电子束能量沉积的相对论Fokker-Planck方程的计算方法

计算物理 ›› 2017, Vol. 34 ›› Issue (5): 555-562.

• 专题:超强激光等离子体相互作用的数值模拟 • 上一篇下一篇

电子束能量沉积的相对论Fokker-Planck方程的计算方法

张华^1,2, 吴思忠¹, 周沧涛^1,2, 何民卿¹, 蔡洪波^1,2, 曹莉华^1,2, 朱少平¹, 贺贤土^1,2

1. 北京应用物理与计算数学研究所, 北京 100094;
2. 北京大学应用物理与技术中心, 北京 100871

收稿日期:2017-03-30 出版日期:2017-09-25 发布日期:2017-09-25
作者简介:张华(1977-),男,博士,副研究员,从事激光等离子体数值模拟研究,E-mail:zhang_hua@iapcm.ac.cn
基金资助:
大科学装置国家重点研发计划（2016YFA0401100）及国家自然科学基金（91230205，11575031）资助项目

Numerical Method of Relativistic Fokker-Planck Equation for Energy Deposition of Fast Electrons

ZHANG Hua^1,2, WU Sizhong¹, ZHOU Cangtao^1,2, HE Minqing¹, CAI Hongbo^1,2, CAO Lihua^1,2, ZHU Shaoping¹, HE Xiantu^1,2

1. Institute of Applied Physics and Computational Mathematics, Beijing 100094, China;
2. Center of Applied Physical Technology, Peking University, Beijing 100871, China

Received:2017-03-30 Online:2017-09-25 Published:2017-09-25

摘要/Abstract

摘要： 针对相对论电子束在高密度等离子体中的能量沉积过程，建立三维动量空间中快电子能量沉积的相对论Fokker-Planck方程的可计算物理模型，构造数值算法并研制数值模拟程序.通过与解析模型和蒙特卡罗模拟相比较，验证数值方法和程序的可靠性.在二维动量空间的模拟基础上，通过计算能量区间为0.5 MeV~3.5 MeV的快电子在背景密度为300 g·cm^-3的氘氚等离子体中的能量沉积过程，发现由于碰撞效应使平均散射角趋近平衡，三维动量空间计算快电子连续射程和穿透深度与二维结果基本一致.

关键词: 电子束, 能量沉积, 相对论Fokker-Planck方程

Abstract: For energy deposition of fast electrons in high density plasma, a relativistic Fokker-Planck equation in three-dimensional momentum space is introduced. It includes both binary collision and contribution from plasma collective response. Numerical method as well as kinetic code of the equation is developed. Typical energy deposition cases are presented with comparison with stopping power model. Energy deposition of fast electrons with energy from 0.5 MeV to 3.5 MeV in 300 g·cm^-3 DT plasma are simulated. It shows that scattering angle ϕ plays minor role on range and penetration depth of energy deposition of fast electrons.

Key words: electron beam, energy deposition, relativistic Fokker-Planck equation

中图分类号:

张华, 吴思忠, 周沧涛, 何民卿, 蔡洪波, 曹莉华, 朱少平, 贺贤土. 电子束能量沉积的相对论Fokker-Planck方程的计算方法[J]. 计算物理, 2017, 34(5): 555-562.

ZHANG Hua, WU Sizhong, ZHOU Cangtao, HE Minqing, CAI Hongbo, CAO Lihua, ZHU Shaoping, HE Xiantu. Numerical Method of Relativistic Fokker-Planck Equation for Energy Deposition of Fast Electrons[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(5): 555-562.

参考文献

[1] TABAK M, HAMMER J, GLINSKY M E, et al. Ignition and high gain with ultrapowerful lasers[J]. Physics of Plasmas, 1994, 1(5):1626-1634.
[2] BETTI R, ANDERSON K, BOEHLY T R, et al. Progress in hydrodynamics theory and experiments for direct-drive and fast ignition inertial confinement fusion[J]. Plasma Physics & Controlled Fusion, 2006, 48(12B):B153.
[3] SHIRAGA H, NAGATOMO H, THEOBALD W, et al. Fast ignition integrated experiments and high-gain point design[J]. Nuclear Fusion, 2014, 54(5):1464-1473.
[4] DEUTSCH C, FURUKAWA H, MIMA K, et al. The interaction physics of the fast ignitor concept[J]. Laser and Particle Beams, 1997, 256(4):2483-2486.
[5] LI C K, PETRASSO R D. Energy deposition of MeV electrons in compressed targets of fast-ignition inertial confinement fusion[J]. Physics of Plasmas, 2006, 13(5):1626.
[6] SOLODOV A A, BETTI R. Stopping power and range of energetic electrons in dense plasmas of fast-ignition fusion targets[J]. Physics of Plasmas, 2008, 15(4):042707-042707-5.
[7] ATZENI S, SCHIAVI A, DAVIES J R. Stopping and scattering of relativistic electron beams in dense plasmas and requirements for fast ignition[J]. Plasma Physics & Controlled Fusion, 2008, 51(1):015016.
[8] SOLODOV A A, ANDERSON K S, BETTI R, et al. Integrated simulations of implosion, electron transport, and heating for direct-drive fast-ignition targets[J]. Physics of Plasmas, 2009, 16(5):056309-056309-9.
[9] ROBICHE J, RAX J M. Relativistic kinetic theory of pitch angle scattering, slowing down, and energy deposition in a plasma[J]. Physics of Plasmas, 2004, 70(4):046405.
[10] TZOUFRAS M, BELL A R, NORREYS P A, et al. A Vlasov-Fokker-Planck code for high energy density physics[J]. Journal of Computational Physics, 2011, 230(17):6475-6494.
[11] YOKOTA T, NAKAO Y, JOHZAKI T, et al. Two-dimensional relativistic Fokker-Planck model for core plasma heating in fast ignition targets[J]. Physics of Plasmas, 2006, 13(2):022702.
[12] WU S Z, ZHOU C T, ZHU S P, et al. Relativistic kinetic model for energy deposition of intense laser-driven electrons in fast ignition scenario[J]. Physics of Plasmas, 2011, 18(2):1626.
[13] WU S Z, ZHANG H, ZHOU C T, et al. Kinetic model for energy deposition in fast ignition[J]. European Physical Journal, 2013,59(1):05021.
[14] 吴思忠, 张华, 周沧涛,等. 快点火中相对论电子束能量沉积的动理学研究[J]. 强激光与粒子束, 2015, 27(3):77-86.
[15] BRAAMS B J, KARNEY C F F. Differential form of the collision integral for a relativistic plasma[J]. Physical Review Letters, 2005, 59(16):1817-1820.
[16] BRAAMS B J, KARNEY C F F. Conductivity of a relativistic plasma[J]. Physics of Fluids, 1989, 1B(7):1355-1368.

电子束能量沉积的相对论Fokker-Planck方程的计算方法

Numerical Method of Relativistic Fokker-Planck Equation for Energy Deposition of Fast Electrons

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[3]	雷威. 利用概率分布计算电子束聚焦状态[J]. 计算物理, 1998, 15(2): 177-183.
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[9]	王晓莎, 陈栋泉, 王正言. 质子束泵浦KrF^*准分子系统化学动力学研究和能量沉积计算[J]. 计算物理, 1992, 9(3): 263-266.