Design and optimization of an energy degrader with a multi-wedge scheme based on Geant4

Nuclear Inst. and Methods in Physics Research, A 890 (2018) 112–118

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Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima

Design and optimization of an energy degrader with a multi-wedge scheme based on Geant4✩ Zhikai Liang, Kaifeng Liu *, Bin Qin *, Wei Chen, Xu Liu, Dong Li, Yongqian Xiong State Key Laboratory of Advanced Electromagnetic Engineering and Technology, School of Electrical and Electronic Engineering, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China

a r t i c l e Keywords: Proton therapy Energy degrader Emittance growth Transmission efficiency Geant4

i n f o

a b s t r a c t A proton therapy facility based on an isochronous superconducting cyclotron is under construction in Huazhong University of Science and Technology (HUST). To meet the clinical requirements, an energy degrader is essential in the beamline to modulate the fixed beam energy extracted from the cyclotron. Because of the multiple Coulomb scattering in the degrader, the beam emittance and the energy spread will be considerably increased during the energy degradation process. Therefore, a set of collimators is designed to restrict the increase in beam emittance after the energy degradation. The energy spread will be reduced in the following beam line which is not discussed in this paper. In this paper, the design considerations of an energy degrader and collimators are introduced, and the properties of the degrader material, degrader structure and the initial beam parameters are discussed using the Geant4 Monte-Carlo toolkit, with the main purpose of improving the overall performance of the degrader by multiple parameter optimization.

1. Introduction A proton therapy facility with two 360 degree gantry treatment rooms and one fixed beamline is under development in Huazhong University of Science and Technology (HUST), that is based on isochronous superconducting cyclotron scheme [1]. In proton therapy the beam energy must be varied to position the Bragg peak at the precise depth of a tumor inside a patient. Because of the fixed energy extracted from the cyclotron, an energy degrader is designed to modulate the energy, which will lead to emittance growth by multiple Coulomb scattering. The collimators are necessary to be placed downstream after the degrader to restrict the beam emittance. The degrader is an important component in proton therapy system, that changes the beam characteristics. The main considerations are: (a) The beam energy shall be modulated continuously, so that the penetration depth of the beam can be arbitrarily controlled to be within an achievable range. (b) High energy modulation speed is essential to realize volumetric repainting, which has been proven to be an effective beam scanning method for the treatment of moving organs. The volumetric repainting method can mitigate the uncontrolled dose inhomogeneity due to organ motion [2,3].

(c) High beam transmission efficiency is the main purpose of the design and optimization. Energy modulation and emittance restriction are both realized at the expense of beam loss. High beam transmission efficiency in a low-energy range will reduce the requirement on beam current extracted from the cyclotron and increase the dose rate. Because of the above requirements, the structure and the material of the degrader are important factors. For HUST proton therapy facility, a multi-wedge structure [4,5] using high-density graphite was chosen. This structure enables continuous energy modulation by precisely adjusting the overall graphite depth. With careful design of the wedge angle and wedge number, the compactness and fast movement during energy degradation can be achieved, which are discussed in Section 3.2. With regard to the material of the degrader, a material with low atomic number is selected because of the weak multiple Coulomb scattering. Paul Scherrer Institute (PSI) proposed the use of 𝐵4 𝐶, which was demonstrated to have higher transmission than graphite. When a 𝐵4 𝐶 block is used to degrade the proton beam from 240 to 85 MeV, the transmission efficiency is increased by about 37% [6]. However, it is very difficult to process 𝐵4 𝐶 into a specific shape, which limits its application. Physical requirements and general design, simulation and

✩ Work supported by The National Key Research and Development Program of China, with grant No. 2016YFC0105305, and National Natural Science Foundation of China with grant No. 11375068. * Corresponding authors. E-mail addresses: [email protected] (K. Liu), [email protected] (B. Qin).

https://doi.org/10.1016/j.nima.2018.01.073 Received 11 October 2017; Received in revised form 19 December 2017; Accepted 21 January 2018 Available online 31 January 2018 0168-9002/© 2018 Elsevier B.V. All rights reserved.

