Today, Dec. 29, I decided to build the ballast! The best idea I found yet is to build a simple choke with ~0.5mm wire. With a little search, I kinda figure out how to have the good voltage and current, I just don't know how to calculate it.

I know that more turns will give more inductance, and more inductance less current, but I can't find how many turns my choke should have if I want 6A - 7a  Is there a way to calculate it? BTW I don't really mind for the voltage.

TiCoune, 0.5mm wire is a bit too thin for 5-7A. If you want your choke to run for a longer time, you need at least 1mm wire.

The number of turns depends on the cross-section of the core you want to use. You calculate the volts per turn of your winding to have something like 1.3T induction in your core at 60Hz (you live in a 120V land right?). I can probably get more details on this if you want.
Then you calculate if the wire fits on your core: if it does, everything is OK, if you have a lot of space left you can use a thicker wire so it will run cooler.
If it doesn't fit, you need a bigger core or use a thinner wire and decrease the current (see below) to not overload the wire.

When you are done winding your choke, you assemble the core back with an air-gap. Start with something like 0.5mm and then experiment with the gap size to obtain the required current.

First, I didn't measure the wire diameter right, it's indeed 1mm, so apparently it's fine.

I use the primary of an old audio system transformer. At first it gave almost no current. I removed progressively turns of wire. I'm almost done, I just need to remove a few more turns and the arc should start.

I just wonder, the air gap of the transformer is HUGE (almost 1 cm), does it matter?

Last thing, I live in the 120V 60Hz land 

It probably doesn't matter as long as the current is OK, what voltage was the original winding for? If 120 volts, I guess adding a 1cm airgap without removing any turns would already have resulted in tens of amps of current with the winding connected to mains, but I may be wrong 

After almost a dozen of unsuccessful tries (which all leaded to MOT overheat), I have another thing to try.

I'd try to use the primary as an inductor (open secondary) and add a 80uF 250V capacitor in series. If I'm right, this should give me +/- 4A, which is perfect. However I tested it and it gave nothing, not a spark. I measured 53.7V across both carbon rods.

So, I'm wondering if the capacitor actually decreases the current to almost nothing....