Greetings,

Previously, I designed a 20 kV, 50 mA thermionic Pierce gun using Vaughan's Iterative method. According to the extracted parameters, I designed the geometry of the gun. But according to some technical issues I had to increase the voltage to 100 kV and current to 100 mA (the geometry is still for a 20 kV, 50 mA gun).

According to Vaughan's algorithm, the geometry is designed to operate in space-charge limit (for 20 kV, 50 mA). But since I changed the emission and voltage, I have to know the space-charge limit emission of the new gun. I thought Perveance is a good figure of merit since it only depends on the geometry. Based on the converged Perveance value in CST Studio Suite I realised that for 100 kV diode, the current is 105 mA, not that bad.

However, I increased the temperature of the cathode in the emission settings on purpose to see it the emission increased or remains same. Unfortunately, the emission increased to 300 mA at the exit. If the gun is in space-charge limit, it must remain at 105 mA not 300 mA. I thought maybe this problem occurred because I chose "Child's Law" as the emission method. I changed it to "Langmuir-Fry" but then I got these warnings,

WARNING: The Langmuir-Fry model converged for 0 voltage values. This is insufficient. Emitter Electron will not emit any particles. Check geometry or try to switch to the Child's Law emission model.

WARNING:The emitted current of particle source Electron is zero. Change the emission settings to get a non-zero current.

I am not sure if the geometry is causing the warning. But I have to somehow find the space-charge limit current of the new gun.

UPDATE:

I realised "space-charge" emission model already exists. I read the CST help and it seems this emission model calculates the maximum extractable current out of the cathode according to the existing field in the geometry. Although I thought Vaughan's iterative method already considers space-charge emission, I tried my older settings (20 kV, 50 mA) and it gave 220-225 mA emission (although the solver did not converge, it was still oscillating after 50 iterations).

Question 1: Considering the fact that I need to be in Space-Charge limit, what should I do to reduce the space-charge emission?

Question 2: The solver does not converge very well in space-charge emission model (standard deviation is too much). What should I do to reduce it?

Question 3: Perveance should be same for both cases since the geometry is same; but I am getting different perveances for each simulation (i.e., 20 kV, 50 mA vs. 100 kV, 100 mA). Why?