Analytically Solvable Model of Nonlinear Oscillations in a Cold but Viscous and Resistive Plasma

TL;DR

This paper presents an analytical method for solving nonlinear plasma oscillation equations considering viscosity and resistivity, yielding solutions that encompass known and new plasma behaviors, including a novel density splitting effect.

Contribution

It introduces a new analytical approach using Lagrangian variables to solve complex nonlinear plasma equations with viscosity and resistivity, including solutions where inverse scattering fails.

Findings

Includes all known solutions for ideal cold plasma

Derives new solutions for realistic plasma conditions

Discovers a nonlinear density splitting effect

Abstract

A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the solution in parametric form is obtained. It involves simple elementary functions. Our solution includes all known exact solutions for an ideal cold plasma and a large class of new ones for a more realistic plasma. A new nonlinear effect is found of splitting of the largest density maximum, with a saddle point between the peaks so obtained. The method may sometimes be useful where Inverse Scattering fails.