I think you mis interpret my post. In his "lecture" movies Stan is talking to (who ever is the class) they talk about needing to increase the voltage on the "water cap", the class responds with increasing the input voltage, to which Stan replies, "or increasing the amount of coils here" to which he adds "coils" to the top inductor (between the diode and the cap). Now what I was pointing out was that if this was just an inductor (regardless of how it is wound) adding coils will not increase the output voltage. This only happens with secondaries on transformers. What I am pointing out is if the "inductors" are actually 2 secondaries in paraelle to each other but in series to the main secondary. Nothing overly new to observe. But this changes the calculation for resonance. I am yet to change the calculation but it will have more to do with the interaction between the inductance of the "inductors" vs the colapse time of their magnetic field vs the charge and colapse time of the secondary vs the capacitance (which changes dependant on gas in the cell).
Now all that is one hell of a calculation, also it means that transformers and cells will need to be specifically built as transformers have a range of frequency that they work in, so you will need to know how much capacitance vs inductance you require to build the frequency to operate in. To all of you thinking this sounds easy enough, manipulating the operable frequency ranges of transformers also changes the inductance of the primary and seconary(ies).
Now to you comment about the diode acting as a pump. I am yet to test this but when put in series with caps diodes also maintain voltage, so by placing the diode in between the inductor and secondary the inductor has the voltage of the cap still present accross it. What happens to the secondary of a transformer when there is a voltage across its winding and you saturate the core with a field? does the voltage increase in proportion? Then when the field colapses and the charge tries to stablize how does this effect the primary? i think there is a lot to the diode, more than making a charge pump out of a resonant tank circuit.
Also in tune with this idea, in a lot of Stans drawings he shows that he is recifying the AC and simply using one side of the recifacation. Could you build a reverse circuit? to use the negative side? technically doubling his output from the same work? BUT one step at a time, i am currently trying to source a soft iron square, or even a torid but it is proving difficult where i am.
As per normal please feel free to disect and tell me where i am wrong, be sure to include the reason also