Asymptotic Dynamics of Dispersive, Collisionless Plasmas

TL;DR

This paper analyzes the long-term behavior of collisionless plasmas modeled by the Vlasov-Poisson system, establishing convergence of particle distributions and electric fields under certain decay assumptions.

Contribution

It provides a detailed description of the asymptotic profiles and convergence properties of solutions to the Vlasov-Poisson system, including modified scattering results.

Findings

Convergence of velocity characteristics and spatial averages as time grows large.

Precise asymptotic profiles of electric field and densities established.

Modified $L^ abla$ scattering for particle distributions shown.

Abstract

A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming that the electric field decays with sufficient rapidity as $t \to\infty$, we show that the velocity characteristics and spatial averages of the particle distributions converge as time grows large. Using these limits we establish the precise asymptotic profile of the electric field and its derivatives, as well as, the charge and current densities. Modified spatial characteristics are then shown to converge using the limiting electric field. Finally, we establish a modified $L^\infty$ scattering result for each particle distribution function, namely we show that they converge as $t \to \infty$ along the modified spatial characteristics. When the plasma is non-neutral, the estimates of these quantities are sharp, while in the neutral case they may imply faster rates of decay.