dc Electrical Conductivity of Strongly Magnetized Plasmas

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 acquire a component perpendicular to their relative drift, producing an additional transverse resistivity term in the generalized Ohm's law that is perpendicular to both the current and the Hall directions. 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 a logarithmic function of the Hall parameter. Correspondingly, the parallel conductivity coefficient is reduced by a factor of 2/3, and the perpendicular conductivity scales proportionally to the logarithm of the Hall parameter divided by the square of the Hall parameter. These results suggest that strong magnetization significantly changes the magnetohydrodynamic evolution of a plasma.