The design electron guns including thermal effects

In order to simulate electron guns at low voltages by numerical calculations it is necessary to consider thermal influence on the electron trajectories, especially for high compression guns. A way is described, where the thermal spread of electron beams is calculated according to Danielson and Rosenfeldt, using a Maxwellian velocity distribution and Lambert's cosine law at the cathode. The correct current is obtained by evaluating the position and the potential of the virtual cathode, as described by Amboss. These implementations to the SLAC electron optics code resulted in good agreement between measurements and calculations. (orig.)