tn /K peSiP M 0t0 for the first SiPMs. b) The ratio of PE conversion coefficients K peSiP M 1tn /K peSiP M 0t0 for the second SiPMs. statistical effects.
5
Range and energy measurements
The NIU image reconstruction software uses the WEPL of a scanned object, weplobj . For each proton the weplobj can be obtained from WEPL of the range stack, weplrs , weplobj = Ebeam (cm) − weplrs , To find weplrs one need calibrate the total energy Ers or the stopping range Rrs measured by the range stack detector using a set of phantoms with known WEPL [3]. Here we compare the accuracy of Rrs and Ers to choose what measurement is preferrable for the WEPL calibration. To find the total energy Ers deposited in the range stack we first search for the frame with a stopping tile (the “stopping” frame), then sum signals (in PE units) from all tiles and all frames including the stopping frame. Only events with no missing frames before the stopping frame were selected. Figure 15(a) shows the total Ers in PE measured in a run with Ebeam = 26 cm. To find Rrs we use the Z-position of the tile with the maximum signal (the “stopping” tile, labeled as ntstop ). We calculate Rrs as Rrs = (ntstop + 1) × (tileW × tileD + alW × alD + mlrW × mlrD)+ nf rame × (alW × alD + mlrW × mlrD), ntstop = [0, 95]; nf rame = [0, 11] where (tileW, alW, mlrW ) = (3.2, 0.00022, 0.00625) mm are the widths of scintillator and wrapper (aluminized mylar) layers, and (tileD, alD, mlrD) = (1.011, 2.700, 1.397) g/cm3 are the densities of these materials. The second term accounts for the extra layer of the wrapper in the end of each range stack frame. Note, the stopping ranges in polysterene and mylar expressed in g/cm2 are approximately equal to the proton stopping range in water Rw : 7
BID= 30, Tile = 0:: Channel 0 ×10
BID= 30, Tile = 16:: Channel 16 ×10
BID= 30, Tile = 0:: Channels (0,16) ×10
3
8
Entries 62024
7
Mean
8.105
RMS
3.432
12
3
h2fitBSpe_bid30_tile0_cnl16
Entries 62024
10
Mean
4.305
RMS
2.328
Events/bin
h2fitBSpe_bid30_tile0_cnl0
Events/bin
Events/bin
3
h2fitBSpe_bid30_tile0
6
Entries 62024 Mean 12.4 RMS 4.366 2 χ / ndf 46.44 / 7 Constant 5955 ± 38.4 Mean 11.46 ± 0.03 Sigma 4.237 ± 0.051
5
6 8
4
5 4 3
6
3
4
2
2
1
2 1 0
0
5
10
15
20
25
30
35 PE counts
0
0
5
10
15
20
(a)
25
30
35 PE counts
0
0
10
20
30
(b)
40
50 PE counts
(c)
Figure 8: Measured signal amplitudes (PE units) in Tile0 at a beam energy of 26 cm (200 MeV) after subtracting pedestals : a) in SiPM1; b) in SiPM2; c) sum of SiPM1 and SiPM2. The means of Gaussian fits of combined signals away from the Bragg peak at a beam energy of 32 cm (225 MeV) were used to extract the normalization coefficients for the range stack tiles.
