Honestly, MadHatter's answer is the closest to being correct, although Tesla coils ARE still a type of transformer. Nobody else here seems to understand, however, that Tesla coils are resonant transformers, so they do not operate in the same way as common iron-core transformers. The most important factor required for a Tesla coil to run correctly is that the secondary coil and topload LC circuit have the same resonant frequency as the primary coil/capacitor LC circuit. This is how you get efficient energy transfer from the primary circuit to the secondary circuit. Putting too many turns on the secondary would add too much inductance (and self-capacitance) that the secondary circuit will be significantly out-of-tune with the primary circuit. You will get very little energy transfer between the two resonant circuits, causing there to be little to no output. You will also run into the issues MadHatter suggested (the waveform will be discontinuous due to current being induced in the wrong portions of the coil). Remove all but one layer of wire and just leave it as-is. Then make sure that the secondary resonates at the same frequency as the primary. You can use the following formula to calculate resonant frequency:
where 'f' is the resonant frequency, 'L' is the inductance of the coil, and 'C' is the capacitance of the system (the tank capacitor in the primary or the topload on the secondary plus the coil's self-capacitance).
Do the calculation for both the primary LC circuit and then the secondary LC circuit and make sure they match. Otherwise your Tesla coil won't work at all.
If they don't match, you can "tune" the Tesla coil using different methods:
If the primary resonant frequency is too low, do one or both of the following:
- "Tap" the primary coil at different points to decrease inductance of the primary coil (shorten the primary)
- Decrease the capacitance of the primary tank capacitor
If the primary resonant frequency is too high, do the opposite.
If the secondary resonant frequency is too low, do one or both of the following:
- Decrease the length of the secondary coil to reduce the inductance of the secondary coil
- Reduce the size of the topload to decrease its capacitance
If the secondary resonant frequency is too high, do the opposite.
You have to use math to determine which of the above to use, and how much to adjust each one.