So, I need a ballast for my arc light. A carbon arc can be quite unstable, so I would need a HX or CWA ballast to have a properly running arc. I was told that such ballasts need special core shapes, which sounds logical. Is there a way to calculate the precise size required?

Thanks

Hi,
you can use a leak transformer (for example a welding transformer with adjustable current) for your carbon arc lamp.
Of course you need a voltmeter and a ampere meter to control the operating voltage and current 

I would love to have a welder LOL, both for its intended purpose and for testing purposes, but I unfortunately don't own one...

Also, as I design an arc light fixture, I rather need something that can be embedded into the fixture. 

Or a big variable transformer and a ballast in series, what is the rated power of your lamp?
And is it an AC or DC carbon arc lamp?

I performed some VERY SUCCESSFUL tests with DC arcs, however I'd prefer to use AC (both rods would burn at the same speed). My goal is to run a 800W arc (give or take 100W).

I also grabbed a couple of microwave ovens today, so I now have 3 MOTs. I could maybe convert one of them into a ballast...

you can convert some MOTs to high current transformers, too, you only have to wind a new secondary with a few windings and connect some in series (the output voltage should amount 40 - 50V)

Edit: nice video of a carbon arc lamp http://www.youtube.com/watch?v=u8e_u_xqN30

Here's what I just did:

I opened two identical MOTs, removed the secondary on the first and replace it by the primary of the second MOT. I use the steel "spacers" of both MOTs to fill the gap. It's basically a transformer with two identical coils. If I'm right, the spacers (which are magnetic shunts right?) would raise the inductance, and then lower the current. That should give me ~120V and ~8A. I was about testing it, but a thunderstorm interrupted me, so I must wait...

I could also add a cap and / or mount the transformer as an autotransformer. I have four 0.86uF 2000V caps and one 80uF 250V cap. I wonder if I could use one or several of them to get a more stable discharge? That would also raise the power factor.

you can also use a big variac (you can get them sometimes cheap on ebay) in series with your convertet "ballast-MOT" and add a voltmeter and an ampere meter to control the current and voltage 

I would love to have a welder LOL, both for its intended purpose and for testing purposes, but I unfortunately don't own one...

Also, as I design an arc light fixture, I rather need something that can be embedded into the fixture. 

I don't think you can do that with a line frequency inductor.  You'll have to use an electronic ballast.

Given the same capacity, lower the frequency, the bigger and heavier it is.  This is why 400 Hz power is used on planes.