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The proton imaging system is composed of four quadrupole magnetic lenses and a collimator. The quadrupole magnetic lenses can realize point-to-point imaging, and the collimator can improve image quality by controlling proton flux and realize material diagnosis. The magnetic field gradient of an ideal quadrupole lens becomes zero at the edge. Inside the lens, the magnetic field gradient is constant along the axis, while the magnetic field boundary of the actual lens extends outward. In the proton imaging system, the fringing field will affect the proton transport state and the performance of the imaging system as well. In this paper, a method to optimize the system is presented when the fringe field is considered. A proton imaging system of 1.6 GeV is established with the Geant 4 program, in which the magnetic field gradient distribution of the actual lens is approximated by the Bell function. In an ideal imaging system, the external drift length is 1.2 m, the internal drift length is 0.5 m, the length of the magnet is 0.8 m, and the magnetic field gradient is 8.09 T/m. The parameters of the practical imaging system can be obtained by using the optimization method: when the integral difference in magnetic field gradient distribution between the actual lens and the ideal lens is equal to zero, the outer drift length of the imaging system is 1.203 m and the inner drift length is 0.506 m; when the integral difference in the magnetic field gradient distribution between the actual lens and the ideal lens is equal to 1%, the outer drift length is 1.208 m and the inner drift length is 0.516 m. In the numerical simulation, a 1mm-thick copper plate and a concentric ball are chosen as the objects, and the influence of the fringing field on the collimator aperture and that on the proton flux error are studied. The results show that the optimized imaging system can reduce the flux error of protons passing through the object, and the difference in the aperture of collimator is on the order of 10–2 when the integral difference is on the order of 10–2 in magnitude.
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Keywords:
- proton radiography /
- angle-cut collimator /
- fringe field of the quadrupole lens /
- Geant 4 code
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Liu L F, Liu C J, Zhang G R, et al. 1991 High Power Laser Part. Beams 3 535
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Google Scholar
Chen F, Xu H B, Zheng N, Jia Q G, She R G, Li X El 2020 Acta Phys. Sin. 69 032901
Google Scholar
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图 1 质子成像系统示意图
Figure 1. Diagram of proton imaging system.
图 2 磁透镜中磁场梯度分布
Figure 2. Magnetic field distribution in the quadrupole lens.
图 3 等效漂移距离随着初始位置的改变
Figure 3. Equivalent drift distance varies with the initial position.
图 4 质子成像系统参数示意图
Figure 4. Diagram of parameters of proton imaging system
图 5 等效漂移距离相对值的优化曲线 (a) 积分差值为0; (b) 积分差值为1%
Figure 5. Optimized curves of relative value of the equivalent drift distance: (a) The difference of integral value is 0; (b) the difference of integral value is 1%.
图 6 前端口传输矩阵元随磁场梯度积分差值的变化 (a) x方向; (b) y方向
Figure 6. Transfer matrix elements of the front port varies with the gradient integral difference: (a) x direction; (b) y direction.
图 7 后端口传输矩阵元随磁场梯度积分差值的变化 (a) x方向; (b) y方向
Figure 7. Transfer matrix elements of the back port varies with the gradient integral difference: (a) x direction; (b) y direction.
图 8 积分差值为0时质子通过铜板的通量分布 (a) 2.0 mrad; (b) 3.5 mrad
Figure 8. Flux distribution after passing the round copper plate while the integral difference is 0: (a) 2.0 mrad; (b) 3.5 mrad
图 9 积分差值等于0时质子通过同心球的通量分布 (a) 2.0 mrad; (b) 3.5 mrad
Figure 9. Flux distribution after passing the concentric spheres while the integral difference is 0: (a) 2.0 mrad; (b) 3.5 mrad
图 10 积分差值等于1%时质子通过铜板的通量分布 (a) 2.0 mrad; (b) 3.5 mrad
Figure 10. Flux distribution after passing the round copper plate while the integral difference is 1%: (a) 2.0 mrad; (b) 3.5 mrad.
图 11 积分差值等于1%时质子通过同心球的通量分布 (a) 2.0 mrad; (b) 3.5 mrad
Figure 11. Flux distribution after passing the concentric spheres while the integral difference is 1%: (a) 2.0 mrad; (b) 3.5 mrad.
表 1 优化前质子成像系统参数
Table 1. Parameters of the proton imaging system before optimization.
类型 积分差值/% $d/{\rm{m}}$ Ds/m $l/{\rm{m}}$ ${G_{\rm{o} } }/({\rm{T} } \cdot { {\rm{m} }^{ - {\rm{1} } } })$ Dt/m 理想 — — 1.2 0.8 8.09 0.5 含边缘
(初值)0 0.073 1.2 0.8 8.09 0.5 1 0.073 1.2 0.8 8.09 0.5 
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表 2 优化后质子成像系统参数
Table 2. Parameters of proton imaging system after optimization.
