On kinetic description of electromagnetic processes in a quantum plasma

TL;DR

This paper derives a nonlinear kinetic equation for nonrelativistic quantum plasma with electromagnetic interactions, enabling easier numerical simulations of quantum effects in plasma phenomena by modifying existing classical Vlasov codes.

Contribution

It introduces a Vlasov-Boltzmann-type equation with a quantum interference integral, facilitating straightforward incorporation of quantum effects into classical plasma simulation codes.

Findings

Provides a form of kinetic equation suitable for numerical implementation

Enables simulation of quantum plasma phenomena with existing Vlasov codes

Separates quantum and classical effects for analysis

Abstract

A nonlinear kinetic equation for nonrelativistic quantum plasma with electromagnetic interaction of particles is obtained in the Hartree's mean-field approximation. It is cast in a convenient form of Vlasov-Boltzmann-type equation with "quantum interference integral", that allows for relatively straightforward modification of existing classical Vlasov codes to incorporate quantum effects (quantum statistics and quantum interference of overlapping particles wave functions), without changing the bulk of the codes. Such modification (upgrade) of existing Vlasov codes may provide a direct and effective path to numerical simulations of nonlinear electrostatic and electromagnetic phenomena in quantum plasmas, especially of processes where kinetic effects are important (e.g., modulational interactions and stimulated scattering phenomena involving plasma modes at short wavelengths or high-order kinetic modes, dynamical screening and interaction of charges in quantum plasma, etc.) Moreover, numerical approaches involving such modified Vlasov codes would provide a useful basis for theoretical analyses of quantum plasmas, as quantum and classical effects can be easily separated there.