Relaxation model for a homogeneous plasmas with spherically symmetric velocity space

doi:10.1088/1674-1056/ad9455

中国物理B ›› 2025, Vol. 34 ›› Issue (1): 15202-015202.doi: 10.1088/1674-1056/ad9455

Relaxation model for a homogeneous plasmas with spherically symmetric velocity space

Yanpeng Wang(王彦鹏)¹, Jianyuan Xiao(肖建元)^1,2,†, Xianhao Rao(饶贤昊)^1,‡, Pengfei Zhang(张鹏飞)³, Yolbarsop Adil(阿迪里)¹, and Ge Zhuang(庄革)¹

1 School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China;
2 Laoshan Laboratory, Qingdao 266100, China;
3 School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China

收稿日期:2024-07-03 修回日期:2024-11-02 接受日期:2024-11-19 发布日期:2025-01-02
通讯作者: Jianyuan Xiao, Xianhao Rao E-mail:xiaojy@ustc.edu.cn;rrxxhh@mail.ustc.edu.cn
基金资助:
Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB0500302 and LSKJ202300305).

Relaxation model for a homogeneous plasmas with spherically symmetric velocity space

Yanpeng Wang(王彦鹏)¹, Jianyuan Xiao(肖建元)^1,2,†, Xianhao Rao(饶贤昊)^1,‡, Pengfei Zhang(张鹏飞)³, Yolbarsop Adil(阿迪里)¹, and Ge Zhuang(庄革)¹

1 School of Nuclear Science and Technology, University of Science and Technology of China, Hefei 230026, China;
2 Laoshan Laboratory, Qingdao 266100, China;
3 School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China

Received:2024-07-03 Revised:2024-11-02 Accepted:2024-11-19 Published:2025-01-02
Contact: Jianyuan Xiao, Xianhao Rao E-mail:xiaojy@ustc.edu.cn;rrxxhh@mail.ustc.edu.cn
Supported by:
Project supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant Nos. XDB0500302 and LSKJ202300305).

摘要/Abstract

摘要： We derive the transport equations from the Vlasov-Fokker-Planck equation when the velocity space is spherically symmetric. The Shkarofsky's form of Fokker-Planck-Rosenbluth collision operator is employed in the Vlasov-Fokker-Planck equation. A closed-form relaxation model for homogeneous plasmas could be presented in terms of Gauss hypergeometric ${}_2$F$_1$ functions. This has been accomplished based on the Maxwellian mixture model. Furthermore, we demonstrate that classic models such as two-temperature thermal equilibrium model and thermodynamic equilibrium model are special cases of our relaxation model and the zeroth-order Braginskii heat transfer model can also be derived. The present relaxation model is a nonequilibrium model based on the hypothesis that the plasmas system possesses finitely distinguishable independent features, without relying on the conventional near-equilibrium assumption.

关键词: finitely distinguishable independent features hypothesis, Maxwellian mixture model, Fokker-Planck-Rosenbluth collision operator, spherical symmetry

Abstract: We derive the transport equations from the Vlasov-Fokker-Planck equation when the velocity space is spherically symmetric. The Shkarofsky's form of Fokker-Planck-Rosenbluth collision operator is employed in the Vlasov-Fokker-Planck equation. A closed-form relaxation model for homogeneous plasmas could be presented in terms of Gauss hypergeometric ${}_2$F$_1$ functions. This has been accomplished based on the Maxwellian mixture model. Furthermore, we demonstrate that classic models such as two-temperature thermal equilibrium model and thermodynamic equilibrium model are special cases of our relaxation model and the zeroth-order Braginskii heat transfer model can also be derived. The present relaxation model is a nonequilibrium model based on the hypothesis that the plasmas system possesses finitely distinguishable independent features, without relying on the conventional near-equilibrium assumption.

Key words: finitely distinguishable independent features hypothesis, Maxwellian mixture model, Fokker-Planck-Rosenbluth collision operator, spherical symmetry

中图分类号: (Fokker-Planck and Vlasov equation)

52.65.Ff

52.25.Fi (Transport properties) 52.25.Dg (Plasma kinetic equations) 52.35.Sb (Solitons; BGK modes)

Yanpeng Wang(王彦鹏), Jianyuan Xiao(肖建元), Xianhao Rao(饶贤昊), Pengfei Zhang(张鹏飞), Yolbarsop Adil(阿迪里), and Ge Zhuang(庄革). Relaxation model for a homogeneous plasmas with spherically symmetric velocity space[J]. 中国物理B, 2025, 34(1): 15202-015202.

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Relaxation model for a homogeneous plasmas with spherically symmetric velocity space

Relaxation model for a homogeneous plasmas with spherically symmetric velocity space

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