Self-similar space-time evolution of an initial density discontinuity
- 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)
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 frequency 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.
- OSTI ID:
- 22227936
- Journal Information:
- Physics of Plasmas, Vol. 20, Issue 7; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
Similar Records
Nonlinear evolution of drift instabilities in the presence of collisions
Current collection by a cylindrical probe in a partly ionized, collisional plasma
Related Subjects
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