Rw (cm) =
Z
Rm
RSPm dL
(3)
0
where RSPm is the proton stopping power of the medium relative to water and L is the physical proton path length along the calorimeter and Rm is the physical depth at which the proton stops in the range stack. Then, neglecting small variations ( < 0.5%) in mean ionization potential between water, polystyrene and mylar, as used in the Bethe Bloch equation, the water equivalent range of the proton becomes Z Rm Z Rm 3 2 ρm dL ρm /ρw dL, and, f orρw = 1.0 g/cm , Rw (g/cm ) ≃ Rw (cm) ≃ 0
0
Thus we expect Rrs to have linear dependency on the beam energy, Ebeam , expressed in cm. Figure 16 shows Rrs in a run with Ebeam = 26 cm. We also can find the Rrs from the total energy Ers using Janni’s range-energy tables This method requires expression of Ers in MeV, and we use the conversion coefficient calculated as the ratio of the mean amplitude of the data signal (in number of photoelectrons) to the mean amplitude of the estimated MC signal (in MeV) in Tile0, in 26 cm runs. Figure 15(b) conv shows the proton stopping range in the range stack Rrs (g/cm2 ) calculated from Ers via (1.78) conv the Rrs = 0.0021 × Ers conversion function obtained from Janni’s tables. Finally, we can find weplrs directly, from the WEPL of a scanned object calculated from Ers using the Bethe-Bloch equation. Howewer, this will also require calibration, as the measured Ers only includes the visible part of deposited energy. Figure 15(c) shows the WEPL of the range calc stack weplrs (cm) calculated from Ers via Z Ers 1 calc dE (4) weplrs = Ebeam (cm) − Ebeam S(Ep ) where S(Ep ) = −dE/dx is a water stopping power for proton with energy Ep . 8
80
7.908 / 36
p0
0.9988 ± 1.506
p1
0.02188 ± 0.2319
p2
-311.2 ± 6.061
p3
-0.8435 ± 0.0169
70
140 120
140
Corrected CDH energy: 30.616 cm Deposited energy: 219.268 MeV Deposited energy: 1771.89 PE
100
60 50 40 30
Signal amplitude, number of photoelectrons
χ2 / ndf
90
Signal amplitude, number of photoelectrons
dE/dX, MeV/(g/cm2)
Proton Energy loss in polystyrene
120
Corrected CDH energy: 31.441 cm Deposited energy: 221.587 MeV Deposited energy: 1790.63 PE
100
80 60 40
80 60 40
20
20
20
10 0 10
102 Proton energy, MeV
0 0
20
40
60
(a)
80
100 Tile number
0 0
(b)
20
40
60
80
100 Tile number
(c)
Figure 9: a) The proton dE/dX dependency in polystyrene as tabulated in Janni’s proton energy-range tables. b) The “true” front run signal profile used for calibration of tiles (0-47) of the range stack. c) The “true” back run signal profile used for calibration of tiles (48-95) of the range stack. We fit peaks of the Rrs and Ers distributions with a Gaussian and use the mean and σ parameters of the fits to study the linearity (Rrs and Ers as functions of the beam energy) and resolution (σ(Ers )/Ers and σ(Rrs )/Rrs as functions of Ers and Rrs ) of the range stack detector. The linearity and resolution plots for the proton stopping position Rrs are shown in Fig. 17 and the linearity and resolution plots for the energy measurement are shown in Fig. 18. The good linearity with a non zero intercept of the Rrs shows there is material in front of the range stack at all energies. The energy measurement has lower accuracy (energy resolution ranges from 5.5% to 3.5% , compared to 2.2-1.2% for Rrs ) and also shows an unexpected suppression at beam energies of 27 cm and 28 cm. Additionally, Figures 15(a) and (b) show that if we try to extract the stopping range or WEPL in the range stack from conv conv the direct energy measurement, the Rrs and distributions with σ(Rrs ) = 11.7 mm and calc σ(weplrs ) = 11.8 mm are significantly wider than Rrs distribution with σ(Rrs ) = 3.3 mm. Thus, the direct Rrs measurement is preferred for the WEPL calibration.
5.1
Comparison with GEANT 4 simulations
g4 A GEANT 4 simulation of the pCT detector was used to obtain the energy deposition Etn in the range stack tiles for different beam energies. We converted the range Rp to energy Ep using the inverse of the Janni fit: Ep = (Rp /0.0022)(1/1.77) . To compare energy profiles and total energy deposition in the range stack, the G4 signals in the tiles were expressed in the number of photoelectrons by normalizing to the data signal in Tile0 in the 26 cm beam run.
5.2
Smearing of simulated tile signals
To account for photo-statistics and SiPM readout, smearing of the G4 signals in each tile was done as: g4 ped g4 ped Stn = G(< Stn >) + P (Etn )− < Stn > , ped g4 where < Stn > is a mean sum of SiPM pedestals in tile n from calibration runs, Etn is the 9
Signal amplitude in Tile0, number of photoelectrons
χ2 / ndf 0.1631 / 11 p0 22.5 ± 0.3634 p1 -0.06578 ± 0.003388 p2 9.186e-05 ± 7.531e-06
24 22 20
Data 18
Janni’s tables
16 14 12 10 0
50
100
150
200
250
300 350 Proton Energy, 0.1*(g/cm2)
Figure 10: Measured signal amplitudes (blue crosses) and expected amplitudes calculated from Janni’s tables (red line) in Tile0 of the range stack for different proton energies. The expected signals normalized to the mean (over 10000 protons) Tile0 data signal in the 32 cm run. ped g4 energy deposition in tile n obtained from GEANT, and G(Stn ) and P (Etn ) are the sum of g4 SiPM pedestals smearing using Gaussian and Etn smeared using Poisson distribution. The effect of smearing is shown in Fig. 19, where the left plot shows the total energy deposition in the range stack at a beam energy of 26 cm (or 200 MeV) in data; the center histogram shows the unsmeared simulated signal, and the right histogram shows the smeared signal. Comparison of data and simulated signals from 200 MeV protons in Tile0 and in Tile74 (the stopping tiles with the maximal signal for this energy) are shown in Fig. 20.
