超热电子能量沉积的Fokker-Planck方程模拟

doi:10.19596/j.cnki.1001-246x.8614

摘要/Abstract

摘要：

围绕超热电子在高密度等离子体中传输和能量沉积问题, 从相对论粒子碰撞基本物理出发, 综合考虑相对论库伦碰撞和集体效应下等能量损失过程、背景等离子体电子回流和升温过程, 建立超热电子相对论Fokker-Planck混合模型; 构造直角-动量球坐标系下Fokker-Planck方程的有限体积算法, 通过计算单能电子束在高密度等离子体中能量沉积和磁场产生过程, 验证数值模拟程序。针对激光惯性聚变中超热电子的预加热效应, 计算超热电子能量为单能和双麦氏分布情形下在靶丸中的能量沉积占比。

关键词: 相对论Fokker-Planck方程, 电子束, 超热电子, 能量沉积

Abstract:

We study the transport and energy deposition of superthermal electrons in high-density plasma, starting from the basic physics of relativistic particle collisions, considering relativistic Coulomb collisions and the collective effect, combined with the background plasma electron return and temperature equation, developed a hybrid model of the electronic relativistic Fokker-Planck equation. The finite volume algorithm of the Fokker-Planck equation in the rectangular-momentum spherical coordinate system is constructed, and the numerical algorithm and numerical simulation program are verified by calculating the energy deposition and magnetic field generation process of the monoenergetic electron beam in the high-density plasma. For evaluating of the preheat effects of superthermal electrons during the implosion process, the energy deposition processes and energy distributions in the implosion target under the single-energy and bi-Maxwellian energy spectrum are calculated.

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

张华, 李明强, 彭力, 何民卿, 吴思忠, 周沧涛. 超热电子能量沉积的Fokker-Planck方程模拟[J]. 计算物理, 2023, 40(2): 222-231.

Hua ZHANG, Mingqiang LI, Li PENG, Minqing HE, Sizhong WU, Cangtao ZHOU. Fokker-Planck Equation for Superthermal Electron Energy Deposition[J]. Chinese Journal of Computational Physics, 2023, 40(2): 222-231.

图/表 8

图1 不同时刻的电子密度、背景等离子体温度和自生磁场空间分布，t = 1.5 ps时，(a) 电子密度; (b) 背景等离子体温度；(c) 自生磁场空间分布；t = 3.0 ps时, (d) 电子密度；(e) 背景等离子体温度；(f) 自生磁场空间分布

Fig.1 At t = 1.5 ps, (a) electron density, (b) plasma temperature and (c) magnetic field contours; At t = 3.0 ps, (d) electron density, (e) plasma temperature and (f) magnetic field contours

图2 能量随时间变化

Fig.2 Energy vs. time

图3 不同能量的电子束穿透深度

Fig.3 Penetration depth vs. electron beam energy

图4 辐射源随时间变化，主脉冲位于18 ns~22 ns区间，t = 21.6 ns达到峰值功率

Fig.4 Radiation vs. time, the main pulse is in the interval of 18 ns~22 ns, with peak power t = 21.6 ns

图5 t = 21.6 ns时刻靶丸中电子、离子温度与等离子体密度分布

Fig.5 Electron, ion temperature and plasma density at t = 21.6 ns

图6 不同时刻等离子体状态和能量为50 keV~200 keV的单能电子能量沉积曲线(a) t = 19 ns；(b) t = 21.6 ns

Fig.6 Energy deposition in energy ranging from 50 keV to 200 keV at (a) t = 19 ns and (b) t = 21.6 ns

图7 超热电子能谱，其中超热电子能量E < 150 keV时Thot = 18 keV

Fig.7 Superthermal electron spectrum, where Thot = 18 keV for E < 150 keV

图8 不同超热电子能谱分布下超热电子预热能量分布 (a) Thot = 60 keV；(b) Thot = 80 keV; (c) Thot = 120 keV; (d) Thot = 150 keV

Fig.8 Superthermal electron preheating under different energy spectrum (a) Thot = 60 keV; (b) Thot = 80 keV; (c) Thot = 120 keV; (d) Thot = 150 keV

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