Landau damping of resonance oscillations in inhomogeneous plasmas

Abstract

A self-consistent solution of the Vlasov—Poisson equations is obtained for a low-temperature, bounded, Maxwellian plasma of arbitrary non-uniform density. An eigenvalue equation for the central frequencies and electric fields of the resonance oscillations is obtained, which agrees with the equation obtained by a low-temperature expansion of the orbital-integral solution. The Landau damping rate is given in a general, explicit form in terms of the central frequencies and fields of the resonances.