The drift-wave dispersion equation revisited

Abstract

In view of some difficulties that appeared in previous work, the drift-wave dispersion equation has been studied in great detail by stressing some features that are not discussed in the usual textbook presentations. It is shown that any analytical approximation of a plasma dispersion equation leads to a singular perturbation problem for the roots of an algebraic equation. This property is associated with a number of parasitic roots, which can be identified and eliminated from the start. The behaviour of the remaining physical roots is discussed in detail by defining characteristic regions in the parameter space spanned by the gradients of density, electron and ion temperatures. Whereas in a large domain the usual behaviour predicted by elementary drift-wave theory is recovered, it is shown that there exists a region (whose existence is not predicted by elementary theory), where the conditions of existence of a drift wave are violated, thus causing the appearance of the (spurious) singularity previously found by Balescu. The explanation of this paradoxical situation is discussed in detail. The smooth connection of these results with the limit of a spatially homogeneous plasma is considered in an appendix.