Damping and dispersion of oscillating modes of a multicomponent ionic mixture in a magnetic field

The collective-mode spectrum of a multicomponent magnetized ionic mixture for small wave number $k$ is studied with the use of magnetohydrodynamics and formal kinetic theory. Apart from the usual thermal and diffusive modes, the spectrum contains a set of four oscillating modes. By evaluating the
k^2 contributions to the eigenfrequencies, the damping and the dispersion of these oscillating modes are determined. The long-range nature of the Coulomb interactions is shown to imply that Burnett terms with higher-order gradients in the linear phenomenological laws have to be taken into account in order to obtain a full description of all damping and dispersion effects.