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where 𝑍∕𝐴 and 𝜌 are the charge mass ratio, material density respectively; 𝛽, 𝛾 and 𝐼 are the relative velocity, relative mass and ionization potential of the incident proton; 𝜌𝑑𝑥 is the reduced medium thickness; and 𝛿/2 represents the density correction term, which can be ignored because the energy is below 1 GeV. Because of the multiple Coulomb scattering, the beam emittance increases considerably during the degradation process. The rms emittance after the thin degrader 𝜀𝑑𝑒𝑔 and the rms multiple scattering angle 𝜃0 can be calculated by Eq. (2) and Eq. (3), respectively. 𝜀𝑑𝑒𝑔 2 = 𝜀0 2 + (𝛽𝜃0 )2

Fig. 1. Layout of the beamline from the superconducting cyclotron to the double bend achromatic (DBA) section.

𝜃0 = Table 1 Main beam parameters before degrader and after double bend achromatic (DBA) section. Parameters

Before degrader

After DBA section

Energy Momentum spread (one 𝜎 value) Current Rms emittance

250 MeV 0.5%

70–238 MeV 0.5%

500 nA 5𝜋 mm ⋅ mrad

0.5–5 nA 5𝜋, 7𝜋, 10𝜋 mm ⋅ mrad

𝐿0 =

𝐿 𝐿 ⋅ [1 + 0.038 ln( )] 𝐿0 𝐿0

(3)

𝐴 716.4 g∕cm2 √ 𝑍 (𝑍 + 1) ln(287∕ 𝑍)

(4)

Collimators with various aperture sizes are used to define the accepted emittance, as shown in Eq. (5). 𝜀𝑐𝑜𝑙 =

2𝑟1 ⋅ 𝑟2 𝐿𝑐𝑜𝑙

(5)

where 𝑟1 and 𝑟2 are the radii at the entrance and exit of the collimator, respectively, and 𝐿𝑐𝑜𝑙 is the overall length of the collimator. Eq. (5) clearly indicates that the final emittance depends on the aperture and overall lengths. Both Col1 and Col2 have three selectable apertures; therefore, the rms emittance after the Col2 can be chosen among 5𝜋, 7𝜋 and 10𝜋 mm⋅mrad. Because both the energy degrader and the collimators realize the desired energy and emittance at the expense of beam loss, the beam transmission efficiency will be considerably reduced, especially in the low-energy range. The major design issue for energy degrader is to optimize its transmission, which are discussed in detail in Section 3.

2. Physical requirements and principles Fig. 1 shows the layout of proton therapy beamline from the superconducting cyclotron (SCC250) to the double bend achromatic (DBA) section [7]. By changing the overlap thickness of multiple wedges, the beam energy can be modulated. The beam emittance will be increased significantly because of the multiple Coulomb scattering of the incident protons at the nuclei of the degrader material. Therefore, a set of collimators (Col1, Halo_col and Col2) placed immediately behind the degrader is used to shape the emittance. Col1 and Col2 are used to limit the beam size and the divergence, respectively, and Halo_col is used to stop the beam halo after Col1. The momentum spread is limited by the slit installed in the DBA section. Main design considerations regarding the beam parameters are as follows:

