Use of output inductor for high-voltage supply circuit
If you don't have an output capacitor, then you will see the switching step voltage at the output. So I would assume the output capacitor is needed.

Now let's see what happens when you add a simple series inductor to the output. When arcing occurs, there will be a sudden drop of load resistance. The intended purpose of the output inductor is to limit/retard the current increase. Consequently the output voltage drops significantly. So now you have a big voltage across the inductor and the voltage ramps up the current through the inductor. Then the arcing stop and the load resistance returns to normal. But the inductor has an excess of current, so the output voltage rises above the nominal voltage. With an increase of voltage and the remnant of an ionized path, it seems highly likely an arc would occur again. So once the circuit arcs, the circuit may become an oscillating arc generating machine.

I hope the following diagram can give you some ideas. Start with a current sense resistor (R sense) at V-/Gnd. The Control block can be simple or complex, for example you may use a high pass filter to detect arcing.







simulate this circuit &ndash; Schematic created using CircuitLab

Additional notes after your comment:

Actually, looking back at this, I want to modify some of the comments. The converter itself is unlikely to be able to hold up the voltage during an arc and it will take time to charge back up again, so an inductor combined with a diode circuit in parallel and reversed to clamp the flyback voltage and discharge the excess current can be useful for your purpose. Both the inductor and the diode would need to withstand the full output voltage.

In my diagram, the current limit block must be able to withstand full output voltage. At 8KV, I am not certain how to implement that. Perhaps a cascade of many FET can give a reliable solution, but it is not going to be simple.