THE DIFFUSION EQUATION WITH A QUADRATIC LOSS TERM APPLIED TO ELECTRON-ION VOLUME RECOMBINATION IN A PLASMA

Journal Article · Thu Feb 01 04:00:00 EST 1962 · Annals of Physics (New York) (U.S.)

DOI:https://doi.org/10.1016/0003-4916(62)90029-5· OSTI ID:4808186

Gray, E P; Kerr, D E

The diffusion equation for charged particles in a plasma, with an additional recombination loss term (quadratic in the particle concentration n) was solved numerically for plasmas in containers having the shape of an infinite cylinder and a sphere. This equation applies to a decaying plasma in therma1 equi1ibrium, with no sources of ionization, no loss mechanisms other than diffusion and volume recombination, and containing no negative and only one species of positive ion. The boundary condition n/sub wall/ = 0 and the initial conditions of uniform coneentration and of the lowest diffusion mode were used. For a given choice of these conditions, each solution is uniquely specified by a single parameter beta , the ratio of the initial central particle loss rate which would prevail in the absence of diffusion, to the corresponding loss rate resulting from only diffusion in the fundamental mode. It is a quantitative measure of the degree of recombination control. These solutions were used to assess the limits of applicability and the accuracy of the microwave cavity method for determining the recombination coefficient alpha as the slope of a plot of the reciprocal of the measured electron concentration vs. time. It is found that a linear region in this plot can exist for beta = 0, and that the slope is unrelated to alpha for sufficiently small beta . Only if beta is very large, and if the linear region is sufficiently extended, does the slope constitute a reasonable approximation to alpha . A criterion is established for the validity of this method of determining alpha , and is applied to previous experiments. It is found that although some experiments satisfy this criterion and presumably yield good values of alpha , others do not and yield values that are too large. (auth)

• Research Organization: Johns Hopkins Univ., Silver Spring, Md.
• NSA Number: NSA-16-011084
• OSTI ID: 4808186
• Journal Information: Annals of Physics (New York) (U.S.), Journal Name: Annals of Physics (New York) (U.S.) Vol. Vol: 17; ISSN APNYA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BOUNDARY CONDITIONS
CIRCUITS
CYLINDERS
DENSITY
DIAGRAMS
DIFFERENTIAL EQUATIONS
DIFFUSION
ELECTRONS
INTERACTIONS
ION RECOMBINATION
IONS
LOSSES
MATHEMATICS
MICROWAVES
NUMERICALS
PHYSICS
PLASMA
RESONANCE
SPHERES
SURFACES
THERMODYNAMICS
VESSELS
VOLUME