Stochastic substitute for coupled rate equations in the modeling of highly ionized transient plasmas

Journal Article · Sun May 01 04:00:00 EDT 1994 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.49.4735· OSTI ID:7279813

Eliezer, S; Falquina, R; Minguez, E ^[1]

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1. Institute of Nuclear Fusion, Escuela Tecnica Superior de Ingenieros Industriales, Jose Gutierrez Abascal 2, 28006 Madrid (Spain)

Plasmas produced by intense laser pulses incident on solid targets often do not satisfy the conditions for local thermodynamic equilibrium, and so cannot be modeled by transport equations relying on equations of state. A proper description involves an excessively large number of coupled rate equations connecting many quantum states of numerous species having different degrees of ionization. Here we pursue a recent suggestion to model the plasma by a few dominant states perturbed by a stochastic driving force. The driving force is taken to be a Poisson impulse process, giving a Langevin equation which is equivalent to a Fokker-Planck equation for the probability density governing the distribution of electron density. An approximate solution to the Langevin equation permits calculation of the characteristic relaxation rate. An exact stationary solution to the Fokker-Planck equation is given as a function of the strength of the stochastic driving force. This stationary solution is used, along with a Laplace transform, to convert the Fokker-Planck equation to one of Schroedinger type. We consider using the classical Hamiltonian formalism and the WKB method to obtain the time-dependent solution.

• OSTI ID: 7279813
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 49:5; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700330 -- Plasma Kinetics
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700350* -- Plasma Production
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COLLISIONS
ELECTRON COLLISIONS
FLUIDS
FULLY IONIZED GASES
GASES
IONIZED GASES
KINETICS
LASER-PRODUCED PLASMA
PLASMA
PLASMA SIMULATION
SIMULATION