I’ve got a resistor in series with the output and it keeps burning up. Do I need a higher wattage resistor?
The issue is the voltage: Few common resistors will handle 10 kV; most are rated at 100 V or 350 V. Further, if the resistor is wirewound, its inductance may cause a high voltage to appear across it. Even if it's not a wirewound type, the entire 10 kV output of the pulser will appear across the resistor if the load device conducts and the voltage across the load device approaches zero.
A non-high-voltage-rated resistor can burn or crack under those conditions. We recommend HV-rated resistors such as made by Kanthal Globar. Or, you can divide the HV among multiple carbon composition resistors in series.