Space Dispersive Properties of Plasma

The "space dispersion," i.e., the occurrence of the term k in the dielectric constant ε(ω, k) can be attributed either to the Doppler effect or to the magnitude of the term ak that may appear in the formulation of the problem. (a is a characteristic distance such as the Debye length.) Using an approach based on the Doppler effect, the macroscopic parameters of a plasma have been represented in the form of four-dimensional tensors of the fourth order (similar to those introduced by Mandelstam and Tamm). The phenomenological description of plasma has also been formulated in a three-dimensional space by means of two macroscopic parameters: the electric susceptibility χₑ and the "proper magnetic susceptibility" χ_μμ. Expressions for these parameters have been given for the general case of a plasma having an electron velocity distribution f(v)dv and for a few typical specific cases. Both parameters are functions of the frequency and of the wave vector. This formulation brings into evidence the fact that a plasma is a magnetically polarizable medium and the term χ_μμ vanishes only if the electron velocity distribution is isotropic. In the current literature on the subject the existence of the term χ_μμ has been taken into account, since, by using a "modified representation" of the dielectric constant, the magnetic properties of plasma have not been brought into evidence. In the "modified representation" the dielectric constant εM is defined by the relationship k×B=-(ωc)εME, whereas in the conventional representation the same relationship has the form $k×{}B={-}({{ω}}{c}){ε}E+4{π}({{{χ}}_{{μ}}}{{μ}})k×{}B$ (where ${ε}=1+4{π}{{χ}}ₑ$). A general formalism has been developed for deriving the electric and magnetic plasma parameters directly from the Boltzmann-Vlasov equations.