The quasi-static approximation for moving and finite temperature plasmas

A stationary plasma in the presence of a magnetic field may be represented by an equivalent dielectric tensor. The equivalent dielectric tensor of a moving plasma, valid within the quasi-static approximation, is found by a Lorentz transformation of the dielectric tensor from a reference frame in which the plasma is at rest to one in which the laboratory is at rest. The range of validity of the dielectric tensor is investigated, and the relation between this tensor and the equivalent dielectric tensor found from Maxwell's curl equation is determined. An infinite number of moving plasma streams with a Maxwellian velocity distribution are summed to obtain the dielectric tensor of a finite temperature plasma. The dielectric tensor leads directly to the dispersion relation for waves on a bounded plasma.