3. Simulation and optimization 3.1. Simulation method The optimization of the energy degrader and collimators is performed using the Geant4 code based on the Monte-Carlo algorithm [9]. The Geant4 code includes the definition of primary particles, detector construction, physical processes and running parameters. The QBBC physics lists are selected because they are appropriate for the 250 MeV protons. The density of the graphite material is 1.95 𝑔∕𝑐𝑚3 , and the mean excitation potential 𝐼 is 81 eV. The production cuts are 0.7 mm for limiting the production of secondary particles. For degradation in a lower energy range 70–110 MeV, to reduce the fluctuations due to the lower transmission efficiency, the simulation is performed with 106 protons. For degradation in a higher energy range 110–238 MeV, the simulation is performed with 5×105 protons [5]. Fig. 2 shows the simulated image by Geant4. Finally, the data can be post-processed to realize the results visualization. The post-process includes the statistical definition of the beam emittance, the beam energy distribution and the transmission efficiency. Considering 𝑋 axis as an example, the statistic rms beam emittance 𝜀𝑟𝑚𝑠 can be defined as shown in Eq. (6) [10].

∙ Modulation range of the beam energy: A beam energy range 70–238 MeV is designed for HUST-PTF based on the clinical requirement, which can almost cover the deepest position of tumors in the body. ∙ Beam emittance: The beam emittance defines the beam size and beam current at the treatment terminal. An optional rms beam emittance of 5𝜋, 7𝜋 and 10𝜋 mm⋅mrad is designed. ∙ Beam current: For treatments, the beam current should not exceed the safety margin during spot scanning in the nozzle; however, its value should not be too low because of the dose rate requirement. A beam current of 0.5–5 nA is required for energy ranging from 70 to 238 MeV. The limitation of the highest current is realized in the following beamline, which is not discussed in this paper. On the basis of the above considerations, the beam specifications are listed in Table 1. The beam can be degraded into an energy in the range from 70 to 238 MeV. The degradation process results from the interactions between the incident protons and the degrader material. In this process, the energy loss is determined according to the Bethe–Bloch formula (see e.g. [8]), given in Eq. (1). 2𝑚 𝑐 2 𝛾 2 𝛽 2 𝑍 1 𝛿 𝑑𝐸 = 4𝜋𝑁𝑎 𝑟2𝑒 𝑚𝑒 𝑐 2 𝑧2 ( )( )[ln( 𝑒 ) − 𝛽2 − ] 2 𝜌𝑑𝑥 𝐴 𝛽 𝐼 2

√

where 𝜀0 is the initial rms beam emittance; 𝛽 in Eq. (2) is the beam twiss parameter; 𝑧, 𝑣 and 𝑝 are the charge, velocity and momentum of the incident particle; 𝐿 is the reduced medium thickness; and 𝐿0 is the material radiation length, which is determined using Eq. (4) [8].

optimization of multiple parameters of the degrader are discussed in this paper.

−

13.6𝑧 𝑣𝑝

(2)

𝜀𝑟𝑚𝑠 = 𝜎𝑥 𝜎𝑥′ 𝑟=

√ 1 − 𝑟2

𝜎𝑥𝑥′ 1 = 𝛴(𝑥𝑖 − 𝑥)(𝑥 ̄ ′𝑖 − 𝑥̄′ ) 𝜎𝑥 𝜎𝑥 ′ 𝑁𝜎𝑥 𝜎𝑥′

(6)

(7)

where 𝜎𝑥 and 𝜎𝑥′ are the rms position and rms divergence, respectively, and 𝑟 is the correlation coefficient between 𝜎𝑥 and 𝜎𝑥′ calculated by Eq.

(1) 113

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Fig. 2. (a) Simulation diagram before running the code; (b) Simulation diagram after running the code. Table 2 Main input parameters of Geant4. Initial beam parameters (1 sigma) Beam radius Beam divergence angle Momentum spread

1.552 mm 3.333 mrad 0.5%

Degrader’s structure parameters Length (along beam direction) Number of wedges (one side) Wedge angle

240 mm 2.5 30 degrees

Collimators’ structure parameters Parameter

Col1

Halo_Col

Col2

𝑟𝑖𝑛 (mm) 𝑟𝑜𝑢𝑡 (mm)

3.5 4.7

6.5 12.5

5.5 6.1

Material, center position and the length of main objects Object

Material

Position (mm)

Length (mm)

Degrader

Graphite (𝜌 = 1.95 ± 0.01 g∕cm3 ) Copper Graphite Copper

0

240

170 290 821

70 120 70

Col1 Halo_Col Col2

Fig. 3. Beam transmission efficiency varies with the degrader overall length when the energy is degraded to 70, 150 and 230 MeV.