5.3
Beam energy correction and smearing for the MC simulations
The total stopping range of all material along the proton path, Rtotal , before the proton stopping position is equal to the nominal beam energy of the accelerator in g/cm2 , Rtotal ≡ beam Etotal . In our test beam configuration, the total stopping range can be expressed as: Rtotal = Rrs + Rbeamline + Rtracker + sf t const, where Rrs , Rbeamline , Rtracker are the proton ranges in the range stack, any material in the accelerator beam line, and the tracker, respectively. The sf t const is the systematic shift of the range measurement due to initial and arbitrary origin of the range calculation. We extract the stopping range using the position of the tile with the maximum signal and the total width of scintillator and wrapping layers including this stopping tile. The definition of stopping position is arbitrary and for consistency estimated with the MC. We estimate the sf t const using simulations of the range stack response in configuration with no tracker. In the GEANT model we do not have any other material before the range stack, and the sf t const can be obtained from the fit of the proton stopping positions at different beam energies, as shown in Fig. 21(a). Evaluation of the fit function at zero beam energy results in sf t const=0.7 ± 0.4 mm in water (the −p0 parameter of the fit). From the fit of the measured proton stopping position Rrs in 10
Mean signal amplitude, PE counts
Mean signal amplitude, PE counts
120
Energy deposition in tiles Run: run_Feb28_001206_bmrun10_r26cm_cdh_pctmonTree
100
, PE counts 80
60
120
100
, PE counts 80
60
40
40
20
20
0
0
10
20
30
40
50
60
70
80
0
90 Tile number
(a)
Energy deposition in tiles Run: run_Feb28_001206_bmrun10_r26cm_cdh_pctmonTree
0
10
20
30
40
50
60
70
80
90 Tile number
(b)
Figure 11: The mean number of photoelectrons in the range stack tiles as a function of tile number produced by protons with energy 26 cm (200 MeV) (a) raw; (b) calibrated. The errors bars reperesent ±1 sigmas of Gaussian fits about the average, for an example see Fig. 8(c) . Fig. 17(a) the Rbeamline + Rtracker + sf t const is equal to 14.3 ± 0.4 mm. This means that the proton energy at the range stack entry point, Epentry , is lower than the nominal accelerator beam energy by 13.6 ± 0.5 mm (after subtracting the 0.7 mm sf t const parameter) for all test runs. To accurately compare the energy and range measurement with simulations, the Epentry should be the same in data and in MC. Figure 21(b) shows the simulated proton stopping positiom Rrs in a configuration with the tracker, and here the Rtracker + sf t const is equal to 7.9 ± 0.5 mm (again 0.7 mm is subtracted from the −p0 parameter of the fit). Thus for simulations we subtract the difference of 5.7 mm (between the 13.6 mm observed in data and the 7.9 mm observed in MC) from all nominal beam energy points in GEANT runs to compensate. The corrected results are shown in Fig. 21(c) and now the Epentry in GEANT runs is equal to the Epentry in data runs. Simulations also predict that this method of upstream material width estimation from the range stack measurements works with an accuracy of about 0.5 mm in a configuration with a variable width of a rectangular water phantom installed before the range stack. For the water phantom width of 2 mm, 5 mm, 10 mm, and 15 mm the simulated measurements are 2.1 mm, 5.4 mm, 10.3 mm and 14.3 mm, respectively. Additionally we smear Epentry in GEANT in a range between 0.05% at 100 MeV to 0.02% at 200 MeV to account for the CDH beam energy spread.
5.4
Comparison of proton stopping position measurements
The linearity and resolution plots for the proton stopping position Rrs are shown in Fig. 22. Fits correspond to the simulated results. We observe excellent agreement both in linearity and resolution. We used the detector model in which the density of the scintillator tiles is decreased by 1% compare to the nominal value of 1.025 ± 0.010 g/cm3, which provides the best agreement between measured and simulated proton stopping positions for different beam energies, as shown in Figure 23.
