Space-charge waves on relativistic elliptic electron beams

This paper reports on results of a small-signal analysis of space-charge waves on a relativistic elliptic electron beam immersed in a strong axial magnet field in a perfectly conducting tunnel with an elliptic cross section. A dispersion relation for the space-charge waves is derived analytically. A computer code, elliptic-beam small signal, is developed and used in studies of the dispersion characteristics of fast- and slow-space-charge waves on relativistic elliptic electron beams. Applications of the theory in elliptic-beam klystrons are discussed.