Effects of a finite axial magnetic field on the beam loading on a cavity

Summary form only given. The effect of a finite axial magnetic field on the beam loading of a cavity is evaluated. The calculation extends Branch´s classic paper on ballistic bunching in that both the conductive and reactive components of the beam-loaded admittance are computed, and for general values of axial magnetic field. Also included is a comparison of the analytic formulation with the 2-dimensional particle-in-cell code, Magic 2D, for a klystron cavity operating at 5.087 GHz. This work suggests that the finite axial magnetic field used in linear beam tubes (typically exceeding 1.5 times the Brillouin field) would only modify the beam-loaded conductance by about 5 percent, and the beam-loaded susceptance by about 15 percent from that computed under the assumption of an infinite axial magnetic field. The analytic formulation yields beam-loaded conductance and admittance within 4 percent MAGIC 2D simulations on this model.