I guess if you get perfect very high vacuum so no ionizable media inside, than if you could release electrons on one side i can't see why you can't get the electrons somewhere else out of the circuit other than the high voltage positive plate that accelerated the electrons.
If the electrons are released at T=0 than at T= 1 high voltage is applied, the electrons takes a time T=x to arrive at the other electrode.
If the electrons are allowed to hit the positive electrode, they will give up their charge and result as a load to the high voltage source.
If the high voltage source is disconnected or interrupted the electrons will hit the plate and make it become negative relative to earth and as such this electrons can be discharged back to ground where they came from initially from the filament circuit which were grounded.
If more electrons make thru the gap and they are such more as to reverse the charge of the capacitor than its not over unity. but if there is a gain in voltage than the system must have absorbed vacuum energy from the electric fields!
For example for a stream of water we can deviate it with an electric field, and change the place it will hit the ground. it didn't really done any work since the definition of the work is that if he is attracted but than lose the attraction at another point it makes counter work too.
Think of a capacitor, it has vaccum dielectric and one of the plates is irradiated with light and ger electrons released its also a glowing hot plate grounded so the electrons come out this way,, , when the amps are restricted to flow to the positive plate the gain in energy might becomes available at the amp restricting device to be discharged.. Maybe??? hehe
I think is not impossible to have such great amounts of electrons available.
Think of nuclear waste? It could generate more power than all the grids are providing together today for many decades, if what we are talking about really makes sense.
Paul Brown dedicated his life to this and got killed as it seems he used resonance and electric fields to add energy to ions inside those nuclear batteries.
I don't know wave equations ... yet. but it seems to me that the epg still a mistery to me.