Multistream model for quantum plasmas
Abstract
The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schrödinger-Poisson system. We consider a multistream model representing a statistical mixture of N pure states, each described by a wave function. The one-stream and two-stream cases are investigated. We derive the dispersion relation for the two-stream instability and show that a new, purely quantum, branch appears. Numerical simulations of the complete Schrödinger-Poisson system confirm the linear analysis, and provide further results in the strongly nonlinear regime. The stationary states of the Schrödinger-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.
- Publication:
-
Physical Review E
- Pub Date:
- August 2000
- DOI:
- 10.1103/PhysRevE.62.2763
- Bibcode:
- 2000PhRvE..62.2763H
- Keywords:
-
- 52.35.-g;
- 03.65.-w;
- 05.60.Gg;
- Waves oscillations and instabilities in plasmas and intense beams;
- Quantum mechanics;
- Quantum transport