Nonlinear steady state structures for inhomogeneous plasma

Abstract

We study the nonlinear steady state structures created in a one-dimensional collisionless electron plasma by a transparent grid raised to a given potential. Moreover, natural structures, i.e., in the absence of a grid and consequently of any external charge, can also be obtained. For the electrons (here ions are supposed motionless and uniform), the structure must involve a hole in the trapped electron density distribution and is consequently attractive. A relationship between the depth of the potential and its possible length is obtained. These studies are preliminary to the problems of stability and waves propagating in strongly inhomogeneous plasma structures. FORMULATIONAND DISCUSSION OF PROBLEMS 2.1. Multiple Water Bag model. In this study we consider collisionless plasma, i.e., one in which the motion of a charged particle is due to the collective action of the other charged particles. In that way, we do not take individual effects into account, compared to the purely collective field, so that the plasma can be described by the V!asov equation. This nonlinear equation cannot be solved directly in most cases; consequently, plasma physicists have had to develop models which simplify the treatment at its beginning.An interesting model of that type is the Water Bag model. Its name, given by De Packh [1962], results from the analogy between a phase-space fluid and a real-space incompressible fluid. Let us consider in the phase space, at a given time t, a domain delineated by a closed surface with a space density constant inside it and equal to zero outside.

Coherent Phase Space Structure in One-Dimensional Electrostatic Plasma

“…First, we create a BGK structure in the beam. This is an inverse problem performed by an already proposed numerical algorithm based on the multiple water bag [8]. To guarantee that the proper modes of the plasma are all damped away and that the plasma has well reached the state described by eq.…”