Abstract
The free electron laser instability is investigated for a relativistic annular or solid electron beam propagating through a helical wiggler magnetic field. It is assumed that ?/?b<<l, where ? is Budker's parameter. In this regard, the stability analysis utilizes the vacuum transverse electric and transverse magnetic waveguide modes as a convenient basis to represent the electromagnetic field perturbations. Stability properties are investigated including the important influence of (a) finite beam geometry in the radial direction, (b) positioning of the beam radius relative to the outer conducting wall radius (Rc) and (c) finite wiggler amplitude. All of these effects are shown to have an important influence on detailed stability behavior.
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