NEAR-EQUILIBRIUM MULTIPLE-WAVE PLASMA STATES

We report results showing that spatially periodic Bernstein-Greene-Kru skal (BGK) waves, which are exact nonlinear traveling wave solutions o f the Vlasov-Maxwell equations for collisionless plasmas, satisfy a no nlinear principle of superposition in the small-amplitude limit. For a n electric potential consisting of N traveling waves, phi(x,t)= SIGMA( i = 1)(N)phi(i)(x-v(i)t), where v(i) is the velocity of the ith wave a nd each wave amplitude phi(i) is of order epsilon which is small, we f irst derive a set of quantities EBAR(i)(x, u, t) which are invariants through first order in epsilon for charged particle motion in this N-w ave field. We then use these functions EBAR(i)(x,u,t) to construct smo oth distribution functions for a multispecies plasma which satisfy the Vlasov equation through first order in epsilon uniformly over the ent ire x-u phase plane for all time. By integrating these distribution fu nctions to obtain the charge and current densities, we also demonstrat e that the Poisson and Ampere equations are satisfied to within errors that are O(epsilon3/2). Thus the constructed distribution functions a nd corresponding field describe a self-consistent superimposed N-wave solution that is accurate through first order in epsilon. The entire a nalysis explicates the notion of small-amplitude multiple-wave BGK sta tes which, as recent numerical calculations suggest, is crucial in the proper description of the time-asymptotic state of a plasma in which a large-amplitude electrostatic wave undergoes nonlinear Landau dampin g.