Due to the boredom that this quarantine thing has inflicted me with, I have been doing all sorts of little experiments and projects. One of them happens to be a small attempted carbon arc lamp. The carbon rods I'm using were taken out of some dead heavy duty AA batteries (though I do want to give #2 pencil leads a try if I can get this working) and what I have been trying to use as my power supply is an old computer PSU.  it's rated at 400w which should be way more than enough. So basically, I have the 2 rods connected across the power supply's 12v rail. When I have the 2 rods touching together they get very hot and all seems good until I try pulling them apart even the slightest bit. Once that happens, there is no evidence of any arc being formed. I eventually was able to get a tiny arc to form across the 2 rods, but it was barely producing any light. (It was more a bunch of sparks than an arc). After a long time of re-trying, enough of the rods had evaporated to the point they each had a very sharp tip. Once those are touched together they produce an intense (and hot) white light more of what I'd expect from a carbon arc lamp, but the electrodes are touching and there's no arc being formed. So I determined that my power source isn't ideal from this and most likely just isn't producing enough voltage. After doing a bit of research on carbon arcs, I learned that most of them connect straight to 120v and have some sort of resistor (usually a heating element) as the "ballast". I don't think it would be a good idea to connect this tiny thing to 120v and I have no idea how to calculate what ohm value I would need for the resistance wire.

So basically, I'd like to know if anyone here could give me some pointers on a suitable power supply. I'd prefer it not be resistance based since that seems incredibly inefficient. I'm starting to wonder if something like an HPS choke would work instead. Can anyone here help? I'd really like to get this working. 

Most choke ballasts would work - providig different power levels

Using 2 identical chokes in series is safer, as the carbon arc can drop to very low voltage (or to 0V if the electrodes touch). If a single choke is left across 120V for long enough time it will overheat, and with 2 chokes in series each will see at most 60V. If you are only doing a quick test (under a few min) then this does not matter as the ballast won't heat up so fast

Maybe you'll need higher voltage, in which case you can use autotransformer ballast or step up the voltage with a transformer (can be before or after the ballast, use a ballast suitable for the voltage/current on the side of the transformer where you connect it). I think it would go well with 120V tho

Carbon electrodes without any ionization agent in them, needs DC current, because the gap around the zero cross is making them very unstable.
Plus the arc needs way higher voltage than 12V. 15..20V is just the cathode fall alone (so the arc length being asymptotically zero), then you need few 10's V for the anode column. So nor 12V, nor 24V would work. By the way the inability of voltages below about 20V to form an arc is the main reason, why motor vehicles used just 12V system. It keeps all the switches and fuses very simple, because there is no need for any arc suppression.

So for an arc power supply:
You would need two chokes and a bridge rectifier.
The first choke regulates the current, connected in series with the rectifier AC input.
Rectifier turns it into DC.
The second coil act as a filter, ensuring the arc gets smooth DC current.
You can not use capacitor filter, because capacitors parallel to arcs tend to quench them (in fact connecting a parallel capacitor to e.g. contacts is one of the most widely used arc suppression method, see e.g. the ignition timing contact points).

I would go for 1.5..3A chokes (so 70 or S55 150W HPS ballasts). The DC filter coil could be the highest current type, there is no problem if you are using lower currents.
I wont be worried that much about the choke heat, because I doubt you would be able to run the lam for that long (the battery electrode carbon is designed as porous, so it is consumed a lot by the arc).
In any way, dont forget the thing is generating quite a lot of UV, but as well a lot of CO, O3, NOx and many more toxic stuff when the other components of the battery rod are exposed to the tip heat, so you need perfect ventilation. And dont forget you are dealing with rather open mains voltage...