Divergences in the solutions of the plasma screening equation

Journal Article · Sat Nov 01 04:00:00 EST 1997 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.532185· OSTI ID:544815

Das, S K; Janaki, M S; Dasgupta, B ^[1]

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1. Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Calcutta---700064 (India)

Classical kinetic theory using Boltzmann statistics shows that the potential distribution {phi}(r) in the screening cloud surrounding a single test charge at rest within a plasma is governed by a three-dimensional spherically symmetric plasma screening equation {nabla}{sup 2}{phi}({bold r})=A{bold (}exp(+{alpha}{phi}){minus}exp({minus}{beta}{phi}){bold )}, {bold r}{ne}0, where A=4{pi}n{sub 0}{epsilon}, {alpha}={epsilon}/T{sub e}, {beta}={epsilon}/T{sub i}, {epsilon}=electronic charge, T{sub e}=electron temperature, T{sub i}=ion temperature, and n{sub 0}=electron and ion density at large distances from the charge Q. In this paper it is proved rigorously that any nontrivial solution of the screening equation must have the following property: If {phi}(r)=potential at a radial distance r and lim{sub r{r_arrow}{infinity}}{phi}(r)=0, then, for any positive integer n, as r{r_arrow}0 either r{sup n}{phi}{r_arrow}+{infinity} and r{sup n}{phi}{sup {prime}}{r_arrow}{minus}{infinity} or r{sup n}{phi}{r_arrow}{minus}{infinity} and r{sup n}{phi}{sup {prime}}{r_arrow}+{infinity}. {copyright} {ital 1997 American Institute of Physics.}

• OSTI ID: 544815
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 11 Vol. 38; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
BOLTZMANN STATISTICS
CHARGES
DIFFERENTIAL EQUATIONS
ELECTRON DENSITY
ELECTRON TEMPERATURE
ION DENSITY
ION TEMPERATURE
KINETIC EQUATIONS
PLASMA
POTENTIALS
SCREENING