Two-stream instability in convergent geometry

Journal Article · Sun Feb 01 04:00:00 EST 1987 · Phys. Fluids; (United States)

DOI:https://doi.org/10.1063/1.866352· OSTI ID:6920614

Gratton, F T; Gnavi, G

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 ..omega../sup 2//sub p/R/V/sub 0/2xi/sub n/, where V/sub 0/ is the beam velocity, xi/sub n/ are the zeros of the Bessel function of zeroth order, and the plasma frequency ..omega../sub p/ is evaluated at one-half the average density of particles.

• Research Organization: Programa de Investigaciones Teoricas y Experimentales en Fisica del Plasma, CONICET and Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
• OSTI ID: 6920614
• Journal Information: Phys. Fluids; (United States), Journal Name: Phys. Fluids; (United States) Vol. 30:2; ISSN PFLDA
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
700107* -- Fusion Energy-- Plasma Research-- Instabilities
BEAM BUNCHING
BEAM DYNAMICS
BEAM-PLASMA SYSTEMS
CHARGED PARTICLES
CONFIGURATION
CYLINDRICAL CONFIGURATION
INSTABILITY
PLASMA INSTABILITY
PLASMA MICROINSTABILITIES
RADIATION STREAMING
SPHERICAL CONFIGURATION
TRAJECTORIES
TWO-STREAM INSTABILITY