Divergences in the solutions of the plasma screening equation
- 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, Vol. 38, Issue 11; Other Information: PBD: Nov 1997
- Country of Publication:
- United States
- Language:
- English
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