Decay in Time for a One-Dimensional Two-Component Plasma

TL;DR

This paper investigates the long-term behavior of solutions to one-dimensional collisionless plasma models, deriving a new mathematical identity to analyze decay properties in both classical and relativistic cases.

Contribution

A novel identity is introduced for the Vlasov-Poisson systems, enabling new insights into the decay and stability of plasma solutions over time.

Findings

Derived a new identity for plasma systems

Analyzed decay behavior of solutions

Applicable to both classical and relativistic models

Abstract

The motion of a collisionless plasma is described by the Vlasov-Poisson system, or in the presence of large velocities, the relativistic Vlasov-Poisson system. Both systems are considered in one space and one momentum dimension, with two species of oppositely charged particles. A new identity is derived for both systems and is used to study the behavior of solutions for large times.