Influence of electromagnetic effects on stability properties of a high-current betatron accelerator

Stability properties of an intense relativisitic electron ring in a betatron are investigated for eigenfrequency ω near harmonics of the relativistic cyclotron frequency in the applied betatron field, including the important influence of electromagnetic effects. A closed algebraic dispersion relation is obtained for the longitudinal instability, assuming that the electron ring is located inside a perfectly conducting shell which has a large-aspect-ratio. In a parameter regime corresponding to the conventional negative-mass instability, it is found that electromagnetic effects can lead to complete stabilization of the instability provided the beam current is above some critical value