NONLINEAR ELECTROSTATIC-WAVES IN COLLISIONLESS PLASMAS

We report results concerning small amplitude Bernstein-Greene-Kruskal (BGK) waves, which are exact undamped traveling wave solutions of the nonlinear Vlasov-Poisson-Ampere equations for collision: less plasmas. Building upon previous work, we first develop a simple but powerful f ormalism that facilitates a methodical investigation of the types and properties of small amplitude BGK plasma waves that can exist near a g iven collisionless plasma equilibrium. Using this formalism, we then s how that any physically relevant spatially uniform plasma equilibrium supports nonlinear spatially periodic BGK waves that are described by the Vlasov dispersion relation in the small amplitude limit. We demons trate also that these equilibria are characterized by a discrete set o f critical velocities v(c)((i)), i = 1,2,..., at which BGK solitary wa ves of vanishingly small amplitude can propagate in the plasma. The ex istence of these exact nonlinear spatially periodic and solitary wave solutions illustrates the fundamental incompleteness of the linear Vla sov-Landau theory of plasma waves since, by virtue of particle trappin g, these nonlinear waves neither damp nor grow even when their amplitu de is arbitrarily small.