The beam emittance after the energy degrader can be influenced by the degrader structure, degrader material and initial beam parameters according to Eq. (2) and Eq. (3). In this section, we discuss how these parameters affect the emittance growth first and then the beam transmission efficiency when the ultimate rms beam emittance after Col2 is invariable (7𝜋 mm⋅mrad) in this study. Moreover, the modulation time and energy range are considered for optimization.

the beam direction remains unchanged so that the beam waist can always be located at the degrader center. Moreover, the energy degrader should be compact to reduce the average 𝛽 value. The degrader overall length along the beam axis includes the wedge overlap length and the gap length. For the same amount of energy degradation, the wedge overlap length will be constant. Fig. 3 shows that shorter length leads to higher beam transmission efficiency. However, enough gap length is essential so that there is a bigger superficial area to emit heat radiation. The maximum dissipated power of the 250 MeV/500 nA proton beam is about 100 W when the energy is degraded to 70 MeV. This will first lead to an increase in the degrader temperature, and then cause thermal deformation [11]. The thermal deformation will result in the disturbance of the degraded energy. Therefore, the water cooling devices are installed at the side of the degrader far away from the beam. Considering both the beam transmission efficiency and the gap to emit heat radiation, a degrader overall length of 240 mm is considered optimum, and the beam transmission efficiency is 0.49% when the beam passes from the degrader to Col2 and the energy is degraded to 70 MeV.

3.2.1. Degrader length The degrader length along the beam axis will influence the emittance growth by affecting the twiss parameter 𝛽. As shown in Eq. (2), smaller twiss parameter 𝛽 will cause smaller beam emittance growth. The average 𝛽 can reach the minimum when the beam waist is focused to the center of the energy degrader. The structure with a pair of symmetric multi-wedge blocks ensures that the center of the energy degrader along

3.2.2. Degrader wedge shape The degrader wedge shape is another important structural parameter, which includes the wedge angle 𝜃 and the number of wedges 𝑛. In this study, the angle and the number of wedges are changed respectively, while the other parameters are kept constant. By changing only the angle or the number of wedges, the energy degradation and the emittance growth cannot be varied according to Eq. (1) and Eq. (2). However, the

(7). 𝑥𝑖 and 𝑥′𝑖 are the position and the divergence of a certain particle, 𝑥̄ and 𝑥̄′ are the average values, and 𝑁 is the number of statistic particles. Beam loss is caused by energy degradation and emittance restriction. When the amount of energy degradation is constant, beam loss will be influenced only by emittance restriction. Therefore, the optimization method should reduce the beam emittance after the energy degrader by changing the input parameters, which are discussed in detail in Section 3.2. Table 2 shows the main input parameters of Geant4. 3.2. Optimization and discussion

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wedges at the same time. However, in reality, the beam is a Gaussian distribution so that most of the protons will be in the area of lower additional overlap thickness. Moreover, the area of the smaller angle wedge is pretty small because the incident beam radius is small. Therefore, the additional degradation energy could be pretty lower than the energy spread. The simulation results as shown in Fig. 5 indicate that the additional degrading energy has a negligible effect on the energy degradation performance. Fig. 6(a) shows that the maximum modulation energy and the displacement ratio vary with the wedge angle when the number of wedges is 2.5. Fig. 6(b) shows the variation curve with respect to the number of wedges when the wedge’s angle is 30 degrees. Considering the energy modulation range and the displacement ratio together, the wedge angle is designed to 30 degrees and the number of wedges is 2.5. The maximum modulation energy is 239 MeV which is higher than the required value (238 MeV) and the displacement ratio is 2.68 so that the modulation time could be lower than 80 ms per step energy (corresponding to 5 mm equivalent depth in water).

