Your schematic, although electrically correct, will be very expensive to build.
http://hvstuff.com/3a-50kv-100ns-high-v ... -frequencyThe link shows a 50 KV diode of which you would need four for the full-wave bridge. Each one is approximately $35.00 USD. I have no idea off the top of my head as to the cost of the capacitor, however, the schematic you have presented could be a problem for the inrush on the capacitor of the output of the full-wave bridge will be a very high inrush. You will need something to compensate between the bridge and the capacitor so as to drop voltage and prevent the diodes from exceeding their current capacity. Further, this can be done with a Load Resistor in parallel with the HV Capacitor to aid in regulation but the need for a series resistor is still required.
The Spark Gap regulator is crude and can be effective, however, the only time the Gravitor will have any displacement (thrust) is when the initial inrush occurs. Otherwise, it will be nothing more than a charged capacitor after the inrush. The design of the Power Supply should be such that the components are valued in excess of the peak input voltage to the bridge by at least ten to twenty percent. The capacitor in your schematic will charge to the peak just as the Gravitor will.
As to the spark gap, if you adjust it for the spark to jump at .637 of the peak voltage, than it will discharge at twice the frequency of the input to the full-wave bridge. This will effectively give you a pulsed output, crude but pulsed output. Essentially, you working off the ripple frequency of the power supply. It will be very dramatic to watch.
Mikado