Landau damping of surface waves at a plasma— vacuum interface

Abstract

The exact surface-wave dispersion relation is expressed in terms of elementary functions for a plasma characterized by a ‘resonance’ velocity distribution function. An approximate form of the relation is derived for the case when the thermal velocity spread is much less than c. The pure surface wave obtained by dropping the term responsible for Landau damping is compared with that predicted on the basis of a fluid model of the plasma. The effect of Landau damping is then investigated, both by analytic approximations and by computation. Two branches of the solution to the dispersion relation are found; and it is shown that the surface wave suffers increasingly severe damping as the frequency grows beyond 1/ √ 2 times the plasma frequency. It is argued that qualitatively similar damping would be present were the plasma to have a Maxwellian equilibrium distribution function.