Asymptotic perpendicular transport in low-beta collisionless plasma

TL;DR

This paper develops a new semi-fluid formalism to accurately model perpendicular transport in collisionless plasmas, improving upon traditional closures by incorporating temperature gradient effects and validating with kinetic simulations.

Contribution

It introduces a semi-fluid asymptotic analysis for the Vlasov equation, providing an adjusted gyroviscous stress closure suitable for collisionless plasmas.

Findings

The adjusted closure accurately corrects Braginskii's gyroviscous stress in temperature gradient scenarios.

Convergence of the semi-fluid expansion with increasing magnetization is demonstrated.

Residuals relate to higher-order terms, indicating the expansion's validity range.

Abstract

Kinetic physics, including finite Larmor radius (FLR) effects, are known to affect the physics of magnetized plasma phenomena such as the Kelvin-Helmholtz and Rayleigh-Taylor instabilities. Accurately incorporating FLR effects into fluid simulations requires moment closures for the heat flux and stress tensor, including the gyroviscous stress in collisionless magnetized plasmas. However, the most commonly used gyroviscous stress tensor closure (Braginskii Rev. Plasma Phys., 1965) is based on a strongly collisional assumption for the asymptotic expansion of the kinetic equation in the so-called fast-dynamics ordering. This collisional assumption becomes less valid for some high-temperature plasmas. To explore perpendicular transport in collisionless and weakly collisional plasmas, an asymptotic analysis of the weakly collisional Vlasov equation in the slow-dynamics or drift ordering is performed in a new "semi-fluid" formalism, which integrates in perpendicular velocity to obtain a five-moment system. The associated heat flux and stress tensor closures are determined via a Hilbert expansion of the kinetic equation. A numerically affordable approximation to the stress tensor is proposed which adjusts the Braginskii closure to account for temperature gradient-driven stress. Continuum kinetic simulations of a family of sheared-flow configurations with variable magnetization and temperature gradients are performed to validate the drift ordering semi-fluid expansion. The expected convergence with magnetization is observed, and residuals are examined and discussed in terms of their relationship to higher-order terms in the expansion. The adjusted Braginskii closure is found to accurately correct for the error committed by the Braginskii gyroviscous stress tensor closure in the presence of temperature gradients.