Exakte Lösung mittels Operatorenmethode, Herleitung der Dispersionsrelation. Allgemeine Lösungstheorie der linearisierten VLASOV-BGK-Gleichung für Mehrkomponentensysteme im Magnetfeld. I



The behaviour of a multi-component system of charged particles under the action of a space- and time-dependent external electric field and a homogeneous and constant external magnetic field is examined on the basis of the linearized VLASOV equation supplemented by complete BHATNAGAR-GROSS-KROOK collision terms. The exact solution of the initial value problem is given using a compact operator techniques and applying the method of characteristics which leads to a coupled system of equations for the moments of the distribution functions. A universal dispersion relation for electrostatic plasma modes is derived for the general case of the wave vector being oblique to the direction of the external magnetic field. This dispersion relation takes LANDAU damping and dissipative collisional damping fully into account.