Long-Wavelength Limit of the Two-Fluid Euler-Poisson System

TL;DR

This paper analyzes the long-wavelength behavior of a two-fluid plasma model described by the Euler-Poisson system, revealing its reduction to the Korteweg-de Vries equation in the limit.

Contribution

It demonstrates that the collisionless two-fluid Euler-Poisson system simplifies to the KdV equation in the long-wavelength limit, combining analytical and computational methods.

Findings

The system reduces to the KdV equation in the long-wavelength limit.

The analysis applies to both hot and cold plasma regimes.

The approach integrates differential equations techniques.

Abstract

Plasma is a medium filled with free electrons and positive ions. Each particle acts as a conducting fluid with a single velocity and temperature when electromagnetic fields are present. This distinction between the roles played by electrons and ions is what we refer to as the two$-$fluid description of plasma. In this paper, we investigate the dynamics of these particles in both hot and cold plasma using a collisionless ''Euler-Poisson'' system. Employing analytical and computational techniques from differential equations, we show this system is governed by the dynamics of the Korteweg$-$de Vries (KdV) equation in the long$-$wavelength limit.