Title: Self-similar space-time evolution of an initial density discontinuity

The space-time evolution of an initial step-like plasma density variation is studied. We give particular attention to formulate the problem in a way that opens for the possibility of realizing the conditions experimentally. After a short transient time interval of the order of the electron plasma period, the solution is self-similar as illustrated by a video where the space-time evolution is reduced to be a function of the ratio x/t. Solutions of this form are usually found for problems without characteristic length and time scales, in our case the quasi-neutral limit. By introducing ion collisions with neutrals into the numerical analysis, we introduce a length scale, the collisional mean free path. We study the breakdown of the self-similarity of the solution as the mean free path is made shorter than the system length. Analytical results are presented for charge exchange collisions, demonstrating a short time collisionless evolution with an ensuing long time diffusive relaxation of the initial perturbation. For large times, we find a diffusion equation as the limiting analytical form for a charge-exchange collisional plasma, with a diffusion coefficient defined as the square of the ion sound speed divided by the (constant) ion collision frequency. The ion-neutral collision frequencymore » acts as a parameter that allows a collisionless result to be obtained in one limit, while the solution of a diffusion equation is recovered in the opposite limit of large collision frequencies.« less

Department of Physics, University of Oslo, Box 1048 Blindern, N-0316 Oslo (Norway)

Institute of Theoretical Astrophysics, University of Oslo, Box 1029 Blindern, N-0315 Oslo (Norway)

Publication Date:

OSTI Identifier:

22227936

Resource Type:

Journal Article

Resource Relation:

Journal Name: Physics of Plasmas; Journal Volume: 20; Journal Issue: 7; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BOLTZMANN-VLASOV EQUATION; CHARGE EXCHANGE; COLLISIONAL PLASMA; DIFFUSION; DIFFUSION EQUATIONS; ELECTRON TEMPERATURE; ELECTRONS; ION COLLISIONS; ION TEMPERATURE; MATHEMATICAL SOLUTIONS; MEAN FREE PATH; NUMERICAL ANALYSIS; PLASMA DENSITY; PLASMA SIMULATION; RELAXATION; SOUND WAVES; SPACE-TIME