ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
Classical kinetic theory using Boltzmann statistics shows that the potential distribution φ(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 ∇2φ(r)=A(exp(+αφ)−exp(−βφ)), r≠0, where A=4πn0ε, α=ε/Te, β=ε/Ti, ε=electronic charge, Te=electron temperature, Ti=ion temperature, and n0=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 φ(r)=potential at a radial distance r and limr→∞ φ(r)=0, then, for any positive integer n, as r→0 either rnφ→+∞ and rnφ′→−∞ or rnφ→−∞ and rnφ′→+∞. © 1997 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.532185
