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Exact solution of the dispersion equation for electromagnetic waves in sheared relativistic electron beams

Published online by Cambridge University Press:  13 March 2009

S. Cuperman  and
D. Heristchi
S. Cuperman
Affiliation:
URA 326, DASOP, Observatoire de Paris, Section de Meudon, 92190, Meudon, France
D. Heristchi
Affiliation:
URA 326, DASOP, Observatoire de Paris, Section de Meudon, 92190, Meudon, France
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Abstract

The transcendental dispersion equation for electromagnetic waves propagating in the slow mode in sheared non-neutral relativistic cylindrical electron beams in strong applied magnetic fields is solved exactly. Thus, rather than truncated power series for the modified Bessel functions involved, use is made of modern algorithms able to compute such functions up to 18-digit accuracy. Consequently, new and significantly more important branches of the velocity shear instability are found. When the shear-factor and/or the geometrical parameter a/b (pipe-to-beam radius ratio) are increased, the unstable branches join, and the higher-frequency, larger-wavenumber modes are significantly enhanced. Since analytical solutions of the exact dispersion relation cannot be obtained, it is suggested that in all similar cases the methods proposed and demonstrated here should be used to carry out a rigorous stability analysis.

Type
Research Article
Information
Journal of Plasma Physics , Volume 48 , Issue 1 , August 1992 , pp. 59 - 70
Copyright
Copyright © Cambridge University Press 1992

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References

REFERENCES

Amos, D. R. 1986 ACM Trans. Math. Software 12, 265.CrossRefGoogle Scholar
Cuperman, S. & Zoler, D. 1989 J. Plasma Phys. 42, 407.CrossRefGoogle Scholar
Davidson, R. C., Tsang, K. T. & Uhms, H. S. 1988 Phys. Fluids 31, 1727.CrossRefGoogle Scholar
Harrison, E. R. 1963 Proc. Phys. Soc. 82, 689.CrossRefGoogle Scholar
Levy, R. H. 1965 Phys. Fluids 8, 1288.CrossRefGoogle Scholar
Thompson, I. J. & Barnett, A. R. 1986 J. Comp. Phys. 64, 490.CrossRefGoogle Scholar
Zhelyazkov, I.I. 1970 Soviet Phys. Tech. Phys. 10, 1644.Google Scholar
Zoler, D. & Cuperman, S. 1991 J. Plasma Phys. 45, 191.CrossRefGoogle Scholar