The Moments Method

The quantum hydrodynamic model for plasmas is extended through the inclusion of higher-order moments of the Wigner function. In this manner, quantum effects appear without the need of the Madelung decomposition of the ensemble wavefunctions. The treatment apply to the electrostatic as well as the electromagnetic cases. To describe nonlinearities and inhomogeneous magnetic fields, a gauge invariant Wigner formulation is unavoidable. Dispersion relations for high-frequency wave propagation are discussed.