On long-time behavior of monocharged and neutral plasma in one and one-half dimensions

TL;DR

This paper investigates the long-time behavior of solutions to the relativistic and classical Vlasov-Poisson systems in one spatial and two momentum dimensions, providing growth estimates and bounds on charge density norms for both monocharged and neutral plasmas.

Contribution

It offers new long-time estimates and bounds for solutions of relativistic and classical Vlasov-Poisson systems in a specific low-dimensional setting, including both monocharged and neutral cases.

Findings

Growth estimates for particle momenta over time

Uniform-in-time lower bounds on charge density norms

Comparison between relativistic and classical systems in similar settings

Abstract

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell system. In the presence of large velocities, relativistic corrections are meaningful, and when symmetry of the particle densities is assumed this formally becomes the relativistic Vlasov-Poisson system. These equations are considered in one space dimension and two momentum dimensions in both the monocharged (i.e., single species of ion) and neutral cases. The behavior of solutions to these systems is studied for large times, yielding estimates on the growth of particle momenta and a lower bound, uniform-in-time, on norms of the charge density. We also present similar results in the same dimensional settings for the classical Vlasov-Poisson system, which excludes relativistic effects.