Mmmm! Had not thought of that angle.
But at most likely signficantly less than a kV of over voltage, it would have to be a very tiny spark gap. I doubt that I could acheive the required prescision with a couple of bolts similar to what you would use with a tesla coil.
How would you suggest I produce such a spark gap? Are there specific components available with spark gaps of specific voltage ratings?
Just two wires with the ends barely separated. It might fire at 100 or 200V. Just for the sake of experimentation to protect other components. There seems to be a small selection of protective devices rated to absorb the spikes.
But absorbing the spikes absorbs energy at the moment when you need it to create a spark between the ladder wires.
I have not built a Jacob's ladder so I don't know exactly what forces are at work. What I have noticed in animated simulations of a flyback converter, is that a load should be on the secondary at all times.
The reason is because a major portion of the current flows (or wants to flow) in the secondary circuit during the switch-Off cycle. This is counter to what we might expect. But that is when the flux field is collapsing.
It's the identical principle as in an old-fashioned ignition system. The spark plug fires when the points open, not when they close. (It seemed incredible to me when I learned about it.)
So I believe it is during times when there is **no** current flowing across your ladder wires (in other words when there is no load), that the high voltage spikes (and heat) are generated in your primary circuit.
The problem might be reduced by moving the lower ends of your ladder wires closer together, so the spark can start to jump more easily, and give the primary an outlet for all that energy.
You may even be able to add a second Jacob's ladder.