We recently improved features in Trak and OmniTrak for adding angular divergence to beams extracted in the space-charge, field-emission and plasma-emission modes. If you specify a source temperature Ts, the program introduces an angular divergence based on a Maxwell distribution of transverse energy. At first glance, one would be tempted to associate the source temperature with the physical temperature of the cathode, Tc. When a customer reported achieving better focal spots than the code prediction, I thought in more detail about the relationship between Ts and Tc.
If the space-charge-limited current density exactly equals the source flux, then every electron emitted from the cathode is extracted. In this case, the source temperature should equal the cathode temperature, Ts = Tc. On the other hand, to achieve uniformity in the presence of cathode surface variations, practical electron guns usually operate with the source flux greater than the space-charge-limited flux. In this mode, the space-charge sheath must provide some degree of electron selection. The electrons that can pass through the surface potential barrier are those with the highest longitudinal energy. On the average, these electrons have lower transverse energy. The degree of selection depends on how much the source flux exceeds the space-charge-limited flux.
The implication is that you should use caution in applying source temperature and recognize that the condition Tc = Ts gives an upper limit on the extracted beam emittance.
Use these links if you want more information about Trak and OmniTrak: http://www.fieldp.com/trak.html and http://www.fieldp.com/omnitrak.html.