Longitudinal electric current in classical collisional Maxwellian plasma, inducted by transversal electromagnetic wave

TL;DR

This paper derives a formula for longitudinal electric current in collisional Maxwellian plasma induced by a transversal electromagnetic wave, revealing nonlinearity effects and comparing collisional and collisionless cases.

Contribution

It introduces a new analytical approach to calculate the longitudinal current in collisional plasma using the Vlasov equation with BGK collision integral, highlighting nonlinearity effects.

Findings

Longitudinal current arises due to nonlinearity in plasma response.

Derived formulas reduce to known collisionless results when collision frequency approaches zero.

Graphical analysis illustrates current density dependence on plasma parameters.

Abstract

Kinetic Vlasov equation for collisional Maxwellian plasmas is used. Collision integral of BGK (Bhatnagar, Gross and Krook) type is applied. From Vlasov equation we find distribution function of electrons in square-law approximation on size of transversal electric field. The formula for electric current calculation is deduced. This formula contains an one-dimensional quadrature. It is shown, that nonlinearity leads to revealing of the longitudinal electric current directed along a wave vector. This longitudinal current is perpendicular to known so-called transversal classical current. The classical current turns out at the linear analysis. The longitudinal current in case of small values of wave numbers is calculated. When frequency of collisions tends to zero, all received formulas for collisional plasmas pass in the known corresponding results for collisionless plasmas. Graphic research of dimensionless density of a current is carried out.