There are a few different types of spark gaps the ones we are going to face on here are the Rotary spark gap, even then there are a couple of different types to chose from, we'll take a look at them and discuss the way I see them working theoretically.
First up is the pin wheel rotary gap, this one I have gone as far as to build a prototype and then it was put on hold while the mats were obtained. In the mean time the next model (to right) was suggested and I feel it more fitting to the application of a Tesla coil is the .
Not to say both do not have their used, the pin wheel having more of a curve waved output as the streamer gets stretched out as before it breaks the later model having more of a square wave, of short sharp pulses, both have their merit in different applications.
Here is a short video of my prototype Pin Wheel
Now lets look at the newer idea brought up by Kent, We are yet to title this one, it consists of a lexan disc with holes cut to on its outer edge to encourage arcing through the disc at timed intervals between 2 electrodes situated either side of the disc as pictured below.