Fig. 4. (a) Minimum overlap thickness exists due to the initial beam dimension (the number of wedges is 2.5 for one side); (b) A new structure of the degrader with variational angle to decrease the minimum overlap thickness when the overall length and the displacement ratio are kept constant.

angle or the number of wedges can significantly influence the energy modulation range and the displacement ratio. The displacement ratio represents the relationship between the overlap length variation along the beam axis and the one-sided wedge movement length perpendicular to the beam axis. The displacement ratio 𝑟 can be calculated by Eq. (8). 𝑟 = 4 ∗ 𝑛 ∗ 𝑡𝑎𝑛(𝜃∕2)

3.2.3. Degrader material The atomic number and the density of degrader material directly influence the multiple Coulomb scattering and ionization processes, which will in turn influence the transmission. The multiple scattering angle is influenced by the material radiation length when the amount of energy degradation is the same. According to Eq. (4), the radiation length scales approximately with 𝐴∕𝑍 2 . Because 𝐴∕𝑍 2 is higher for elements with a low atomic number 𝑍, the radiation length for low-𝑍 material is higher. Therefore, scattering by low-𝑍 material is less, and hence, the emittance growth after the degrader will be smaller. Although the density cannot affect the multiple scattering angle, it can have an effect on the twiss parameter 𝛽, thus affecting the beam emittance growth. According to the Bethe–Bloch formula, as shown in Eq. (1), for the same amount of energy degradation, the degrader material with a higher density will require a shorter overlap length as shown in Fig. 7 so that the degrader’s overall length could be shorter when the gap length is constant and then the twiss parameter 𝛽 will be smaller. This will lead to a 22% increase in beam transmission efficiency at 70 MeV when the graphite density changes from 1.65 to 1.95 𝑔∕𝑐𝑚3 as the degrader material, which is shown in Fig. 8. The source of the fluctuations of the points in Fig. 8 is statistics and the red and blue curves are produced by polynomial fits.

(8)

Therefore, more wedges and larger angle will result in a larger displacement ratio. For the same amount of energy degradation, a larger displacement ratio requires shorter wedge movement length. Thus, the energy modulation time of the degrader can be shorter to meet the rapid treatment demand. Regarding the energy modulation range, the incident beam has an initial radius (one sigma value is 1.552 mm) such that the degrader has minimum overlap length to ensure the uniformity of the energy degradation, as shown in Fig. 4(a). Fewer wedges and smaller angle will result in lower minimum overlap thickness and subsequently a higher maximum modulation energy. Fig. 4(b) shows a new structure with a variational angle of the degrader’s wedge. Smaller angle at the tip and larger angle at the end of the wedge could first decrease the minimum overlap thickness and then increase the maximum modulation energy, when the overall length and the displacement ratio are constant. However, the variation in the wedge angle will create an additional overlap when beam passes through both the smaller and larger angle

Fig. 5. Beam energy distribution of the degrader with variational wedge angle. The first and last subgraph represent the status when beam passes through the smaller and larger angle wedge, respectively. The seven subplots in the middle represent the status when beam passes through both the smaller and larger angle wedges at the same time. The smaller and larger angles are set to 15 degrees and 30 degrees, respectively. 115

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Fig. 7. Beam energy varying with the degrader overlap length.

