Multistream model for quantum plasmas

The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schrodinger-Poisson system. We consider a multistream model repre senting a statistical mixture of N pure states, each described by a wave fu nction. The one-stream and two-stream cases are investigated. We derive the dispersion relation for the two-stream instability and show that a new, pu rely quantum, branch appears. Numerical simulations of the complete Schrodi nger-Poisson system confirm the linear analysis, and provide further result s in the strongly nonlinear regime. The stationary states of the Schrodinge r-Poisson system are also investigated.-These can be viewed as the quantum mechanical counterpart of the classical Bernstein-Greene-Kruskal modes, and are described by a set of coupled nonlinear differential equations for the electrostatic potential and the stream amplitudes.