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

S. Cuperman, D. Heristchi

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)59-70
Number of pages12
JournalJournal of Plasma Physics
Volume48
Issue number1
DOIs
StatePublished - Aug 1992
Externally publishedYes

Fingerprint

Dive into the research topics of 'Exact solution of the dispersion equation for electromagnetic waves in sheared relativistic electron beams'. Together they form a unique fingerprint.

Cite this