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 -