Conduction mode variation and intertial conductivity

Abstract

Using separation of variables in space and time we find two-dimensional solutions consistent with simple forms of the inertial Ohm's law, Maxwell's equations, and the equation of momentum transport. conduction mode variation (a temporal change in electrical conductivity due, e.g., to onset of a plasma instability) is frequently found necessary. The result for the effective conductivity shows that either the conduction mode variation or inertial effects may dominate. In the inertial limit and in the absence of conduction mode variation the results are similar to the limiting results of Speiser. However, the important time constant is the inverse growth rate of the current density rather than the lifetime of a particle in the system. Several solutions have magnetic field structures with neutral points.