Fig. 6. (a) The maximum modulation energy and the displacement ratio vary with the wedge angle when the number of wedges is 2.5; (b) The maximum modulation energy and the displacement ratio vary with the number of wedges when the wedge angle is 30 degrees. Fig. 8. Beam transmission efficiency after Col2 varying with the density of graphite when the gap lengths are the same. The lengths shown in this figure are the overall lengths of the degrader. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

When choosing the degrader material, not only the atomic number and the density but also machinability, nontoxicity, melting temperature and other parameters should be considered. Beryllium is not an appropriate material because of its toxicity, mechanical fragility and the large neutron production cross-section. Furthermore, it is very difficult to process boron carbide (𝐵4 𝐶) into a specific shape. At present, graphite is the widely used degrader material in proton therapy facilities [12]. The density of graphite can reach 1.95 ± 0.01 g∕cm3 offered by ICCCAS (Institute of Coal Chemistry, Chinese Academy of Sciences). We propose a new energy degrader made of 𝐵4 𝐶/graphite composites (BGC). The BGC material has lower average atomic number and higher density than graphite. The density of the BGC material varies with different 𝐵4 𝐶 to graphite ratios. Moreover, it is easier to process the BGC material than 𝐵4 𝐶 because of the presence of soft graphite in it [13]. The BGC material remains under study. Therefore, the current project chooses the conventional graphite as the degrader’s material whose density is 1.95 ± 0.01 g∕cm3 .

Table 3 Variations in beam parameters with the initial rms beam emittance. Parameter

Unit

Value

𝜀0 𝛼 𝛽 𝑥 ′ 𝑥 𝑇230 MeV 𝑇150 MeV 𝑇70 MeV

mm ⋅ mrad – m mm mrad % % %

2𝜋 0.292 0.44 0.939 2.219 18.69 2.37 0.53

5𝜋 0.267 0.482 1.552 3.333 16.63 2.07 0.49

10𝜋 0.248 0.514 2.267 4.545 12.68 1.67 0.41

5𝜋 mm⋅mrad is selected as the initial beam emittance because this value can be easily realized by the cyclotron.

3.2.4. Initial beam emittance Initial beam emittance is another factor that affects the emittance after degrader according to Eq. (2). In addition to the direct influence on the beam emittance after degrader, the initial emittance will also influence the beam twiss parameter 𝛽 which has a great contribution to the emittance growth. The twiss parameter, rms size and divergence after the degrader and the transmission efficiency when the initial rms beam emittance varies among 2𝜋, 5𝜋 and 10𝜋 mm⋅mrad are listed in Table 3, while the beam waist is focused to the degrader center. The initial beam emittance depends on the cyclotron. In the current design,

3.3. Results of the selected parameters From the above discussion, the parameters are optimized. The degrader overall length is 240 mm while the angle of the degrader wedge is 30 degrees and the number is 2.5 for one-sided wedge. Graphite is chosen as the degrader material whose density is 1.95 ± 0.05 g∕cm3 . The initial rms beam emittance is 5𝜋 mm⋅mrad. Phase space plot after Col2 is shown in Fig. 9 when the energy is degraded to 70 MeV. The beam is no longer 2D Gaussian distribution after Col2 because of the stop of 116

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Fig. 10. Beam emittances after each component varying with the beam energy in the range from 70 to 239 MeV. Fig. 9. Phase space plot after Col2 when the energy is degraded to 70 MeV.

the collimators, and this will cause that the rms emittances after Col2 change from 7.73 to 5.14𝜋 mm⋅mrad varying with the energy. The rms emittance of 7.06𝜋 mm⋅mrad in the medium energy (150 MeV) after Col2 is close to the design value (7𝜋 mm⋅mrad). The change in emittance and transmission efficiency is shown as a function of degraded beam energy in Fig. 10 and Fig. 11, respectively. However, the transmission efficiency to the gantries will be further decreased when the beam momentum spread is degraded to 0.5% by the energy selection system. The increase in beam energy spread is displayed in Fig. 12. When the energy is degraded to 70 MeV, the transmission is approximately 24.5% that can decrease the momentum spread for beamline design not described in this paper. Therefore, the minimum beam transmission efficiency is 0.12%, and then the minimum beam current is 0.6 nA which is higher than the design value 0.5 nA. 4. Discussions and conclusions Fig. 11. Beam transmission efficiencies after each component varying with the beam energy in the range from 70 to 239 MeV.

