Electronic Resource
[S.l.]
:
American Institute of Physics (AIP)
Physics of Fluids
30 (1987), S. 548-556
ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
The problem of the instability of counterstreaming beams of charged particles is extended to cylindrical and spherical geometries. For well-focused configurations it can be solved by complex contour integral representations. The effects of the convergence of the flow and the density gradient along the trajectories of the particles are considered. The linear spectrum for the cylindrical case is obtained, together with the proof that the solution has finite energy and satisfies two physical matching conditions through the origin. The properties of the special functions which solve this problem are presented. Although the density of the ideally focused model diverges as 1/r at the origin, the growth rate of the instability, for a system of radius R, is given by ω2pR/V02ξn, where V0 is the beam velocity, ξn are the zeros of the Bessel function of zeroth order, and the plasma frequency ωp is evaluated at one-half the average density of particles.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.866352
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