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Two‐Fluid Theory of Presheath and Space Charge Sheath in Low Pressure Plasmas
Author(s) -
Valentini H. B.
Publication year - 1991
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.2150310206
Subject(s) - plasma , physics , boundary value problem , poisson's equation , mechanics , hypersonic speed , space charge , debye sheath , electron , ion , classical mechanics , atomic physics , quantum mechanics
Abstract In low pressure plasmas the transition between the presheath and the sheath is investigated taking into account solutions of a two‐fluid model in the whole plasma. The kinetic theory is reviewed only shortly. The hydrodynamic theory is described in detail. In addition, new results are given. Boundary conditions necessary for the hydrodynamic description are derived from the electron kinetics. The two‐fluid equations supplemented by the Poisson equation constitute a set of nonlinear differential equations with isolated singular points. In addition, this is a singularly perturbated problem if the space charge sheath is thin. Singular points occur if the ions or the electrons attain the corresponding sound speed. The mathematical problem can be split into a boundary value problem for subsonic ion velocities and in an initial value problem for the hypersonic range. Solutions are obtained by combination of analytical and numerical methods. The numerical integration involvesinstabilities in the subsonic range if simultaneously the plasma is collision dominated and the space charge density is very small in the interior. Several methods are given to reduce or to avoid these difficulties. It is shown that a magnetic field, directed parallel to the tube wall, can reduce the voltage drop across the sheath substantially. In a positive column the radial variation of the electron temperature is calculated by means of the two‐fluid model. Sheath criteria are discussed.