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

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.