Exchange fluid model derived from first principles quantum kinetic theory for plasmas

TL;DR

This paper derives quantum hydrodynamic equations for plasmas from first principles quantum kinetic theory, incorporating exchange effects, and compares the resulting dispersion relations with exchange quantum kinetic theory.

Contribution

It introduces a derivation of quantum hydrodynamic equations with exchange effects from first principles and compares their predictions with quantum kinetic theory.

Findings

Qualitative agreement in ion-acoustic wave dispersion relations

Exchange effects are a correction within ideal, long wavelength approximations

Derived equations applicable to electron-ion plasmas with classical ions

Abstract

Starting from first principles quantum kinetic theory for ideal plasmas with exchange effects, the quantum hydrodynamic equations are derived taking moments of the corresponding exchange-Vlasov equation. The case of an electron-ion plasma where ions are entirely classical is considered. The linear dispersion relation for ion-acoustic waves is found from the macroscopic equations and compared with exchange quantum kinetic theory, yielding a qualitative agreement apart from a numerical factor of order one in the exchange contribution, assuming a Maxwellian background as a first step, for analytical simplicity. The validity conditions of the treatment are discussed and exchange effects are shown to be necessarily a correction, within the ideal and long wavelength approximations.