The magnetized plasma permittivity tensor

An alternative form of the nonrelativistic permittivity tensor for a homoge neous magnetized plasma in thermal equilibrium is derived in the linear app roximation. The derivation follows the lines of Trubnikov's derivation of t he relativistic permittivity tensor and is restricted to a collisionless el ectron plasma. In the case of a Maxwellian equilibrium distribution, the fi nal form is equivalent to Gordeev's integral form of the permittivity tenso r. The analysis is, with minor modification, applicable to plasma comprised of multiple particle species. Unlike the standard formulas, the alternativ e formula presented in this article yields the components of the permittivi ty tensor by means of partial derivatives of a scalar kernel integral. Besi des the cyclotron harmonic resonance frequencies, where the permittivities in the nonrelativistic approximation become singular, the alternative formu la is manifestly valid for all wave frequencies without any restrictions on the wave vector and the thermal energy. (C) 2000 American Institute of Phy sics. [S1070-664X(00)03908-2].