I already have some small HV transformers, which I have modified to have less windings that can handle higher current (probably up to 10 amps, at least for a few seconds). I need to find out the approximate inductance and turn ratio.

For power I will probably get or make a 3s 18650 pack. While it may make it more expensive than commercial options, I could also use it for other projects.

My plan to figure out the inductance is to have an arduino drive a mosfet at 10s of kHz and 50% duty cycle. It will switch 10V or so and the primary and a 20 ohm resistor will be in series with it. I will measure the voltage across each of them and do calculations. I will then increase the frequency and drop the voltage to get .1-.2V (peak) across the primary. Then I'll measure the voltage across the secondary with my meter. It should give me the aproximate turn ratio with it being very lightly loaded. I will then modify it to have a turn ratio of about 1500.

So here is the main issue here. I want a fairly constant power of 30-40W a voltage range of 13-19kV. But P=V^2 / R. So with a constant impedance/resistance, the power is half as much at 9V than it is at 12.6V (the range of a 3s 18650 pack). 9^2 / 12.6^2 = .51! This is a graph of the current under a constant resistive load. This one is power, and this is current for constant power.

So I think I need to go with a circuit that combines a VCO and limits the input current by increasing the frequency when it gets too high. This prevents it from delivering dangerous amounts of current when a human is on the output. There would either be a center tap and two fets or a full H-bridge. The only issue is I do not really know how to go about designing such a circuit. I know you would need probably a shunt resistor and some comparators and passives, but do not know too much more. I could really use help making such a circuit. And do people think adding the current limiting feature is excessive, or that another circuit would be better here?