A Robust Method for Handling Low Density Regions in Hybrid Simulations for Collisionless Plasmas

TL;DR

This paper introduces a new hybrid simulation method for collisionless plasmas that effectively manages vacuum and low-density regions by modifying the electric field correction and incorporating variable ion-electron mass ratios, enhancing stability.

Contribution

The paper proposes a novel approach that introduces a correction to the electric field and uses a variable ion-electron mass ratio to improve hybrid plasma simulations in low-density regions.

Findings

Successfully handles vacuum and near vacuum regions in simulations.

Maintains numerical stability without ad hoc techniques.

Accurately models nonlinear development in plasma systems.

Abstract

A robust method to handle vacuum and near vacuum regions in hybrid simulations for space and astrophysical plasmas is presented. The conventional hybrid simulation model dealing with kinetic ions and a massless charge-neutralizing electron fluid is known to be susceptible to numerical instability due to divergence of the whistler-mode wave dispersion, as well as division-by-density operation in regions of low density. Consequently, a pure vacuum region is not allowed to exist in the simulation domain unless some ad hoc technique is used. To resolve this difficulty, an alternative way to introduce finite electron inertia effect is proposed. Contrary to the conventional method, the proposed one introduces a correction to the electric field rather than the magnetic field. It is shown that the generalized Ohm's law correctly reduces to Laplace's equation in a vacuum which therefore does not involve any numerical problems. In addition, a variable ion-to-electron mass ratio is introduced to reduce the phase velocity of high frequency whistler waves at low density regions so that the stability condition is always satisfied. It is demonstrated that the proposed model is able to handle near vacuum regions generated as a result of nonlinear self-consistent development of the system, as well as pure vacuum regions set up at the initial condition, without losing the advantages of the standard hybrid code.