Non-linear equations for electron waves in Maxwellian low-collision ion-electron plasmas

TL;DR

This paper develops a method to analyze electron wave propagation in Maxwellian plasmas, deriving non-linear equations that include collision damping and quadratic effects, revealing damping behavior near the Langmuir frequency.

Contribution

It introduces a novel approach using 2D Laplace transforms to derive non-linear equations for electron waves in Maxwellian plasmas, accounting for collision damping and overtones.

Findings

Damping increases infinitely as frequency approaches the Langmuir frequency from above.

Collisionless damping at frequencies above the Langmuir frequency occurs only in non-Maxwellian plasmas.

Recurrent relations for wave overtones are established, describing the non-linear wave solutions.

Abstract

The before described general principles and methodology of calculating electron wave propagation in homogeneous isotropic half-infinity slab of Maxwellian plasma with indefinite but in principal value sense taken integrals in characteristic equations, and the use of 2D Laplace transform method are applied to an evaluation of collision damping decrements of plane electron longitudinal and transverse waves. Damping decrement tends to infinity when the wave frequency tends to electron Langmuir frequency from above values. We considered recurrent relations for amplitudes of the overtones which form in their sum the all solution of the plasma wave non-linear equations including collision damping and quadratic (non-linear) terms. Collisionless damping at frequencies more the Langmuir one is possible only in non-Maxwellian plasmas.