Analytical model for scattering effect of energetic charged-particle beam in radiography of steep density gradient region

Li Liang-Liang; Wang Xiao-Fang

doi:10.7498/aps.70.20212269

Abstract

Energetic charged-particle beams produced from ultrashort ultra-intense laser plasma interactions play a vital role in charged-particle radiography. When such an energetic beam penetrates through a foil target, its energy loss is negligible, and the main physics process is small-angle scattering. Owing to this scattering effect, charged-particle radiography of a target with a transversely distributed steep density gradient region will produce a modulation structure in the fluence distribution on the detection plane, which could be used to diagnose the steep density gradient region. In the past, the theoretical work on the scattering effect and the resulting modulation structure was done with Monte-Carlo simulations, which cost a lot of computing time and the studied parameter range was limited. In the present work, an analytical model is developed to deal with the scattering effect inside the target and the modulation structure on the detection plane in radiography, which can quickly present the results that coincide with Monte-Carlo simulations very well. By using this analytical model, the characteristics of modulation structures are analyzed. A dimensionless characteristic parameter related to radiography conditions is put forward, and its range determines different modulation structures and also the probability of diagnosing a steep density gradient region with a width $\lesssim $ 2 μm.

Keywords:

Authors and contacts

School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China

Corresponding author: Wang Xiao-Fang, wang1@ustc.edu.cn

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References

[1]	Zohuri B 2017 Inertial Confinement Fusion Driven Thermonuclear Energy (Cham: Springer International Publishing AG)
[2]	Lindl J 1995 Phys. Plasmas 2 3933 Google Scholar
[3]	Chen B, Yang Z, Wei M, Pu Y, Hu X, Chen T, Liu S, Yan J, Huang T, Jiang S, Ding Y 2014 Phys. Plasmas. 21 122705 Google Scholar
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Cited By

图 1 准直带电粒子束被平面靶散射后的角分布示意图

Figure 1. The schematic diagram of the angular distribution of a collimated charged particle beam scattered by a plane target.

DownLoad: Full-Size Img PowerPoint

图 2 带电粒子束照相一维密度梯度分布靶　(a) 照相示意图; (b) 梯度靶的密度分布示意图

Figure 2. A charged particle beam radiographs a planar target with a one-dimensional density gradient: (a) The schematic diagram of radiography; (b) the schematic of density profile around the density gradient region.

DownLoad: Full-Size Img PowerPoint

图 3 沿x方向的电子通量密度分布　(a)单能电子束; (b)不同能散电子束

Figure 3. The electron fluence distribution along x direction for an incident electron beam: (a) Mono energy; (b) different energy spread.

DownLoad: Full-Size Img PowerPoint

图 4 沿x方向的电子通量密度分布　(a) d = 0 μm; (b) d = 1 μm

Figure 4. The electron fluence distribution along x direction: (a) d = 0 μm; (b) d = 1 μm.

DownLoad: Full-Size Img PowerPoint

图 5 电子束对多层球靶照相的示意图

Figure 5. Schematic diagram for an electron beam radiographing a spherically multilayer capsule.

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图 6 Fluka模拟结果　(a) 探测面上电子图像; (b) y = 0附近沿x方向的通量密度分布

Figure 6. Results from Fluka simulation: (a) Electron radiograph on the detection plane; (b) fluence distribution along the x direction around y = 0.

DownLoad: Full-Size Img PowerPoint

图 7 解析模型的结果　(a) 散射角宽度的径向分布; (b) y = 0处通量密度分布和Fluka模拟结果

Figure 7. Results from the analytical model: (a) Distribution of the scattered angle in the radial direction; (b) the fluence distributions from the analytical model and Fluka simulation, respectively.

DownLoad: Full-Size Img PowerPoint

图 8 不同照相参数条件下典型调制信号形状

Figure 8. Representative modulation structures under different radiography conditions.

DownLoad: Full-Size Img PowerPoint

图 9 调制信号特征量和ω随照相参数的变化　(a) 点源发散束情况下改变梯度区宽度; (b) 改变点源与靶的间距; (c) 点源发散束和平行束条件下改变靶与探测面距离; (d) 无量纲的调制信号特征量随ω的变化关系

Figure 9. Dependence of the characteristic quantities and ω on the change of: (a) Density gradient width by using a point-source beam for radiography; (b) point source-to-target distance; (c) target-to-detection plane distance by using a parallel beam or a point-source beam for radiography, respectively; (d) the relation of the dimensionless characteristic quantities to ω.

