A multistream model for quantum plasmas

TL;DR

This paper introduces a multistream quantum plasma model using the nonlinear Schroedinger-Poisson system, deriving a new quantum instability branch and exploring stationary states analogous to classical modes.

Contribution

It develops a multistream quantum plasma model, derives the dispersion relation for quantum instabilities, and investigates stationary states as quantum analogs of classical modes.

Findings

Discovery of a new purely quantum branch of the two-stream instability.

Numerical confirmation of linear analysis and nonlinear regime behaviors.

Characterization of stationary states as quantum counterparts of classical BGK modes.

Abstract

The dynamics of a quantum plasma can be described self-consistently by the nonlinear Schroedinger-Poisson system. Here, we consider a multistream model representing a statistical mixture of N pure states, each described by a wavefunction. 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 Schroedinger-Poisson system confirm the linear analysis, and provide further results in the strongly nonlinear regime. The stationary states of the Schroedinger-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.