dc electrical conductivity in strongly magnetized plasmas

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.