Electrical – Tesla Coil/Slayer Exciter : Aluminium or Copper wire

The Slayer oscillator is actually a crude form of a resonant power supply. It runs at a resonant frequency. The resonant frequency is determined by L and C. Switching losses are reduced so that a BJT will run cool at sensible frequencies. You are stepping up so this makes L big and lots of turns make C significant. R has nothing to do with frequency. R is just for starting.

The transformer does have parasitic capacitance to ground. That is why C is drawn the way it is. If there was no parasitic capacitance to ground the oscillator would not work because its feedback path would be broken. Your diode does get reverse biased because AC current is flowing. I have used a red LED in place of D1 to indicate operation and give higher negative voltage on the transistor base to improve turnoff and possibly switching losses.

On your circuit, making R too small will actually make starting unreliable. You can ballpark R to give a small current that gives reasonable beta for Q. If your step-up ratio is too high, the oscillator won't start because the total gain would be less than unity. Make the step-up ratio N 10 or less so the oscillator won't need an exotic or nonexistent transistor.

Slayer exciter circuits are by design very inefficient. It is nothing more then a simple resonant circuit operating in a lossy manner. To get bigger sparks you need something more like a Tesla coil operating as a class D amplifier. Adding more turns will add resistance and reduce the resonant Q factor of the circuit, eventually giving you even less voltage gains for exponentially increasing amounts of power.

I would suggest you spend some time reading up on Tesla coils. Basically you are switching FETs or IGBTs on and off, not partially driving them in a class A style like the slayer exciter does.

A small half bridge Tesla coil can get you 1-2 ft arks and cost under $50 to build if you keep it simple. That being said, if you are not aware of the dangers of working with high voltages, building a Tesla coil is a good way to toast yourself.