Longitudinal and transversal current in collisional plasma, generated by two transversal electromagnetic waves

TL;DR

This paper derives a formula for electric currents in collisional plasmas influenced by two transversal electromagnetic waves, revealing nonlinear effects and the transition to collisionless plasma behavior as collision frequency approaches zero.

Contribution

It introduces a new nonlinear model for calculating longitudinal and transversal currents in collisional plasmas using the Vlasov equation with BGK collision integral, applicable at any temperature.

Findings

Longitudinal current arises due to nonlinearity and is orthogonal to classical transversal current.

Results reduce to known collisionless plasma formulas when collision frequency tends to zero.

Graphical analysis shows how current depends on wave number, collision frequency, and oscillation frequencies.

Abstract

From kinetic Vlasov equation for collisional plasmas distribution function in square-law approximation on sizes of intensivities of electric fields is received. The known integral of collisions of relaxation type, so-called BGK (Bhatnagar, Gross, Krook) integral of collisions is considered. The formula for calculation electric current at any temperature (any degree of degeneration of electronic gas) is deduced. This formula contains an one-dimensional quadrature. It is shown, that the nonlinearity account leads to occurrence the longitudinal electric current directed along a wave vector. This longitudinal current is orthogonal to a known transversal classical current, received at the linear analysis. When frequency of collisions tends to the zero, all received results for collisional plasmas pass in corresponding formulas for collisionless plasmas. The case of small values of wave number is considered. It is shown, that the received quantity of longitudinal current at aspiration of frequency of collisions to zero also passes in corresponding expression of current for collisionless plasmas. Graphic comparison of dimensionless quantity of current depending on wave number, frequency of oscillations of electromagnetic field and frequencies of electron collisions with plasma particles is carry out.