But what about what I observed in the circuit simulator? There seemed to be bugger all current through the primary coil if the frequency of the square wave input to the FET gates did not at least roughly match the indicated frequency, according to the equation, of those capacitors combined with the primary coil/inductor?
Surely if they do not roughly match the FETs will be fighting against the LC circuit formed by the primary coil and two capacitors?
I'm trying a simple simulation. It displays the same thing you state, several Amperes through the primary during one half of a cycle. These are ringing oscillations.
I doubt my values match those in the schematic. The transformer has several unknown specs.
This may be the chief resonance. It might just require slightly different values, and then the entire circuit might resonate at this frequency.
I see this scenario:
(a) On powerup, the 555 generates pulses, just to start things going.
(b) This induces ringing in the transformer.
(c) The ringing becomes the dominant frequency.
(d) The secondary winding radiates EM at this frequency.
(e) The antenna picks it up and feeds it to the amplifier. (The 555 pulses are overridden.)
(f) The mosfets are driven continually at the resonant frequency.
I guess this means you can choose any reasonable value for the capacitors.
I have no experience with tesla coils. I don't know if the secondary winding has a different frequency that it tries to resonate at. Etc.