The degrader has a great impact on beam parameters including the beam energy, emittance and current, which will lead to significant beam loss when shaping the beam according to clinical requirements. This paper describes design considerations regarding physical and technical

Fig. 12. Beam energy spread statistical histograms with mean energy and one 𝜎 value dE. 117

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References

issues, especially the optimization of the degrader structure, degrader material and beam optics. Some conclusions can be obtained as follows:

[1] B. Qin, K.J. Fan, M.W. Fan, et al., Fast scanning beamline design applied to proton therapy system based on superconducting cyclotrons, in: Proc. 21th International Conference on Cyclotrons and their Applications, CYC2016, Zurich, Switzerland, 2016, Paper MOP12. [2] X. Liu, B. Qin, K.F. Liu, et al., Eddy current analysis and optimization of fast scanning magnet for a proton therapy system, Nucl. Instrum. Methods Phys. Res. A 862 (2017) 1–7. [3] D. Meer, New fast scanning techniques using a dedicated cyclotron at PSI, in: Proc. Workshop on Hadron Beam Therapy of Cancer, Erice, Italy, 2009. [4] V. Anferov, Energy degrader optimization for medical beam lines, Nucl. Instrum. Methods Phys. Res. A 496 (2003) 222–227. [5] M.J. van Goethem, et al., Geant4 simulations of proton beam transport through a carbon or beryllium degrader and following a beam line, Phys. Med. Biol. 54 (2009) 5831–5846. [6] A. Gerbershagen, et al., Measurements and simulations of boron carbide as degrader material for proton therapy, Phys. Med. Biol. 61 (2016) N337– N348. [7] J.M. Schippers, Beam delivery systems for particle radiation therapy: Current status and recent developments, Rev. Accel. Sci. Technol. 02 (2009) 179. [8] W.R. Leo, Techniques for Nuclear and Particle Physics Experiments: a How-to Approach, Springer Science and Business Media, 2012, pp. 24–45. [9] Geant4 reference, http://geant4.web.cern.ch/geant4/. [10] S.Y. Lee, Accelerator Physics, second ed., World Scientific Publishing Company, 2004, pp. 77–79. [11] H. Reist, et al., A Fast Degrader to Set the Energies for the Application of the Depth Dose in Proton Therapy, PSI Scientific and Technical Report 2001, VI, 2001, pp. 20– 21. [12] J.M. Farley Francis, Optimum strategy for energy degraders and ionization cooling, Nucl. Instrum. Methods Phys. Res. A 540 (2005) 235–244. [13] H. Wang, Q. Guo, J. Yang, et al., Microstructure and thermophysical properties of B4C/graphite composites containing substitutional boron, CARBON 52 (2013) 10– 16.

(1) The compactness of the degrader wedge contributes to the increase in beam transmission. However, an enough gap to emit heat radiation should be considered. (2) By optimizing the angle and the number of degrader wedges, wider energy modulation range and higher energy modulation speed can be achieved. (3) The degrader with variational angles of the wedge could achieve a higher maximum energy, while the energy modulation speed could be also higher. (4) The degrader’s material should have lower atomic number and higher density. Graphite is the conventional material. The 𝐵4 𝐶/graphite composites are proposed and under study. (5) Smaller initial beam emittance will influence the beam transmission, which leads to a 20% increase in beam transmission efficiency when the rms emittance is 5𝜋 mm⋅mrad compared to 10𝜋 mm⋅mrad. According to the above analysis, the energy degrader system is optimized, and the energy range is 70–239 MeV. Besides the physical design, the preliminary engineering design was performed including the radiation hardness of the material and the new degrader material. For instance, the aluminum alloy vacuum box and EPDM seal ring is adopted due to high radiation hardness. And the new degrader material such as BGC or other composite is our significant research content in the next stage. The project HUST-PTF was started during August 2016 and is now under design.

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