Undamped plasma waves

Abstract

In this paper we describe small-amplitude nonlinear plasma wave solutions to the one-dimensional Vlasov-Maxwell equations. The methods used to construct these waves rely on the decomposition of the distribution functions into odd and even parts and on using BGK forms to represent these pairs of functions; further manipulations using dimensional-reduction techniques from nonlinear functional analysis reduce the problem exactly to an algebraic equation that can be analyzed using bifurcation theory. Using these methods, we first develop a sufficient condition for waves of a given phase velocity to exist arbitrarily close to a given spatially uniform Vlasov equilibrium. Along with this condition we derive sufficient analytical information for the construction of approximate expressions for the electric potential and distribution functions, with exact knowlege of the asymptotic behavior of the error terms. These results have a very surprising physical implication: the Landau damping of small-amplitude waves is not inevitable. Instead, there exist plasma waves that trap particles even at arbitrarily small amplitude and do not damp.