Exchange fluid model derived from quantum kinetic theory for plasmas. Issue 2 (14th May 2021) - Haas, Fernando
Abstract: Starting from quantum kinetic theory for ideal plasmas with exchange effects, the quantum hydrodynamic equations are derived from 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.