Landau Damping to all Orders

Abstract

Recent results for an asymptotic series expansion of the nonlinear equations for an electronic plasma in the "collisionless" regime are extended. Substantially, the result is that for a wide class of initial disturbances, the presence of the so-called "Landau damping" in first order indicates its persistence to all orders in perturbation theory. Similarly, exponentially growing solutions in first order imply their existence in all higher orders. The problem is considered both from the Laplace transform point of view, and by normal modes.