How to control High Voltage Power Supply (HVPS) voltage output?
What's the max wattage expected on your load?  Or, the max current?   Can you tolerate some 120Hz hum, or do you require a cleaner signal?

Also, why not just find an old used controlled-hvps, with 0-5V or 0-10V ctrl voltage?  Spellman CZE1000 or X3000 are 10watt, 30KV, max 300uA output.  They use a 24V 1.5amp DC supply.  They're often $100 on eBay, sometimes much lower.  Actually these two are those sealed boxes found inside the expensive rack-mount Spellman supplies, the ones with the big panel meters.  They can be controlled with DC signals, or just use a couple of 10K pots (to set Vout and current-limit.)

Also, for 30watt and below, you can find little HV modules on eBay, search Emco and Ultravolt.

If you must build your own from scratch ...typical modern supplies control the HV by controlling the input to the step-up section (control the 120VAC with a dimmer, or adjust the regulated DC that runs the HV.)   For low noise they'll use a power-oscillator driving a high-freq transformer and diode/capacitor voltage multiplier.  A high-ohms divider (100M or 1000M resistor) measures the output and provides a feedback signal for your regulator.

But for old-school low-watts supplies, the usual method was "shunt regulator" using a vacuum-tube triode to partially short out the HV output!  Sorta like an adjustable 10KV zener diode.  These gave a clean output without needing a (noisy) high-freq oscillator section.

For more than 30watts or so, projects with funding would instead use a "plasma generator," a high-power RF source at 13.56MHz or 27.2MHz.  These can create discharge without chamber electrodes, just a tuned coil outside the glass envelope.   Lots of items on eBay from ENI Co., search: ENI plasma, or ENI rf