Canonical variables based numerical schemes for hybrid plasma models with kinetic ions and massless electrons

TL;DR

This paper develops numerical schemes for a hybrid plasma model with kinetic ions and massless electrons, utilizing canonical variables, finite element methods, and splitting techniques to improve accuracy and conservation.

Contribution

It introduces two formulations of the hybrid plasma model using canonical variables and demonstrates the superiority of one formulation with enhanced numerical properties.

Findings

Second formulation is numerically superior.

Schemes based on anti-symmetric brackets have better conservation.

Filtering can improve schemes of the first formulation.

Abstract

We study the canonical variables based numerical schemes of a hybrid model with kinetic ions and mass-less electrons. Two equivalent formulations of the hybrid model are presented with the vector potentials in different gauges and the distribution functions depending on canonical momentum (not velocity), which constitutes a pair of canonical variables with the position variable. Particle-in-cell methods are used for the distribution functions, and the vector potentials are discretized by the finite element methods in the framework of finite element exterior calculus. Splitting methods are used for the time discretizations. It is illustrated that the second formulation is numerically superior and the schemes constructed based on the anti-symmetric bracket proposed have better conservation properties and lower noise, although the filters can be used to improve the schemes of the first formulation.