Nonlinear longitudinal current in quantum plasma generated by two transversal electromagnetic waves

TL;DR

This paper derives a formula for the nonlinear longitudinal electric current in quantum plasma under two electromagnetic waves, showing it differs from the linear case and aligns with classical plasma results at small wave numbers.

Contribution

It presents a new quantum kinetic approach to calculate nonlinear longitudinal currents in plasma with arbitrary degeneration, including a formula with a one-dimensional quadrature.

Findings

Nonlinear longitudinal current appears along wave vectors.

Longitudinal current differs from the known transverse current.

Quantum and classical plasma currents coincide at small wave numbers.

Abstract

Quantum plasma with arbitrary degree degeneration of electronic gas is considered. Plasma is in two external electromagnetic fields. It is required to find the plasma response on this fields. From Wigner kinetic equation for the quantum collisionless plasmas distribution function in square-law approach on sizes of vector potentials of two electric fields is received. 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 vectors. This longitudinal current is orthogonal to a known transversal current, received at the linear analysis. The case of small values of wave numbers is considered. It is shown, that in case of small values of wave numbers a longitudinal current in quantum plasma coincides with a longitudinal current in classical plasma.