Abstract
A quantum fluid model is derived from the Wigner–Poisson system. Quantum statistical effects can be incorporated using a convenient equation of state. Quantum diffraction effects manifest through a Bohm potential term. The derivation is based on the Madelung representation of the ensemble wavefunctions, so that the second-order moment of the Wigner function appear as the sum of kinetic and osmotic pressures and the Bohm potential. The case of an one-dimensional zero-temperature Fermi gas is treated, for both one and two-stream plasmas. The validity conditions for the quantum hydrodynamic model for plasmas are discussed. The derivation of the equation of state for a zero-temperature Fermi gas is detailed for one, two, and three spatial dimensions. The long wavelength condition to avoid kinetic effects is treated in the case of a degenerate plasma. The question of the representation of a given Wigner function in terms of a set of ensemble wavefunctions is worked out.
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Haas, F. (2011). A Fluid Model for Quantum Plasmas. In: Quantum Plasmas. Springer Series on Atomic, Optical, and Plasma Physics, vol 65. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-8201-8_4
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DOI: https://doi.org/10.1007/978-1-4419-8201-8_4
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