Hi John,
Even Tesla Coils adhere to Conservation of Energy (COE).
In a tuned lossless Tesla coil, Lpri*Cpri = Lsec*Csec. It can also be
shown (from COE) that a "lossless" Tesla Coil will have a
secondary-to-primary voltage ratio that is limited to no more than
sqrt(Lsec/Lpri) or sqrt(Cpri/Csec)). The maximum output voltage versus
the tank capacitor voltage when the gap fires (Vpri) for a lossless coil
is:
Vsec ~ Vpri*sqrt(Lsec/Lpri)
In the case of a 12 kV RMS NST, the peak primary voltage may be
approximated as 1.414*12 or about 17 kV. Under some conditions, it can
be significantly higher due to mains frequency series resonance effects
between the NST's current-limiting leakage inductance and the tank
capacitor.
In order to reach maximum output voltage, the secondary toroid must also
be large enough to prevent corona and streamers from breaking out and
introducing secondary losses. In practice, heavy losses from the primary
spark gap combine with winding and tank cap resistive losses to reduce
the "no-breakout" output voltage to perhaps 75-85% of the theoretical
maximum for typical spark gap Tesla Coils. You can plug in the
measurements for your coil into JavaTC to gain a fairly accurate
estimate of Lpri and Lsec, and then use 17 kV for Vpri to get a fair
estimate of the theoretical maximum output voltage for your system.
However, once streamers form, the output voltage will drop significantly
below the calculated maximum output voltage.
Bert