Theory of Free Electron Laser Instability in a Relativistic Annular Electron Beam.
SCIENCE APPLICATIONS INC BOULDER CO PLASMA RESEARCH INST
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A self-consistent theory of the free electron laser instability is developed for a hollow electron beam propagating through an undulator multiple mirror magnetic field. The stability analysis is carried out within the framework of the linearized Vlasov-Maxwell equations. The dispersion relation describing the free electron laser instability in a hollow relativistic electron beam is obtained for an equilibrium distribution function in which all electrons have same value of transverse energy and the same value of canonical angular momentum, and a Lorentian distribution in axial momentum. It is shown that the influence of finite radial geometry plays a critical role in determining detailed stability behavior. Moreover, the growth rate and bandwidth of the instability can be expressed in terms of Budkers parameter upsilon, instead of the plasma frequency as in the case of a uniform density beam. Furthermore, it is found that free electron laser stability properties exhibit a sensitive dependence on axial momentum spread.
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