Numerical modeling of the stationary electron distribution function in a weakly ionized gas in nonuniform electric fields

1990 ◽  
Vol 30 (5) ◽  
pp. 671-675 ◽  
Author(s):  
V. A. Shveigert
Keyword(s):  
Numerical Modeling ◽  
Distribution Function ◽  
Electric Fields ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Ionized Gas ◽  
Weakly Ionized ◽  
Stationary Electron

Slowly propagating instabilities in plasmas with Margenau-Davydov electron distribution function

1980 ◽  
Vol 24 (3) ◽  
pp. 503-514 ◽  
Author(s):  
V. J. Žigman ◽  
B. S. Milić
Keyword(s):  
Distribution Function ◽  
Steady State ◽  
Absolute Stability ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Electron Drift ◽  
Steady State Distribution ◽  
State Distribution ◽  
Weakly Ionized ◽  
Weakly Ionized Plasma

The properties of certain wave modes excited in a weakly ionized plasma placed in an external d.c. electric field are analyzed from the standpoint of the linearized kinetic equation, the electron steady-state distribution function being taken in the form of the extended Margenau–Davydov and, in particular, Druyvesteinian. The presence of absolute stability cones formed by certain propagation directions is found. The corresponding critical values of the electron drift, destabilizing each of the modes considered, is also evaluated for a plasma with a Druyvesteinian distribution.

Generalized Electron Cyclotron Resonance in Weakly Ionized Time-Varying Magnetoplasmas

1969 ◽  
Vol 24 (4) ◽  
pp. 555-559 ◽  
Author(s):  
Wolfgang Stiller ◽  
Günter Vojta
Keyword(s):  
Magnetic Field ◽  
Distribution Function ◽  
Cyclotron Resonance ◽  
Electron Distribution ◽  
Electron Cyclotron Resonance ◽  
Electron Distribution Function ◽  
Resonance Phenomenon ◽  
Alternating Electric Field ◽  
Special Cases ◽  
Weakly Ionized

Abstract The electron distribution function is calculated explicitly for a weakly ionized plasma under the action of an alternating electric field E = {0 , 0 , Eoz cos ω t} and a circularly polarized magnetic field BR = Bc{cos ωB t, sin ωB t, 0} rotating perpendicular to the a.c. field. Furthermore, a constant magnetic field B0 = {0, 0, B0} is taken into account. The isotropic part f0 of the electron distribution function which contains, in special cases, well-known standard distributions (distributions of Druyvensteyn, Davydov, Margenau, Allis, Fain, Gurevic) shows a resonance behaviour if the frequencies ω, ωc = (q/m) Bc , ω0 = (q/m) B0 , and ωB satisfy the relation ω= This can be understood as a generalized cyclotron resonance phenomenon.

Solution with Third-order Accuracy for the Electron Distribution Function in Weakly Ionized Gases (or in Intrinsic Semiconductors): Application to the Drift Velocity

1981 ◽  
Vol 34 (4) ◽  
pp. 361 ◽  
Author(s):  
G Cavalleri
Keyword(s):  
Distribution Function ◽  
Legendre Polynomials ◽  
Taylor Expansion ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Mean Free Path ◽  
Third Order ◽  
Order Accuracy ◽  
Weakly Ionized ◽  
The Mean

The first four components 10, I" 12 and 13 of the expansion in Legendre polynomials of the electron distribution function I are shown to be of order t:D, et, e2 and e3 respectively, with e = (m/M)'/2 where m and M are the masses of the electron and molecule respectively. This allows the solution of the so-called P3 approximation to the Boltzmann equation applied to a weakly ionized gas (or to an intrinsic semiconductor) in steady-state and uniform conditions and for dominant elastic collisions. However, nonphysical divergences appear in 10 and in the drift velocity W. This can be understood by the equivalence of the Boltzmann-Legendre formulation and the mean free path formulation in which a Taylor expansion is performed around the 'origin', i.e. for a -+ 0, where a = eE/m is the acceleration due to an external electric field E. Indeed, one sees that the expansion under the integral sign (integrals appear in the evaluation of transport quantities) leads to divergent integrals if the expansion is around a = O. Fortunately, it is easy to perform a Taylor expansion around a oft 0 in the mean free path formulation and then to find the corresponding expansion in Legendre polynomials outside the origin. In this way, explicit convergent expressions are found for 10, I" 12, 13 and W, with third-order accuracy in e = (m/M)'/2. This is better than the best preceding expression, that by Davydov-Chapman-Cowling, which has first-order accuracy only (it is the solution of the P, approximation to the Boltzmann equation).

Relaxation of Electrons in the Boundary Layer of a Weakly Ionized Plasma

1984 ◽  
Vol 39 (1) ◽  
pp. 13-21
Author(s):  
A. Schumacher
Keyword(s):  
Boundary Layer ◽  
Distribution Function ◽  
Electron Distribution ◽  
Electron Distribution Function ◽  
Approximation Procedure ◽  
Unknown Parameters ◽  
Potential Jump ◽  
Weighted Residuals ◽  
Weakly Ionized ◽  
Angular Dependency

We study the kinetics of fast electrons in a weakly ionized collision dominated plasma in front of a planar negative wall. For small Debye lengths the potential variation in the boundary layer can be approximated by a potential jump representing the space charge sheath. We propose an approximation method to calculate the electron distribution function which accounts for general boundary conditions (absorption, reflection and emission). This method is based on a parametrization of the angular dependency, the unknown parameters being determined by a suitable adaption of the Method of Weighted Residuals. The error inherent in our approximation procedure is discussed and shown to be small. As result we get a straightforward analytic representation of the electron distribution function in the boundary layer. For the special case of a totally absorbing wall our results are in good agreement with exact analytical solutions in the literature.

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