Radio-frequency defocusing of electron beams

At medium relativistic velocities and high r.f. power levels, the defocusing of an electron beam is mainly due to r.f. radial forces, the space charge usually being negligible. Under these conditions, there is no opposing force preventing an electron from crossing the beam axis or coming close to it. In either case, severe scalloping or defocusing is produced. It is shown that the absence of space charge may be compensated for by allowing some axial magnetic flux to cross the cathode. Also, a partially shielded cathode is essential to avoid defocusing due to the phase oscillations or variation in the beam radius at the injection plane.