quadFormer

quadFormer/Ferrite Pole Pig is an 10KVA ferrite transformer built for the sole purpose of drawing arcs. It's actually the second iteration of this transformer; the original arced over after a few runs and died.

Lots of delicious ferrite

The transformer in this case is four transformers in series, each capable of handling ~3KW. The primaries are three turns, and the secondaries are around 150 turns each, so theoretically it will produce 15KV peak when running on 300V primary.
One end of each secondary is tied to each core, and the cores all float roughly 3KV away from the secondary. This makes secondary-to-core insulation a breeze - 3KV can't really do much. Each secondary is wound with 28AWG magnet wire.
The primaries are all isolated from the floating cores. The idea here is that its much easier to insulate a primary than to insulate a secondary (if necessary, the primaries can have insulation on them that can hold off 15KV by sheer brute force!). The downside of this is if there is ever an arcover, the driver is likely to die, and of course, floating cores is death waiting to happen.

My friend Tyler built the driver for this transformer (he also came up with the concept of giant-transformer-for-brute-force-arcs) The driver is an SLR driver using a full-bridge of CM400DU-12F IGBT's running off of 3-phase. To summarize, normally a transformer presents itself as an inductive load (because of the leakage inductance). Driving a purely inductive load is tough on the driver since it will switch at the peaks of the current waveform, leading to tremendous losses and excessive voltage overshoot.

Hard-switched sadness

To compensate for this, we put a capacitor in series with the inductor. If we switch at the resonant frequency of  the tank, the current and voltage will be exactly in phase and the driver will be happy:

Soft and almost happy

Now we see another problem - even completely unloaded, the transformer draws immense amounts of current (the above simulation shows the tank current increasing as the driver adds energy cycle after cycle). This would result in an uncontrolled ringup on the secondary side, not to mention high conduction losses in the driver.
In order to prevent this, we kill the ringing after a half-cycle.

SLR Happiness

In this case we still draw some reactive current. In this case the no-load current is given by V/sqrt(L/C). We can reduce this by increasing L, but magnetics are bulky, so the usual tradeoffs apply (losses vs. component size/power density).

Construction photos:

And here are the equations to make sure the transformer doesn't saturate:

P is the target transformer (peak) power, V_pri is the primary drive voltage, u_r is the relative permeability, B_max is the maximum permitted core field, A is the core cross-sectional area, and l_c is the core magnetic path length. N gives the minimum primary turns, l_g gives the minimum gap size.
These equations assume a square primary voltage waveform.