11
Mean signal amplitude, PE counts
Mean signal amplitude, PE counts
120
Energy deposition in tiles Run: run_Feb28_001206_bmrun10_r26cm_cdh_pctmonTree
100
, PE counts 80
60
120
100
, PE counts 80
60
40
40
20
20
0
0
10
20
30
40
50
60
70
80
0
90 Tile number
Energy deposition in tiles Run: run_Feb28_024905_bmr31_r32_stackBack_cdh_pctmonTree
0
10
20
(a)
30
40
50
60
70
80
90 Tile number
(b)
Figure 12: The mean number of photoelectrons in the range stack tiles as a function of tile number produced by protons with energy (a) 32 cm (225 MeV), “front” run ; (b) 32 cm (225 MeV), “back” run, no tracker. The errors bars reperesent ±1 sigmas of Gaussian fits about the average.
5.5
Comparison of energy measurements
P The linearity and resolution plots for the energy measurements Ers = Etn in the range stack are shown in Fig. 24. Fits correspond to the simulated results. The instrumental depression in the data linearity plot at beam energies of 27 cm and 28 cm is not present in simulations. The MC model response shows good linearity. The resolution is between 4% and 2% that is higher than observed in data (between 5% and 3%). A comparison of measured (blue crosses) and simulated (black square) energy measurements in Tile0 for different proton energies is shown in Fig. 25. The normalized simulated energy amplitude profiles in the range stack in Fig. 27 (red histograms) show fair agreement with the calibrated data (black dots) but diverge in amplitude at low proton energies (consistent with Fig. 25). The divergence could be due to higher event rates in high proton energy runs, shown in Fig. 26.
6
Stopping range measurements in presence of a phantom
Figure 28(a) and Fig. 28(b), respectively, show the distribution of proton stopping range in the range stack and the simulated (X, Y ) distribution of protons at the first tracker station of the GEANT 4 detector model obtained in the presence of a spherical (D = 14 cm) water phantom. The first peak in the stopping range distribution corresponds to protons going through the center of the phantom, while the second peak corresponds to the stopping range of protons that missed the phantom. Different colors for the reconstructed tracks correspond to the simulated proton stopping ranges. Figures 29(a) and (b) show similar plots for the head phantom obtained using 50K reconstructed protons of energy 200 MeV at CDH. Contours corresponding to the different material width are clearly visible. The missing bands correspond to missing tracking channels.
12
Mean signal amplitude, PE counts
Mean signal amplitude, PE counts
120
Energy deposition in tiles Run: run_Feb28_001206_bmrun10_r26cm_cdh_pctmonTree
100
, PE counts 80
60
120
100
, PE counts 80
60
40
40
20
20
0
0
10
20
30
40
50
60
70
80
0
90 Tile number
(a)
Energy deposition in tiles Run: run_Feb28_024340_bmr30_r26_stackBack_cdh_pctmonTree
0
10
20
30
40
50
60
70
80
90 Tile number
(b)
Figure 13: The mean number of photoelectrons in the range stack tiles as a function of tile number produced by protons with energy (a) 26 cm (200 MeV, “front run” ) ; (b) 26 cm (200 MeV, “back run” ), no tracker. The errors bars reperesent ±1 sigmas of Gaussian fits about the average. The three tile difference in the stopping position (ntstop = 74 in the front run, while ntstop =77 in the back run run without the tracker) agrees with the tracker stopping power, 3.2 × 1.01 × 3 = 0.97 cm.
7
Summary
The stopping position measurements have better linearity and accuracy (2.2-1.2%) than the energy measurements (5.5% to 3.5%), confirmed by simulations, and thus are expected to provide more accurate WEPL calibration for the image reconstruction. The behavior of range stack detector is well modelled by GEANT, with a few dicrepancies in energy deposition at low energy and energy resolution.
References [1] G. Coutrakon et al., Proceedings AccApp 2013, Bruges, Belgium; S. A. Uzunyan et al., arXiv:1409.0049 (2014). [2] S. Uzunyan et al., Proceedings of the New Trends in High-Energy Physics, p. 152-157, Alushta, Crimea, Ukraine, Sep. 2013, ISBN 978-966-02-7015-2. [3] R. F. Hurleyet al., “Water-equivalent path lengh claibration of a prototype proton CT scaner”, Med. Phys. 39(5), May 2012. [4] J. F. Janni, ”Proton Range-Energy Tables, 1 keV-10 GeV, Energy Loss, Range, Path Length, Time-of-Flight, Straggling, Multiple Scattering, and Nuclear Interaction Probability. Part I. For 63 Compounds”, Atomic Data and Nuclear Data Tables, 27, 147, (1982).
