Is there a replacement for high voltage capacitors?
It would be possible to implement a "somewhat clunky" version of what you're wanting using digital control, solid-state HV switchgear, and multiple fixed-value HV caps...something similar to the illustration below (incomplete, but I think it conveys the intent).







simulate this circuit &ndash; Schematic created using CircuitLab
Now, the caps themselves aren't a problem, you can find all of them for under $10USD at you favorite mail/internet-order component supplier. HOWEVER solid-state switching of 4KV+ is an WNTIRELY different story! The transistor I labelled in the diagram will cost about $30/each for ordering quantities of 25+ (which you'll need), not to mention the diodes &amp; the control circuitry (did I mention that all the MOSFETS I found had a Vgs MAX of +-20V?...you'll have to match the control signals to your 4KV signal frequency)

With that all said, there will most definitely be some unwanted noise/parasitics in the circuit from all those diodes &amp; MOSFETS, any you may end up having to gate both ends of each cap (for better isolation of "switched off caps")...but it would be 4kV capable, solid-state, and (somewhat) adjustable between 5pF &amp; 1nF+.

(P.S. the 1uH inductor in the illustration is just a placeholder for your fixed inductor in the amplifier tank)