Higher-order moment convergent method in weakly anisotropic plasma and the NLVFP code for solution of the 0D-2V Vlasov-Fokker-Planck equation

TL;DR

This paper presents a numerical method using higher-order moments and spherical harmonics expansion to simulate weakly anisotropic plasma, ensuring conservation laws and convergence in the Vlasov-Fokker-Planck framework.

Contribution

It introduces the NLVFP code for 0D-2V plasma simulation employing spherical harmonics and King basis, addressing nonlinearity, collisions, and higher-order moments.

Findings

Demonstrates conservation of mass, momentum, and energy in simulations.

Achieves higher-order moment convergence in weakly anisotropic plasma.

Provides a validated numerical framework for non-equilibrium plasma modeling.

Abstract

Fusion plasma and space plasma are typical non-equilibrium and nonlinear systems, with the interactions between different species well described by the Vlasov-Fokker-Planck (VFP) equations. The transport of mass, momentum, energy, and temperature relaxation are important issues, which are affected by the collision term of VFP even in so-called collisionless plasma domain. Hence, nonlinearity and collisions are important features in large regime. A successful numerical simulation for non-equilibrium plasma has to be able to conserve mass, momentum and energy, while satisfying Boltzmann's H-theorem and higher-order moment convergence. An expansion of the distribution function in spherical harmonics (Legendre basis when the velocity space exhibits axisymmetry) in angle coordinate and in King basis in speed coordinate of velocity space is well suited to address these requirements. This paper reviews the formulation of the 0D-2V VFP equation in terms of spherical harmonics coupled with King function and its solution in our NLVFP code. In this topic review, we will introduce the background physics related to the nonlinear VFP simulation, then describe NLVFP for 0D-2V homogeneous, weakly anisotropic plasma with utilization of the Shkarofsky's form of Fokker-Planck-Rosenbluth (FPRS) collision operator.