Nonlinear Resistivity for Magnetohydrodynamical Models

TL;DR

This paper introduces a comprehensive nonlinear resistivity model for magnetohydrodynamics that accounts for velocity-space moments, extending classical formulations and impacting plasma phenomena like magnetic reconnection.

Contribution

It presents a novel nonlinear anisotropic resistivity formulation that incorporates higher-order moments of the distribution function, unifying and extending existing resistivity models.

Findings

The new resistivity formalism recovers Spitzer resistivity.

It includes effects of pressure tensor and heat flux on resistivity.

The nonlinear terms' significance is analyzed in plasma dynamics.

Abstract

A new formulation of the plasma resistivity that arises from the collisional momentum-transfer rate between electrons and ions is presented. The resistivity computed herein is shown to depend not only on the temperature and density but also on all other polynomial velocity-space moments of the distribution function, such as the pressure tensor and heat flux vector. The exact expression for the collisional momentum-transfer rate is determined, and is used to formulate the nonlinear anisotropic resistivity. The new formalism recovers the Spitzer resistivity, as well as the concept of thermal force if the heat flux is assumed to be proportional to a temperature gradient. Furthermore, if the pressure tensor is related to viscous stress, the latter enters the expression for the resistivity. The relative importance of the nonlinear term(s) with respect to the well-established electron inertia and Hall terms is also examined. The subtle implications of the nonlinear resistivity, and its dependence on the fluid variables, are discussed in the context of magnetized plasma environments and phenomena such as magnetic reconnection.