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I did TIG welding myself but I am not sure what the characteristics are with a tungsten electrodes, it could stick on the batteries with high temperature and the arc, brass or copper on the other hand wont melt in to another metal, that's why welders use copper plate if they weld two pieces and things get to hot on a metal work table or in a narrow spaces.
But since you are the real mechanist, I stand corrected if I am wrong
(so... covered my arse if i am wrong)[/quote]
Copper melts to other metals as well, they even use copper plate/shim for serious high current battery packs. Obviously spot welding copper is royal pain, but doable with right equipment.
I was less than satisfied with pure copper electrodes, too soft and tends to stick to workpiece. Copper-molybdenium and copper-tungsten should be better alternatives but availability is not that great..
Next I was planning to try 4mm pure tungsten TIG electrodes.
Another way around capacitor problem is to use 350v caps coupled trough transformer. Much easier to get required energy this way than with 12v caps. 350 to 450 volt inverter electrolytics are much easier to find and biggest ones put out serious punch. Also easier for your thyristor/igbt.
Transformer coupling also has its problems, like redesign the windings for short duty pulse and if you use toroid transformer you probably have take care of the core (pre-)demagnetizing before each shot.