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Starting from first principles quantum kinetic theory for ideal plasmas withexchange effects, the quantum hydrodynamic equations are derived taking momentsof the corresponding exchange-Vlasov equation. The case of an electron-ionplasma where ions are entirely classical is considered. The linear dispersionrelation for ion-acoustic waves is found from the macroscopic equations andcompared with exchange quantum kinetic theory, yielding a qualitative agreementapart 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 areshown to be necessarily a correction, within the ideal and long wavelengthapproximations.

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