13
, PE counts 80
60
120
Energy deposition in tiles Run: run_Feb28_005432_bmrun17_r12cm_cdh_pctmonTree
100
, PE counts 80
60
, PE counts 80
60
40
40
20
20
0
0
10
20
30
40
50
60
70
80
90 Tile number
0
10
20
30
40
120
50
60
70
80
0
90 Tile number
Energy deposition in tiles Run: run_Feb28_004427_bmrun15_r18cm_cdh_pctmonTree
100
, PE counts 80
60
120
Energy deposition in tiles Run: run_Feb28_002114_bmrun11_r20cm_cdh_pctmonTree
100
, PE counts 80
60
20
70
80
90 Tile number
0
10
20
30
40
Energy deposition in tiles Run: run_Feb28_002708_bmrun12_r25cm_cdh_pctmonTree
100
, PE counts 80
60
40
80
120
10
20
30
40
50
(g)
60
70
80
90 Tile number
Energy deposition in tiles Run: run_Feb28_000751_bmrun9_r27cm_cdh_pctmonTree
100
, PE counts 80
60
0
90 Tile number
0
10
20
30
40
50
60
70
80
90 Tile number
(f ) 120
Energy deposition in tiles Run: run_Feb27_234837_bmrun5_r31cm_cdh_pctmonTree
100
, PE counts 80
60
40
20
0
0
90 Tile number
40
20
0
70
Mean signal amplitude, PE counts
120
60
80
Energy deposition in tiles
(e) Mean signal amplitude, PE counts
(d)
50
70
60
0
60
60
, PE counts
0
50
50
80
40
40
40
Run: run_Feb28_003157_bmrun13_r24cm_cdh_pctmonTree
20
30
30
100
20
20
20
120
40
10
10
(c)
40
0
0
(b) Mean signal amplitude, PE counts
0
Energy deposition in tiles Run: run_Feb28_004928_bmrun16_r16cm_cdh_pctmonTree
100
20
Mean signal amplitude, PE counts
Mean signal amplitude, PE counts
120
40
(a)
Mean signal amplitude, PE counts
Mean signal amplitude, PE counts
Energy deposition in tiles Run: run_Feb28_010631_bmrun19_r8cm_cdh_pctmonTree
100
Mean signal amplitude, PE counts
Mean signal amplitude, PE counts
120
20
0
10
20
30
40
50
60
(h)
70
80
90 Tile number
0
0
10
20
30
40
50
60
70
80
90 Tile number
(i)
Figure 14: The mean number of photoelectrons in the range stack tiles as a function of tile number produced by protons with energy (a) 8 cm (103 MeV); (b) 12 cm (117 MeV); (c) 16 cm (129 MeV); (d) 18 cm (162 MeV) ; (e) 20 cm (172 MeV); (f) 24 cm (191 MeV); (g) 25 cm (196 MeV) ; (h) 27 cm (204 MeV); (i) 31 cm (221 MeV).
14
χ2 / ndf Constant Mean Sigma
2 1.8
×10
3
9.404 / 10 2112 ± 20.4 1468 ± 0.5 46.8 ± 0.6
hrange_wtr_conv_r26cm
Entries Mean RMS χ2 / ndf
27803 190.7 16.85 718.9 / 30 Constant 2840 ± 24.1 Mean 188.7 ± 0.1 Sigma 11.67 ± 0.07
3
2.5
1.6 2
1.4
×10
3
Events/bin
Events/bin
3
Events/bin
×10 2.2
3
2.5
2
hrange_wtr_calc_r26cm Entries 27803 Mean 187.9 RMS 13.12 χ2 / ndf 720.5 / 24 Constant 2818 ± 24.0 Mean 186.7 ± 0.1 Sigma 11.81 ± 0.07
1.2
Beam range =r26cm
1
1.5
1.5
1
1
0.5
0.5
0.8 0.6 0.4 0.2 ×10
3
0
1.3
1.4
1.5
1.6 1.7 1.8 1.9 Proton energy deposition, PE
0 160 180 200 220 240 260 280 300 320 340 Stopping range in the range stack (via Janni’s tables), 0.1*g/cm2
(a)
0 160 180 200 220 240 260 280 300 320 340 Proton WEPL in the range stack (via Bethe-Bloch), mm
(b)
(c)
Figure 15: (a) the total energy, Ers , in P E measured with the range stack detector in a conv Ebeam = 26 cm run; (b) the proton stopping range in the range stack Rrs (g/cm2 ) obtained (1.77) conv calc from Ers via Rrs = 0.0022 × Ers ; (c) the proton WEPL in the range stack weplrs , mm calculated from Ers via energy loss equation.
