The width of the the negative HV pulse is determined by the time constant of the series capacitor and the load resistance, provided that the width of the ON drive to the MOSFET is long enough. Otherwise, not all the energy in the capacitor is delivered to the load.

The time constant of the capacitor and the resistor from MOSFET drain to the ~300Vdc determines the recharge time and therefore the maximum PRF.

For an cheap HV supply without winding a special transformer, I'd TRY a small transformer (say) 240V mains to 12-0-12V (24V centretapped) then use a couple of power transistors to turn it into an oscillator. From a bridge rectifier and smoothing on the 240V winding, which is now NOT connected to mains but acts as an output, I'd expect to get the 300Vdc (the actual voltage would depend on the DC input voltage to the drive transistors).

TAKE CARE, EVEN THOUGH IT COMES FROM A LOW DC VOLTAGE SOURCE, YOU COULD STILL GET A NASTY SHOCK.

You may also find HV sources on the internet (for flash tubes???)