TY - JOUR

T1 - Exact solution of the dispersion equation for electromagnetic waves in sheared relativistic electron beams

AU - Cuperman, S.

AU - Heristchi, D.

PY - 1992/8

Y1 - 1992/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84971149834&partnerID=8YFLogxK

U2 - 10.1017/S0022377800016366

DO - 10.1017/S0022377800016366

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AN - SCOPUS:84971149834

SN - 0022-3778

VL - 48

SP - 59

EP - 70

JO - Journal of Plasma Physics

JF - Journal of Plasma Physics

IS - 1

ER -