Signal maximum is in tile 74 ×10
Events/bin
3
hrange_wtr_r26cm
10
Entries
27803
Mean
243.2
RMS χ2 / ndf
5.112 462.5 / 9
Constant 1.037e+04 ± 7.716e+01
8
Mean Sigma
243.6 ± 0.0 3.383 ± 0.015
6
Beam range =r26cm 4
2
0 160 180 200 220 240 260 280 300 320 340 Stopping position in the range stack (measured), 0.1*g/cm2
Figure 16: The measured proton stopping range, Rrs , in the range stack, Ebeam = 26 cm run.
15
300
10.5 / 13
p0
-14.25 ± 0.3956
p1
0.9913 ± 0.001863
σ(Pstop)/Pstop, %
Proton stopping position, 0.1*g/cm2
Proton stopping position resolution χ2 / ndf
250
χ2 / ndf
3
p0
2.5
7369 / 11 2.887 ± 0.01851
p1
-0.01124 ± 0.0001965
p2
1.772e-05 ± 4.866e-07
2
200 1.5 150 1 100 0.5
50
0 0
50
100
150
200
0 0
250 300 350 Beam energy, 0.1*g/cm2
50
100
150
(a)
200 250 300 350 Stopping position, 0.1*g/cm2
(b)
Figure 17: (a) The linearity of the directly measured proton stopping position measurement Rrs ; (b) the Rrs resolution. The linearity fit allows an estimate of the width of the extra material in front of the range stack (≈14.0 mm).
PE linearity Proton energy deposition, PE
σ(E)/E, %
2000
PE resolution
1800
7
6
1600 5
1400 1200
4
1000 3
800 600
2
400 1 200 ×10
3
0 0
50
100
150
200
0 0.4
250 300 350 Beam energy, MeV
(a)
0.6
0.8
1
1.2 1.4 1.6 1.8 2 Proton energy deposition, PE
(b)
Figure 18: (a) the linearity of the energy measurement Ers ; (b) the Ers resolution.
16
χ2 / ndf Constant
1468 ± 0.5
Mean Sigma
2
9.404 / 10 2112 ± 20.4 46.8 ± 0.6
1.8
×10
3
4.5
χ2 / ndf
29.06 / 1 4292 ± 66.5
Constant
1454 ± 0.1
Mean
4
Sigma
6.688 ± 0.071
3.5
χ2 / ndf
Events/bin
Events/bin
3
Events/bin
×10 2.2
800
7.593 / 5
Constant 740.4 ± 15.3 Mean Sigma
700
1451 ± 1.0 38.67 ± 1.90
600
1.6 3 1.4
500 2.5
1.2
400
Beam range =r26cm
1
2 300
0.8
1.5
0.6
200
1 0.4
100
0.5
0.2 ×10
3
0
1.3
1.4
1.5
1.6 1.7 1.8 1.9 Proton energy deposition, PE
×10
3
0
1.3
1.4
1.5
(a)
1.6 1.7 1.8 1.9 Proton energy deposition, PE
×10
3
0
1.3
1.4
1.5
1.6 1.7 1.8 1.9 Proton energy deposition, PE
(b)
(c)
Figure 19: (a) the total energy deposition in the range stack at beam energy of 26 cm (200 MeV ) in data; (b) the unsmeared total energy deposition in the range stack at beam energy of 26 cm (200 MeV) in GEANT; (c) the smeared range stack energy measurement at beam energy of 26 cm (200 MeV) in GEANT.
