An invariant theory of the constitutive parameters of a plasma and a ferrite

Abstract

Under the influence of a constant magnetic field, the electric property of a plasma and the magnetic property of a ferrite are anisotropic. In this paper, the general coordinatefree invariant forms of the dielectric tensor of a plasma and the permeability tensor of a ferrite are obtained. The tensors are expressed explicitly as a sum of three tensors: a unit tensor, a symmetric tensor and an antisymmetric tensor, each of which is weighted by different constants. The symmetric and antisymmetric tensors are related to the unit vector of the constant magnetic field. The invariant forms in terms of the sum of the projectors of the tensors are also derived. When a Cartesian coordinate system is introduced, the invariant forms are easily reduced to the commonly used matrix representations. The invariant forms clearly show the effects of the constant magnetic field on the anisotropies of the media. Moreover, they effectuate and simplify the deduction of the general solutions of problems involving wave propagation and excitation in plasma and ferrite and thus facilitate interpretations of the final results.