Abstract: The EGUN code has been used to design electron optics system of a C-band multi-beam klystron.A gun has been designed with nearly uniform beam density.The trajectories have no intersections and uniformly distributed in the collector.Then the gun is used to study the change of the trajectories while varying magnetic field on the cathode surface,the whole area and the uniform part.With the increase of the magnetic field on the cathode surface,wave amplitude and equilibrium radius of the electron beam increase;while the factor of the whole magnetic field increases,wave amplitude decreases and frequency increases.When uniform part of the working area has small fluctuations,magnetic field increase then wave amplitude decreases,magnetic field dcreases then wave amplitude increnses.