Two-dimension electrostatic particle-in-cell simulation of two-stream instability

doi:10.16568/j.0254-6086.202202014

Abstract

Abstract: In order to study the evolution process of two-stream instability in two-temperature electron plasma, two-dimensional electrostatic particle-in-cell simulation was conducted, where Poisson equation was solved by relaxation iteration method, and the code satisfied the conditions of charge conservation, momentum conservation and energy conservation. In the nonlinear evolution process of electron two-stream instability, the cavity structure in phase space was obtained, and the electron cavity appeared correspondingly in real space. The growth rate of instability and the corresponding dispersion relation were given.

Key words: Particle-in-cell, Two-stream instability, Two-temperature electrons, Phase space cavity

摘要： 为研究双温电子等离子体中束流不稳定性的演化过程，用二维粒子模拟(PIC)代码对双温电子束流不稳定性进行了模拟，其中泊松方程用松弛迭代法求解，代码满足电荷守恒、动量守恒和能量守恒条件。在电子双流不稳定性的非线性演化过程中，得到相空间的空洞结构，实空间也相应出现了电子空洞。给出了不稳定性增长率以及相应色散关系。

关键词: 粒子模拟, 双流不稳定性, 双温电子, 相空间空洞

CLC Number:

ZHAO Bing-yan, CHEN Zong-hua. Two-dimension electrostatic particle-in-cell simulation of two-stream instability [J]. Nuclear Fusion and Plasma Physics, 2022, 42(2): 257-263.

赵炳炎, 陈宗华. 二维双流不稳定性静电粒子模拟[J]. 核聚变与等离子体物理, 2022, 42(2): 257-263.

References

[1] Plasma Theory and Simulation Group. Particle simulations of 1-D Vlasov problems [Z]. 2019.

[2] Lapenta G. Particle simulations of space weather [J]. Journal of Computational Physics. 2012, 231(3): 795− 821.

[3] 袁忠才, 时家明. PIC/MCC数值模拟四阳极直流辉光放电 [J]. 核聚变与等离子体物理, 2005, 25(4): 68−73．

[4] 况龙钰, 巫顺超, 江少恩, 等．金属靶背向超热电子运动特性的PIC模拟 [J]．核聚变与等离子体物理, 2009, 29(1): 78−81．

[5] Lapenta G. Particle in cell methods with application to simulations in space weather [J]. Centrum Voor Plasma Astrofysica, 2010, doi: 10.1.1.471.420.

[6] 赵书霞, 张连珠. 氮气辉光放电等离子体过程的PIC/MCC模拟 [J]. 核聚变与等离子体物理, 2009, 29(1): 39−43．

[7] 张连珠, 孟秀兰, 田中涛, 等. N2空心阴极放电向微空心阴极放电转变的PIC/MC模拟 [J]. 核聚变与等离子体物理, 2010, 30(2): 131−137.

[8] Decyk V K, Singh T V. Adaptable particle-in-cell algorithms for graphical processing units [J]. Computer Physics Communications, 2011, 182(3): 641−648.

[9] 杨莹, 付东儒, 张连珠. N2射频放电带电粒子(e, N2+, N+)的PIC-MC模拟 [J]. 核聚变与等离子体物理, 2012, 32(3): 206−212.

[10] Decyk V K, Singh T V. Particle-in-cell algorithms for emerging computer architectures [J]. Computer Physics Communications, 2014, 185(3): 708−719.

[11] Berk H L, Roberts K V. Nonlinear evolution of a two-stream instability [J]. Phys. Rev. Lett., 1967, 19(6): 297−300.

[12] SANG Longlong, WU Mingyu, LU Quanming, et al. Electrostatic structure of the electron phase-space holes generated by the electron two-stream instability with a finite width [J]. Chin. J. Space Sci., 2017, 37(5): 517−523.

[13] Birdsall C K, Langdon A B. Plasma physics via computer simulation [M]. Adam Hilger, 1991.

[14] Hockney R W, Eastwood J W. Computer simulation using particles [M]. Crc Press, 1988.

[15] Dawson J M. Particle simulation of plasmas [J]. Reviews of Modern Physics, 1983, 55(2): 403.

[16] Omura Y, Matsumoto H. KEMPO1: Technical guide to one-dimensional electromagnetic particle code [J]. Computer Space Plasma Physics, Simulation Techniques and Software, Terra Scientific Pub., 1993: 21−65.

[17] Verboncoeur J P, Langdon A B, Gladd N T. An object-oriented electromagnetic PIC code [J]. Computer Physics Communications, 1995, 87(1): 199-211.

[18] Kourakis I, Shukla P K. Nonlinear Lagrangian theory of envelope electrostatic plasma waves in a two-electron- temperature plasma [J]. Physics of Plasmas, 2004, 11(9): 4506.

[19] Buti B, Yu M Y. Langmuir solitons in a two-temperature plasma [J]. Journal of Plasma Physics, 1981, 26(2): 309−316.

[20] Focia R J, Rose H A, Russell D A, et al. Observation of Stimulated Electron-Acoustic-Wave Scattering [J]. Phys. Rev. Lett., 2001, 87(15): 155001.

[21] Chakraborty D, Das K P. Existence and stability of solitary kinetic Alfvén, ion-acoustic and electron-acoustic waves in a two electron temperature plasma [J]. Physics of Plasmas, 2003, 10(6): 2236.

[22] Ou J, Xiang N, Gan C, et al. Effect of two-temperature electrons distribution on an electrostatic plasma sheath [J]. Physics of Plasmas, 2013, 20(6): 63502.

[23] Chen Z H, Yang X S, Chen X C, et al. Two-temperature- electron Zakharov equations for the dynamics of modulated collapse [J]. Physics of Plasmas, 2016, 23(5): 52303.

[24] Verboncoeur J P. Particle simulation of plasmas: review and advances [J]. Plasma Phys. Contr. Fusion, 2005, 47(5A): A231−A260.

[25] Omura Y. One-dimensional electromagnetic particle code: KEMPO1 [J]. Advanced Methods for Space Simulations, Terra Scientific Pub, Tokyo, 2007: 1-21.

[26] Lapenta G, Jiang W. Implicit temporal discretization and exact energy conservation for particle methods applied to the Poisson-Boltzmann equation [J]. Plasma, 2018, 1(2): 242−258.

[27] XIE Huasheng, XIAO Yong. PDRK: A general kinetic dispersion relation solver for magnetized plasma [J]. Plasma Science and Technology, 2016, 18(2): 97.