A unified gas kinetic scheme for transport and collision effects in plasma

TL;DR

This paper introduces a unified gas kinetic scheme (UGKS) for plasma that effectively models transport and collision effects, accurately solving the Vlasov-Poisson equation with larger time steps than traditional methods.

Contribution

The paper develops a finite volume UGKS that couples free transport and long-range interactions, incorporating collision models and solving Poisson's equation efficiently for plasma simulations.

Findings

Accurately simulates linear Landau damping and Gaussian beam propagation.

Able to use larger time steps than previous methods while maintaining accuracy.

Validates the method with numerical tests showing good agreement with theoretical results.

Abstract

In this study, the Vlasov-Poisson equation with or without collision term for plasma is solved by the unified gas kinetic scheme (UGKS). The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction. The distribution function is discretized in discrete particle velocity space. After the Vlasov equation is integrated in finite volumes of physical space, the numerical flux across a cell interface and source term for particle acceleration are computed to update the distribution function at next time step. The flux is decided by Riemann problem and variation of distribution function in discrete particle velocity space is evaluated with central difference method. A electron-ion collision model is introduced in the Vlasov equation. This finite volume method for the UGKS couples the free transport and long-range interaction between particles. The electric field induced by charged particles is controlled by the Poisson's equation. In this paper, the Poisson's equation is solved using the Green's function for two dimensional plasma system subjected to the symmetry or periodic boundary conditions. Two numerical tests of the linear Landau damping and the Gaussian beam are carried out to validate the proposed method. The linear electron plasma wave damping is simulated based on electron-ion collision operator. Compared with previous methods, it is shown that the current method is able to obtain accurate results of the Vlasov-Poisson equation with a time step much larger than the particle collision time. Highly non-equilibrium and rarefied plasma flows, such as electron flows driven by electromagnetic field, can be simulated easily.