Abstract
The resistive wall stability of an electron beam is studied, and application of the theory to the modified betatron accelerator is considered. Only flute-like perturbations are analyzed (n=0, l≥1, where n and l are the toroidal and poloidal mode numbers, respectively). Included in the analysis are the effects of relativistic velocities, equilibrium and perturbed self-electromagnetic fields, and resonant particle effects due to density and velocity profiles. The principal results are (1) l≥2 modes are much more difficult to stabilize than is the l=1 mode; (2) the velocity gradient along the beam can provide an important stabilizing mechanism; (3) the stabilizing effect of the density gradient is reduced by relativistic effects; and (4) magnetic perturbations can be important even for nonrelativistic beams.
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