The magnetized plasma permittivity tensor

An alternative form of the nonrelativistic permittivity tensor for a homogeneous magnetized plasma in thermal equilibrium is derived in the linear approximation. The derivation follows the lines of Trubnikov's derivation of the relativistic permittivity tensor and is restricted to a collisionless electron plasma. In the case of a Maxwellian equilibrium distribution, the final form is equivalent to Gordeev's integral form of the permittivity tensor. The analysis is, with minor modification, applicable to plasma comprised of multiple particle species. Unlike the standard formulas, the alternative formula presented in this article yields the components of the permittivity tensor by means of partial derivatives of a scalar kernel integral. Besides the cyclotron harmonic resonance frequencies, where the permittivities in the nonrelativistic approximation become singular, the alternative formula is manifestly valid for all wave frequencies without any restrictions on the wave vector and the thermal energy. (C) 2000 American Institute of Physics. [S1070-664X(00)03908-2].