A new framework for magnetohydrodynamic simulations with anisotropic pressure

TL;DR

This paper introduces a novel magnetohydrodynamic simulation framework that incorporates anisotropic pressure tensors, effectively addressing limitations of classical models near neutral regions and ensuring accurate plasma behavior modeling.

Contribution

The authors develop a new numerical framework combining the 2nd-moment of the Vlasov equation with a gyrotropization model to handle anisotropic pressure without singularities.

Findings

Successfully removes singularities in anisotropic pressure modeling.

Reduces to standard MHD or double adiabatic models in appropriate limits.

Verifies the model's accuracy through numerical tests.

Abstract

We describe a new theoretical and numerical framework of the magnetohydrodynamic simulation incorporated with an anisotropic pressure tensor, which can play an important role in a collisionless plasma. A classical approach to handle the anisotropy is based on the double adiabatic approximation assuming that a pressure tensor is well described only by the components parallel and perpendicular to the local magnetic field. This gyrotropic assumption, however, fails around a magnetically neutral region, where the cyclotron period may get comparable to or even longer than a dynamical time in a system, and causes a singularity in the mathematical expression. In this paper, we demonstrate that this singularity can be completely removed away by the combination of direct use of the 2nd-moment of the Vlasov equation and an ingenious gyrotropization model. Numerical tests also verify that the present model properly reduces to the standard MHD or the double adiabatic formulation in an asymptotic manner under an appropriate limit.