This post is a bit time-delayed, but a couple of weeks ago, after spending way too long designing and building my first Tesla coil, I finally put the whole system together for some low-power testing. After switching from wired USB control to XBee wireless, there seems to be no more serial port hang-up at primary currents greater than 40A. So I can control the driving frequency, pulse length, and pulse duty cycle (including ramping) from my laptop. This should prove to be very useful for tuning the coil.
The supply voltage in the video is 30V and the maximum duty cycle is 50%. Driving frequency was 155kHz, which was experimentally determined to be the primary resonant frequency. I think the pulse length was ~15 pulses. Using a long insulated stick with secondary ground connection on the end, I drew small arcs out of the breakout point just to confirm that I was in fact getting high voltage. Nothing has been tuned yet, so the spark is very small. But yay, sparks!
I think the secondary resonant frequency is significantly lower, so I will adjust both the primary coil tap (to increase inductance, add more turns or fractions of a turn) and the driving frequency to attempt to get better amplification. The goal isn't to match the frequencies exactly, but rather to get them separated by the right amount to achieve good energy transfer during one pulse sequence of N cycles. For practical purposes, I can just tweak the tap point and drive frequency to get the best arc length at a given pulse length or maximum drive current.
Once it's tuned well at low power, I will incrementally add more voltage. :P