skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Three species one-dimensional kinetic model for weakly ionized plasmas

Abstract

A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting set of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.

Authors:
; ;  [1]
  1. Department of Applied Physics, Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, Universidad Politécnica de Madrid, 28040 Madrid (Spain)
Publication Date:
OSTI Identifier:
22598988
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 6; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPEALS; COLLISIONS; COMPARATIVE EVALUATIONS; DISTRIBUTION FUNCTIONS; ELECTRIC CHARGES; ELECTRIC FIELDS; GEOMETRY; INTEGRO-DIFFERENTIAL EQUATIONS; LANDAU DAMPING; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PLASMA; SOLUTIONS; TEMPERATURE DEPENDENCE

Citation Formats

Gonzalez, J., E-mail: jorge.gonzalez@upm.es, Donoso, J. M., and Tierno, S. P. Three species one-dimensional kinetic model for weakly ionized plasmas. United States: N. p., 2016. Web. doi:10.1063/1.4953901.
Gonzalez, J., E-mail: jorge.gonzalez@upm.es, Donoso, J. M., & Tierno, S. P. Three species one-dimensional kinetic model for weakly ionized plasmas. United States. doi:10.1063/1.4953901.
Gonzalez, J., E-mail: jorge.gonzalez@upm.es, Donoso, J. M., and Tierno, S. P. 2016. "Three species one-dimensional kinetic model for weakly ionized plasmas". United States. doi:10.1063/1.4953901.
@article{osti_22598988,
title = {Three species one-dimensional kinetic model for weakly ionized plasmas},
author = {Gonzalez, J., E-mail: jorge.gonzalez@upm.es and Donoso, J. M. and Tierno, S. P.},
abstractNote = {A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting set of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.},
doi = {10.1063/1.4953901},
journal = {Physics of Plasmas},
number = 6,
volume = 23,
place = {United States},
year = 2016,
month = 6
}
  • A model of steady spherical contactors that takes into account small transverse gradients in plasma variables is presented. The effects of non-uniform boundary conditions on the electric potential profile, the collection of current, and the position of the double layer that confines the emitted plasma cloud, are studied. Appropriate jump conditions across the double layer are derived. Plasma profiles and parameters are calculated for different values of Legendre index l, dimensionless contactor potential {chi}{sub {ital R}}, and dimensionless collected current {ital j}{sub {ital e}0}. For high contactor potentials, small non-uniformities in the plasma emission can substantially affect the approximate sphericalmore » symmetry of the plasma. Also, for definite values of index l and double layer mean position, the symmetrical boundary-value problem can sustain free, stationary, non-symmetrical modes. The nature of these modes and its relevancy to the global stability of the plasma field are discussed. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.« less
  • A hierarchy of equations for the distribution functions of electrons and ions in weakly ionized plasma in magnetic fields was derived using the Bogolyubov method. The collisions of charged particles with neutral particles were considered with the Boltzmann or Fokker-Planck collision terms. Closed equations for the distribution functions of the first or second order were found from a series development. Under the assumption of a Maxwell distribution of the pulse, corresponding equations for the spatial distribution functions were found. The equations established are also valid for electrolytes, although electrophoretic effects are still not attainable. The theory developed was used inmore » order to investigate the relaxation of the ion atmosphere and the frequency dispersion of the tensors of the complex dielectric constants in exterior magnetic fields.« less
  • Analytical relations are given for estimating the energy of the stochastic motion of an individual dust grain heated by electrostatic ion oscillations in a weakly ionized gas-discharge plasma. Dust grain charging processes are analyzed, and an empirical approximation is obtained for the ion current to the grain surface. The processes are simulated under conditions similar to those of laboratory experiments on dusty plasmas. It is found that the kinetic temperature of a dust grain heated by electrostatic ion oscillations in a gas-discharge plasma can exceed the background gas temperature.