Welder High Frequency (HF) Circuit Design - High Voltage >10kV

You can see my progress so far in the picture at the end of the post.

It is currently producing some small 3-4mm sparks from the secondary. Does anyone know how to find the resonance frequency of the secondary to get them a bit longer?

The way this works is very similar to a Tesla coil. The capacitor(s) discharge into the primary through a spark gap, just like in a Tesla coil. The secondary is ideally solid bar or heavy wire to carry the welding current. Around 1.5 - 4kV in the primary is stepped up through transformer action, as well as resonance to around 10 - 15kV. This is superimposed onto the welding current to produce a more stable arc for TIG welding, get the arc started without contaminating the tungsten/workpiece, etc.

The ferrite core is from a large television flyback transformer. It's currently being held together with some gorilla glue, so there is zero gap. Some of the mass produced units use a toroid. Others are air core. I was thinking that with the ferrite I could lower the frequency and push more current through.

So any thoughts? It's a simple circuit, but I can produce a schematic if that would help.

The HF pulse needs to go into the workpiece and not back into
the source. So you will want a narrow pulse and a lot of source
inductance. I would check that your DC source indeed has that
kind of inductance.

You might prefer to deliver the HF to the torch directly so that
the welding cable inductance is in your favor rather than against.

Look to your flyback transistor turnoff time and snubber circuit
as ways to improve the output pulse.

An automotive ignition coil will likely produce a hotter spark,
more easily (perhaps too much kick, I've been knocked cold
by playing with them).

You do not need a lot of current in the HF, you only need to
ionize the gap so the real current can do the work. You want
maybe 8 zaps per sine wave cycle (if you're working with sine
wave AC power, which is not so popular anymore) or you could
sync the thing to the edges of the square-wave AC if it's an
inverter style deal because you only need to initiate when the
arc has snuffed at zero-crossings.

Your TIG working distance is only a couple of mm anyway so
what you're getting already might do (presuming it doesn't
get lost when hooked to the welder output).

Thanks. Maybe I already have what I need.