Application of coulomb collision cross-section in particle-in-cell simulation of plasma

Song Mengmeng; Zhou Qianhong; Sun Qiang; Yang Wei; Dong Ye

doi:10.11884/HPLPB202133.200179

Volume 33 Issue 3

Mar. 2021

Turn off MathJax

Article Contents

Article Navigation > High Power Laser and Particle Beams > 2021 > 33(3): 034004

Song Mengmeng, Zhou Qianhong, Sun Qiang, et al. Application of coulomb collision cross-section in particle-in-cell simulation of plasma[J]. High Power Laser and Particle Beams, 2021, 33: 034004. doi: 10.11884/HPLPB202133.200179

Citation:

Song Mengmeng, Zhou Qianhong, Sun Qiang, et al. Application of coulomb collision cross-section in particle-in-cell simulation of plasma[J]. High Power Laser and Particle Beams, 2021, 33: 034004. doi: 10.11884/HPLPB202133.200179

Citation:

PDF( 1691 KB)

Application of coulomb collision cross-section in particle-in-cell simulation of plasma

doi: 10.11884/HPLPB202133.200179

Song Mengmeng^{1, 2
,},
Zhou Qianhong^{1
,
,},
Sun Qiang¹,
Yang Wei¹,
Dong Ye¹

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100094, China
2.
Graduate School of China Academy of Engineering Physics, Beijing 100088, China

Received Date: 2020-06-29
Rev Recd Date: 2020-11-12

Available Online: 2021-03-30

Publish Date: 2021-03-05

Abstract

Abstract

In particle-in-cell simulation of plasma, TA and Nanbu models have been widely used for Coulomb collision. Both models require all particles to collide. In this paper, a cross-section-based method is introduced to give a probability of Coulomb collision for each particle pair and accelerate the computation. To test this method, the relaxations of an electron gas due to e-e collisions were simulated. Comparing the simulated with the theoretical values of velocity distribution function, electron temperature, the ratio of electron temperature in x, y direction to electron temperature, the accuracy of the cross-section-based method was verified. The calculation efficiency of this method can be improved by more than 40% than the TA model at the same small time step. Furthermore, at a large time step, the simulations show agreement with the theoretical solutions, the efficiency is also improved than the Nanbu model. The simulation about the equilibration of electron and ion temperature showes that this method is also suitable for e-i collisions. Therefore in the acceleration of simulating Coulomb collision, this method has two advantages as follows: first, there is a small number of particles to collide within a step, and second, it is suitable for large time steps.
- particle-in-cell simulation,
- cross-section of Coulomb collision,
- Monte-Carlo methods,
- TA model,
- Nanbu model,
- plasma

FullText(HTML)

References(17)

References

[1]	Hagelaar G J M, Donko Z, Dyatko N. Modification of the Coulomb logarithm due to electron-neutral collisions[J]. Physical Review Letters, 2019, 123: 025004. doi: 10.1103/PhysRevLett.123.025004
[2]	Birdsall C K. Particle-in-cell charged-particle simulations, plus Monte Carlo collisions with neutral atoms[J]. IEEE Transactions on Plasma Science, 1991, 19(2): 65-85. doi: 10.1109/27.106800
[3]	Takizuka T, Abe H. A binary collision model for plasma simulation with a particle code[J]. Journal of Computational Physics, 1977, 25(3): 205-219. doi: 10.1016/0021-9991(77)90099-7
[4]	Veske M, Kyritsakis A, Djurabekova F. Dynamic coupling between particle-in-cell and atomistic simulations[J]. Physical Review E, 2020, 101: 053307. doi: 10.1103/PhysRevE.101.053307
[5]	杨超, 刘大刚, 王小敏, 等. 基于负氢离子源的全三维PIC/MCC 模拟算法研究[J]. 物理学报, 2012, 61:045204. (Yang Chao, Liu Dagang, Wang Xiaomin, et al. A three-dimensional particle-in-cell/Monte Carlo computer simulation based on negative hydrogen ion source[J]. Acta Physica Sinica, 2012, 61: 045204 doi: 10.7498/aps.61.045204
[6]	Nanbu K. Theory of cumulative small-angle collisions in plasmas[J]. Physical Review E—Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1997, 55(4): 4642-4652.
[7]	王辉辉, 杨超, 刘大刚, 等. Ta及Nanbu库仑碰撞模型数值对比研究[J]. 物理学报, 2013, 62:015206. (Wang Huihui, Yang Chao, Liu Dagang, et al. Numerical comparison between Ta and Nanbu models of Coulomb collisions[J]. Acta Physica Sinica, 2013, 62: 015206 doi: 10.7498/aps.62.015206
[8]	Dominguez-Vázquez A, Taccogna F, Ahedo E. Particle modeling of radial electron dynamics in a controlled discharge of a Hall thruster[J]. Plasma Sources Science and Technology, 2018, 27: 064006. doi: 10.1088/1361-6595/aac968
[9]	Wang C, Lin T, Caflisch R, et al. Particle simulation of Coulomb collisions: Comparing the methods of Takizuka & Abe and Nanbu[J]. Journal of Computational Physics, 2008, 227(9): 4308-4329. doi: 10.1016/j.jcp.2007.12.027
[10]	Caflisch R, Wang R, Dimarco G, Dimarco, et al. A hybrid method for accelerated simulation of Coulomb collisions in a plasma[J]. Multiscale Model Simul, 2008, 7(2): 865-887. doi: 10.1137/070704939
[11]	Ricketson L F, Rosin M S, Caflisch R E, et al. An entropy based thermalization scheme for hybrid simulations of Coulomb collisions[J]. Journal of Computational Physics, 2014, 273: 77-99. doi: 10.1016/j.jcp.2014.04.059
[12]	Lemons D S, Winske D, Daughton W, et al. Small-angle Coulomb collision model for particle-in-cell simulations[J]. Journal of Computational Physics, 2009, 228(5): 1391-1403. doi: 10.1016/j.jcp.2008.10.025
[13]	Vahedi V, Surendra M. A Monte Carlo collision model for the particle-in-cell method: applications to argon and oxygen discharges[J]. Computer Physics Communications, 1995, 87(1/2): 179-198.
[14]	Sjobak K, Helga T. 2D ArcPIC code description: description of methods and user/developer manual (Second Edition)[R]. CLIC-Note-1032, 2014.
[15]	姜巍. 射频容性耦合等离子体的两维隐格式PIC/MC模拟[D]. 大连理工大学, 2010: 33-34. Jiang Wei. Two-dimensional implicit PIC/MC simulations for radio-frequency capacitively coupled plasma[D]. Dalian: Dalian University of Technology, 2010: 33-34
[16]	徐家鸾, 金尚宪. 等离子体物理学[M]. 北京: 原子能出版社, 1981: 34-37. Xu Jialuan, Jin Shangxian. Plasma physics[M]. Beijing: Atomic Energy Press, 1981: 34-37
[17]	Diver D A. Plasma formulary for physics, astronomy, and technology[M]. Germany: Wiley-VCH Verlag GmbH & Co. KGaA, 2013: 91-92