MC:: BID= 30, Tile = 0:: Channels (0,16)
MC:: BID= 61, Tile = 2:: Channels (2,18)
h2fitBSpe_data_bid30_tile0 h2fitBSpe_mc_bid30_tile0
0.24
h2fitBSpe_data_bid61_tile2 h2fitBSpe_mc_bid61_tile2
Entries Entries 27803 7741
0.22 0.2 0.18
Mean Mean
12.13 12.4
RMS RMS
4.434 3.782
Entries Entries 27803 7642
0.14 0.12
0.16
Mean Mean
49.79 48.62
RMS RMS
25.24 25.16
0.1
0.14 0.08
0.12 0.1
0.06
0.08 0.04
0.06 0.04
0.02
0.02 0
0
20
40
60
0
80 100 number of PE
(a)
0
20
40
60
80 100 number of PE
(b)
Figure 20: Comparison of data (blue histograms) and simulated signals (red histograms) from 200 MeV protons in (a) Tile0 and (b) Tile74 (the stopping tile, maximal signal).
17
300
19.49 / 12
p0
-0.6793 ± 0.4105
p1
0.9935 ± 0.002021
250
200
150
100
50
Width of extra material MC (0.1*g/cm2) = 14.4346
Width of extra material MC (0.1*g/cm2) = 8.60488 χ2 / ndf p0
300
p1
18.84 / 13
Proton stopping position (MC), 0.1*g/cm2
χ2 / ndf
Proton stopping position (MC), 0.1*g/cm2
Proton stopping position (MC), 0.1*g/cm2
Width of extra material MC (0.1*g/cm2) = 0.67928
-8.605 ± 0.3967 0.993 ± 0.001871
250
200
150
100
50
0 0
50
100
150
200
250 300 350 Beam energy, 0.1*g/cm2
0 0
χ2 / ndf
300
27.61 / 13
p0
-14.43 ± 0.3969
p1
0.9943 ± 0.001871
250
200
150
100
50
50
100
(a)
150
200
0 0
250 300 350 Beam energy, 0.1*g/cm2
50
100
150
200
250 300 350 Beam energy, 0.1*g/cm2
(b)
(c)
Figure 21: (a) the linearity of the proton stopping position measurement Rrs obtained with GEANT using the nominal CDH beam energy points in a configuration with no tracker before the range stack; (b) the Rrs linearity for nominal CDH beam energy points including the tracker; (c) the Rrs linearity after correcting beam energies by adding “extra material” observed in data (5.7 mm).
300
27.61 / 13
p0
-14.43 ± 0.3969
p1
0.9943 ± 0.001871
σ(Pstop)/Pstop, %
Proton stopping position, 0.1*g/cm2
Proton stopping position resolution χ2 / ndf
250
χ2 / ndf
3
2.5
1375 / 12
p0
2.945 ± 0.02589
p1
-0.01186 ± 0.0002809
p2
2.04e-05 ± 7.112e-07
2
200 1.5 150 1 100 0.5
50
0 0
50
100
150
200
0 0
250 300 350 Beam energy, 0.1*g/cm2
(a)
50
100
150
200 250 300 350 Stopping position, 0.1*g/cm2
(b)
Figure 22: Comparison of (a) the linearity and (b) resolution of the proton stopping position measurement Rrs in data and GEANT. Fits correspond to simulated results (black squares). Data shown as “blue crosses“.
18
4 3 2 1 0 -1 -2
5
Range difference(MC-DATA), 0.1*g/cm2
Range difference(MC-DATA), 0.1*g/cm2
Range difference(MC-DATA), 0.1*g/cm2
5
4 3 2 1 0 -1 -2
5 Rdiff/AbsRdiff/SigmaRdiff2 -2.52/2.56/1.03
4 3 2 1 0 -1 -2
-3
-3
-3
-4
-4
-4
-5 0
-5 0
50
100
150
200
250 300 350 Beam energy, 0.1*g/cm2
50
100
(a)
150
200
250 300 350 Beam energy, 0.1*g/cm2
-5 0
50
100
150
200
(b)
250 300 350 Beam energy, 0.1*g/cm2
(c)
Figure 23: The difference between measured and simulated proton stopping positions for a GEANT models with (a) nominal scintillator density of 1.025 ± 0.010 g/cm3; (b) nominal density decreased by 1% (used in this Note); (c) nominal density decreased by 2%.
