Sources of velocity spread in electron beams from magnetron injection guns

Calculated trajectories for the electron beam of a known gyrotron have been analysed to determine the relative importance of some of the contributions to velocity spread. For the geometry analysed, space-charge and thermal velocities at the cathode produced only a small part of the calculated velocity spread; much more was generated by the variation of electric field over the length of the cathode surface. The total range of transverse velocity was substantially reduced by adjustment of the shape of one electrode.