Hi, what formula I can use to determine correct number of turns required for feedback core of Tesla coil. The schematic recommends 50 turns but I would like to calculate it with a formula. I tested my Tesla coil with a simple slayer Exciter circuit and oscilloscope showed resonant frequency of 650kHz. I have attached the schematic. I am using this core for feedback:
https://www.digikey.ca/en/products/...XNjTsYU7hg0s4PnGu99_a2KDMPHkxPbxl_x63vJ1XxbiY

 

To apply a formula you will need to know the minimum current for starting the oscillation and I see no way to know that

 

Actually, it is a transformer setup, but air core instead of iron,So fair approximation will come from the volts per turn input on the driving coil, multiplied by the coupling coefficient, will give the volts per turn of the secondary coil.
If the primary really has 339 volts applied to seven turns, volts per turn will be 339/7, about 48 volts per turn at the peak, except that the capacitor will reduce that a bit. And the coupling will be a lot less than 100%, depending on the size and distance between the coils. Of course the circuit will clamp the voltage to about 5 volts if the diodes do not fail