类型 积分差值/% $d/{\rm{m}}$ ${D_{\rm{s}}}/{\rm{m}}$ $l/{\rm{m}}$ ${G_{\rm{o} } }/({\rm{T} } \cdot { {\rm{m} }^{ - {\rm{1} } } })$ ${D_{\rm{t}}}/{\rm{m}}$ 理想 — — 1.2 0.8 8.09 0.500 含边缘 0 0.073 1.203 0.8 8.09 0.506 1 0.073 1.208 0.8 8.09 0.516
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表 3 准直器孔径参数
Table 3. Aperture parameters of the angle-cut collimator.
截断角
/mrad系统
类型积分
差值/%前端/cm 后端/cm 厚度/m 材料 x y x y 2.0 理想 — 1.49 1.70 0.61 0.61 0.5 W 含边缘 优化前 1.49 1.70 0.61 0.61 0 1.49 1.70 0.61 0.61 1 1.48 1.70 0.61 0.61 3.5 理想 — 1.87 2.24 1.07 1.07 含边缘 优化前 1.87 2.24 1.07 1.07 0 1.87 2.24 1.07 1.07 1 1.87 2.24 1.08 1.07
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[1] Gavton A, Morris C L, Ziock H J, et al. 1996 Los Alamos National Report 96 420
[2] Mottershead C T, Zumbro J D 1997 Proceedings of the 1997 Particle Accelerator Conference Vancouver B C, Canada, May 12–16, 1997 p1397
[3] Jason AJ, Barlow D B, Blind B, et al. 2001 Proceedings of the 2001 Particle Accelerator Conference Chicago, USA, June 18–22, 2001 p3374
[4] King N S P, Ables E, Adams K, et al. 1999 Nucl. Instrum. Methods Phys. Res., Sect. A 424 84
Google Scholar
[5] Rigg P A, Schwartz C L, Hixson R S, et al. 2008 Phys. Rev. B 77 220101
Google Scholar
[6] MorrisC L, AblesE, Alrick KR, et al. 2011 J. Appl. Phys. 109 104905
Google Scholar
[7] Matthew S. F, Jason A, Camilo E, et al. 2016 Proc. of SPIE 9783 97831X
[8] Matthew S. F, Jason A, Malcolm A, et al. 2017 Rev. Sci. Instrum. 88 013709
Google Scholar
[9] AntipovaYM, AfoninaA G, Vasilevskii A V, et al. 2010 Instrum. Exp. Tech. 53 319
Google Scholar
[10] GolubevA A, DemidovVS, DemidovaE V, et al. 2010 Tech. Phys. Lett. 36 177
Google Scholar
[11] Burtsev V V, Lebedev A I, Mikhailov A L, et al. 2011 Combust., Explos. Shock Waves 47 627
Google Scholar
[12] Varentsov D, Antonov O, Bakhmutova A, et al. 2016 Rev. Sci. Instrum. 87 023303
Google Scholar
[13] Yang J J, Zhen X, Wei S M, et al. 2016 CYC 2016 Proceedings of the 21st International Conference on Cyclotrons and their Applications Zurich, Switzerland, September 11–16, 2016 p401
[14] Sheng L N, Zhao Y T, Yang G J, et al. 2014 Laser Part. Beams 32 651
Google Scholar
[15] Zhao Y, Zhang Z, Gai W, et al. 2016 Laser Part. Beams 16 1
[16] Wei T, Yang G J, Li Y D, et al. 2014 Chin. Phys. C 38 087003
Google Scholar
[17] Wei T, Yang G J, Long J D, et al. 2013 Chin. Phys. C 37 068201
Google Scholar
[18] Zhou Z, Fang Y, Chen H, et al. 2019 Matter Radiat. Extremes 4 065402
Google Scholar
[19] Aufderheide M B, ParkH, Hartouni E P1999 AIP Conference Proceedings Sydney, Australia, June 28–July 2, 1999 p497
[20] Maksimov A V, Tyurin N E, Fedotov Y S 2014 Tech. Phys. 59 132
[21] Morris C L, Brown E N, Agee C, et al. 2016 Exp. Mech. 56 111
Google Scholar
[22] Li Y D, Yang G J, Zhang X D, et al. 2016 Nucl. Instrum. Methods Phys. Res., Sect. A 814 104
Google Scholar
[23] 刘烈烽, 刘承俊, 章冠人 1991 强激光与粒子束 3 535
Liu L F, Liu C J, Zhang G R, et al. 1991 High Power Laser Part. Beams 3 535
[24] Agostinelli S, Allison J, Amako K A, et al. 2003 Nucl. Instrum. Meth. Phys. Res. Sect. A 506 250
Google Scholar
[25] Allison J, Amako K, Apostolakis J, et al. 2006 IEEE Trans. Nucl. Sci. 53 270
Google Scholar
[26] Schott W, Springer K, Winter H J, et al. 1973 Nucl. Instrum. Methods 111 541
Google Scholar
[27] 陈锋, 许海波, 郑娜, 贾清刚, 佘若谷, 李兴娥 2020 物理学报 69 032901
Google Scholar
Chen F, Xu H B, Zheng N, Jia Q G, She R G, Li X El 2020 Acta Phys. Sin. 69 032901
Google Scholar
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