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Velocity-shear instability of relativistic electron beams: a systematic exploration of the entire(ω, k) space

Published online by Cambridge University Press:  13 March 2009

D. Heristchi  and
S. Cuperman
D. Heristchi
Affiliation:
URA 326, DASOP, Observatoire de Paris, Section de Meudon, 92190 Meudon, France
S. Cuperman
Affiliation:
School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69978, Israel
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Abstract

Using the exact solution methods developed and illustrated previously, we systematically explore (ω, k) space in order to determine all the unstable modes of velocity-shear-produced electromagnetic waves in magnetized, relativistic electron beams (here ω and k are the complex frequency and real wavenumber). This is done for various physical parameters of the problem, namely shear factor and ratio of pipe to beam radii. The solution of the dispersion relation is supplemented by a marginal stability analysis based on the behaviour of the turning points of the purely real-frequency solution ωr, (k): these are bifurcation points where complex solutions originate or terminate.

Type
Research Article
Information
Journal of Plasma Physics , Volume 48 , Issue 3 , December 1992 , pp. 453 - 464
Copyright
Copyright © Cambridge University Press 1992

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References

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