DownLoad: Full-Size Img PowerPoint

[1]	Zohuri B 2017 Inertial Confinement Fusion Driven Thermonuclear Energy (Cham: Springer International Publishing AG)
[2]	Lindl J 1995 Phys. Plasmas 2 3933 Google Scholar
[3]	Chen B, Yang Z, Wei M, Pu Y, Hu X, Chen T, Liu S, Yan J, Huang T, Jiang S, Ding Y 2014 Phys. Plasmas. 21 122705 Google Scholar
[4]	陆中伟, 王晓方 2019 物理学报 68 035202 Google Scholar Lu Z W, Wang X F 2019 Acta Phys. Sin. 68 035202 Google Scholar
[5]	Marshall F J, Ivancic S T, Mileham C, Nilson P M, Ruby J J, Stoeckl C, Scheiner B S, Schmitt M J 2021 Rev. Sci. Instrum. 92 033701 Google Scholar
[6]	Higginson A, Gray R J, King M, et al. 2018 Nat. Commun. 9 724 Google Scholar
[7]	Gonsalves A J, Nakamura K, Daniels J, et al. 2019 Phys. Rev. Lett. 122 084801 Google Scholar
[8]	Li C K, Séguin F H, Frenje J A, et al. 2006 Phys. Rev. Lett. 97 135003 Google Scholar
[9]	Du B, Wang X F 2018 AIP Adv. 8 125328 Google Scholar
[10]	Mackinnon A J, Patel P K, Borghesi M, et al. 2006 Phys. Rev. Lett. 97 045001 Google Scholar
[11]	Cobble J A, Johnson R P, Cowan T E, Renard-Le Galloudec N, Allen M 2002 J. Appl. Phys. 92 1775 Google Scholar
[12]	温树槐, 丁永坤 2012 激光惯性约束聚变诊断学 (北京: 国防工业出版社) Wen S H, Ding Y K 2012 Laser Inertial Confinement Fusion Diagnostics (Beijing: National Defense Industry Press) (in Chinese)
[13]	滕建, 洪伟, 赵宗清, 巫顺超, 秦孝尊, 何颖玲, 谷渝秋, 丁永坤 2009 物理学报 58 1635 Google Scholar Teng J, Hong W, Zhao Z Q, Wu S C, Qin X Z, He Y L, Gu Y Q, Ding Y K 2009 Acta Phys. Sin. 58 1635 Google Scholar
[14]	肖渊, 王晓方, 滕建, 陈晓虎, 陈媛, 洪伟 2012 物理学报 61 234102 Google Scholar Xiao Y, Wang X F, Teng J, Chen X H, Chen Y, Hong W 2012 Acta Phys. Sin. 61 234102 Google Scholar
[15]	陈媛, 王晓方, 邵光超 2015 物理学报 64 154101 Google Scholar Chen Y, Wang X F, Shao G C 2015 Acta Phys. Sin. 64 154101 Google Scholar
[16]	Bethe H A 1953 Phys. Rev. 89 1256 Google Scholar
[17]	Highland V L 1975 Nucl. Instrum. Methods 129 497 Google Scholar
[18]	Shao G, Wang X 2016 Phys. Plasmas 23 092703 Google Scholar
[19]	Zhang Y, Wang X 2020 Plasma Phys. Control. Fusion 62 095023 Google Scholar
[20]	Wu X J, Wang X F, Chen X H 2016 Chin. Phys. Lett. 33 065201 Google Scholar
[21]	Ferrari A, Sala P R, Fassò A, Ranft J, Siegen U 2005 FLUKA: A Multi-particle Transport Code No. SLAC-R-773 Stanford Linear Accelerator Center (SLAC)
[22]	Jackson J D 2005 Classical Electrodynamics (3rd Ed.) (Beijing: Higher Education Press)
[23]	汪晓莲, 李澄, 邵明, 陈宏芳 2009 粒子探测技术 (合肥: 中国科学技术大学出版社) Wang X L, Li C, Shao M, Chen H F 2009 The Technique of Particle Detection (Hefei: USTC Press) (in Chinese)

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Vol. 71, Issue 11 - 2022-06-05

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