The concept of conductivity

Abstract

The concept of conductivity in a hot plasma is reviewed and criticized. In particular, it is shown that even for arbitrarily small field strengths, a proportionality constant (tensor) does not in general exist between a frequency component of the field strength and the corresponding component of current density. Rather, insisting upon such a proportionality for a homogeneous plasma, defines a complete set of spatial field configurations (eigenfunctions of the conductivity). Each of these eigenfunctions separately satisfies Maxwell's equations. However, for an inhomogeneous plasma, even this is not possible, since, the eigenfunctions of conductivity are not solutions of Maxwell's equations. Consequently, no intrinsic property of the medium can be found to relate current density to electric field strength. (Author)