dc electrical conductivity in strongly magnetized plasmas

TL;DR

This paper derives a generalized Ohm's law for strongly magnetized plasmas, revealing how intense magnetic fields alter resistivity and conductivity, impacting plasma behavior in magnetohydrodynamics.

Contribution

It introduces a new formulation of Ohm's law accounting for strong magnetization effects, including additional resistivity terms and modified conductivity coefficients.

Findings

Perpendicular resistivity scales as ln(ω_ce τ_e)

Parallel resistivity increases by 3/2 times

Parallel conductivity decreases by 2/3

Abstract

A generalized Ohm's law is derived to treat strongly magnetized plasmas in which the electron gyrofrequency significantly exceeds the electron plasma frequency. The frictional drag due to Coulomb collisions between electrons and ions is found to shift, producing an additional transverse resistivity term in the generalized Ohm's law that is perpendicular to both the current ($\vc{J}$) and the Hall ($\vc{J} \times \vc{B}$) direction. In the limit of very strong magnetization, the parallel resistivity is found to increase by a factor of 3/2, and the perpendicular resistivity to scale as $\ln (\omega_{ce} \tau_e)$, where $\omega_{ce} \tau_e$ is the Hall parameter. Correspondingly, the parallel conductivity coefficient is reduced by a factor of 2/3, and the perpendicular conductivity scales as $\ln(\omega_{ce} \tau_e)/(\omega_{ce} \tau_e)^2$. These results suggest that strong magnetization significantly changes the magnetohydrodynamic evolution of a plasma.