PE linearity
PE resolution
2 ×10
σ(E)/E, %
Proton energy deposition, PE
3
1.8
χ2 / ndf
7
6
1.6
11.4 / 12
p0
5.694 ± 0.3765
p1
-0.003038 ± 0.0006752
p2
6.334e-07 ± 2.854e-07
5
1.4 1.2
χ2 / ndf
1
3.823 / 13
p0
-244.7 ± 5.4
p1
8.495 ± 0.03158
4
3
0.8 0.6
2
0.4 1 0.2 0 0
50
100
150
200
0 400
250 300 350 Beam energy, MeV
(a)
600
800
1000 1200 1400 1600 1800 2000 Proton energy deposition, PE
(b)
Figure 24: Comparison of (a) the linearity and (b) resolution of the energy measurements in the range stack in data and GEANT. Fits correspond to simulated results (black squares). Data shown as “blue crosses“.
19
Mean signal amplitude in Tile0, PE counts
24 22 20 18 16 14 12 10 0
50
100
150
200
250
300 350 Proton Energy, mm
Event rate, MHz
Figure 25: Comparison of the measured (blue crosses) and simulated (black square) signal amplitudes in Tile0 for different proton energies.
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
50
100
150
200 250 300 350 Proton energy, 0.1*g/cm2
Figure 26: Event rate as function of beam energy.
20
Beam range =8cm 60 50 40
80 70
Beam range =12cm 60 50 40
70
Beam range =16cm 60 50 40
30
30
20
20
20
10
10
10
20
30
40
50
60
70
0 0
80 90 Tile number
10
20
30
40
50
60
70
0 0
80 90 Tile number
70
Beam range =18cm 60 50 40
Mean energy deposition, PE
80
80 70
Beam range =20cm 60 50 40
20 10
70
0 0
80 90 Tile number
10
20
30
40
60
70
0 0
80 90 Tile number
70
Beam range =26cm 60 50 40
80 70
Beam range =28cm 60 50 40
10
10
10
(g)
60
70
80 90 Tile number
10
20
30
40
50
60
(h)
80 90 Tile number
40
20
50
70
50
20
0 0
60
Beam range =31cm
20
40
50
60
30
30
40
70
30
20
30
80
30
10
20
(f ) Mean energy deposition, PE
80
0 0
10
(e) Mean energy deposition, PE
(d)
50
80 90 Tile number
40
10
60
70
50
20
50
60
Beam range =24cm
10
40
50
60
20
30
40
70
30
20
30
80
30
10
20
(c)
30
0 0
10
(b) Mean energy deposition, PE
10
(a) Mean energy deposition, PE
80
30
0 0
Mean energy deposition, PE
Mean energy deposition, PE
70
Mean energy deposition, PE
Mean energy deposition, PE
80
70
80 90 Tile number
0 0
10
20
30
40
50
60
70
80 90 Tile number
(i)
Figure 27: Comparison of the measured (black dots) and expected (red histograms) signal profiles in the range stack from protons of incident energy of (a) 8 cm (103 MeV); (b) 12 cm (117 MeV); (c) 16 cm (129 MeV); (d) 18 cm (162 MeV); (e) 20 cm (172 MeV); (f) 24 cm (191 MeV); (g) 26 cm (200 MeV); (h) 28 cm (208 MeV); (i) 31 cm (221 MeV).
21
Stopping Range (profile) via UTP1 ×10
h1wR
150
300
100
250
50
200
0
150
10
-50
100
5
-100
50
Entries 261253 Mean 170.2 RMS 59.1
25
20
15
0 0
50
100
150
Track Y position (UTP1), mm
Events/bin
3
-150 -150
200 250 300 350 Proton stopping position, 0.1*g/cm2
-100
-50
0
50
100
150
0
Track X position (UTP1), mm
(a)
(b)
Figure 28: Water phantom (diameter of 14 cm) exposed to 300K protons of energy 200 MeV in GEANT simulations (a) the stopping range distribution (b) the stopping range profile as function of incident proton position at the first tracker station.
Stopping Range (profile) via UTP1 ×10
h1wR Entries Mean RMS
4 3.5
48675 145.8 73.11
3 2.5 2
150
300
100
250
50
200
0
150
-50
100
-100
50
Track Y position (UTP1), mm
Events/bin
3
1.5 1 0.5 0 0
50
100
150
-150 -150
200 250 300 350 Proton stopping position, 0.1*g/cm2
-100
-50
0
50
100
150
0
Track X position (UTP1), mm
(a)
(b)
Figure 29: Head phantom exposed to 50K protons of energy 200 MeV at CDH (a) the stopping range distribution (b) the stopping range profile as a function of incident proton position at the first tracker station.
22
