Wave Motion in a Plasma Based on a Fokker-Planck Equation

Abstract

An isotropic Fokker-Planck collision model is introduced in Boltzmann's equations in order to study the small amplitude wave motion of an unbounded, fully ionized, neutral, two-component plasma in a uniform applied magnetic field. In the Laplace and Fourier transformed space the linearized Boltzmann's equations with Maxwell's equations are solved and the dispersion relation is constructed. Because the isotropic Fokker-Planck operators describe a diffusion process in velocity space while the previously considered Krook relaxation models do not, an infinite number of new Larmor resonance modes is found at arbitrary directions of propagation with respect to the applied magnetic field. These new resonances remain in the limit of long macroscopic wavelengths and small collision frequencies. At propagation parallel to the applied magnetic field new resonances are found for wavelengths large and small with respect to the mean free path. In other macroscopic ranges such as the cold plasma regime and the long wavelength magnetohydrodynamic regime the Krook and the isotropic Fokker-Planck models give the same results to lowest order.