Arbitrary Polynomial Decay Rates of Neutral, Collisionless Plasmas

Abstract

A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming the plasma is neutral and the electric field decays with sufficient rapidity as $t \to\infty$, we show that solutions can be constructed with arbitrarily fast, polynomial rates of decay, depending upon the properties of the limiting spatial average and its derivatives. In doing so, we establish, for the first time, a countably infinite number of asymptotic profiles for the charge density, electric field, and their derivatives, each of which is necessarily realized by a sufficiently smooth solution and exceeds the established dispersive decay rates. Finally, in each case we establish a linear $L^\infty$ scattering result for every particle distribution function, namely we show that they converge as $t \to \infty$ along the transported spatial characteristics at increasingly faster rates.