To specify a thermionic cathode the user has a choice of working in terms of either
(1) the cathode temperature, work function and Richardson’s constant, or
(2) the current density and kT.
(The program uses the number in the ‘temperature/current density’ box to recognise which choice is required -greater than 200 gives the temperature choice.)
If the first choice is made then the specified temperature is used to evaluate the emission energy kT and the emitted current density, using the Richardson-Dushman formula. This formula is, in the units used by CPO3DS:
j = 10*R*T^2*exp(-11604W/T)
where R is Richardson’s constant for the material of the cathode, W is the work function in eV and the factor 10 converts the units to those required by the program. Note that the values of R, W and T used need not be the physical values for the cathode -the program uses them only to calculate j.
The above parameters have to be specified twice for cathode iterations, once for the initial conditions and secondly for the final limiting values.
When the current density at a segment of the cathode is clearly space-charge limited or temperature limited then the program distributes the charge density in the cathode region according to the relevant theory.
A more difficult task however is to distribute the charge density when the current is between these two limits. Here there are no theoretical studies known to the authors of CPO. The programs therefore accomplish this empirically -see publication number 60 on the simulation of thermionic cathodes. This gives a smoothly varying current, but the accuracy of the empirical method is not known.
If the program reports that the cathode current is temperature limited when this is not expected, then either the final temperature or the maximum cathode current density have been set too low..