A Coherent Nonlinear Theory of a Cyclotron Instability.
NAVAL RESEARCH LAB WASHINGTON D C
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A general nonlinear theory of coherent instabilities is presented and applied to the generation of microwaves by a relativistic beam. The instability is driven both by partial fpartial p perpendicular 7 0 and the relativistic dependence on cyclotron frequency on particle energy. This dependence can cause a bunching in azimuthal angle in such a way as to cause net particle energy to decrease. The nonlinear evolution of this system is studied by writing the orbit equations for a small number of pariticles averaged over the fast time scale. The orbit equations are then integrated numerically. The equation for the mode amplitude is found by converving energy between waves and particles. A simple analytic theory is also presented which successfully predicts the maximum field amplitude and also the behavior of the system for times long after saturation. Author
- Plasma Physics and Magnetohydrodynamics