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

1992 ◽  
Vol 48 (3) ◽  
pp. 453-464
Author(s):  
D. Heristchi ◽  
S. Cuperman
Keyword(s):  
Relativistic Electron ◽  
Electromagnetic Waves ◽  
Electron Beams ◽  
Velocity Shear ◽  
Shear Instability ◽  
Marginal Stability ◽  
Physical Parameters ◽  
Complex Frequency ◽  
Relativistic Electron Beams ◽  
Solution Methods

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.

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

1992 ◽  
Vol 48 (1) ◽  
pp. 59-70 ◽  
Author(s):  
S. Cuperman ◽  
D. Heristchi
Keyword(s):  
Dispersion Equation ◽  
Electromagnetic Waves ◽  
Bessel Functions ◽  
Electron Beams ◽  
Velocity Shear ◽  
Shear Instability ◽  
Beam Radius ◽  
Slow Mode ◽  
Modified Bessel Functions ◽  
Relativistic Electron Beams

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.

The Features of the Modified Treatment of the Low-Carbon Steels by the High-Current Relativistic Electron Beams

2017 ◽  
Vol 9 (4) ◽  
pp. 04013-1-04013-6
Author(s):  
S. V. Bytkin ◽  
◽  
О. О. Isaenko ◽  
S. E. Donets ◽  
V. F. Кlepikov ◽  
...  
Keyword(s):  
Relativistic Electron ◽  
Electron Beams ◽  
Carbon Steels ◽  
High Current ◽  
Low Carbon ◽  
Low Carbon Steels ◽  
Relativistic Electron Beams
Sign in / Sign up

Export Citation Format

Share Document