Annealing coils of tubing is one thing, a small case neck is a whole 'nother ball game    The biggest issue will be Ohm's Law working against you using a relatively heavy material over a short distance. You will have no literally no resistance and no way to generate impedance in the material; therefore, when the power from the capacitor or a circuit enters the case mouth on opposite sides you have a dead short.  It will be very difficult to find any happy medium between meltdown and exhausting your power supply without making any noticeable heat.  

Probably the easiest way to make the device in question work would be to make a induction coil around a piece of ferrous metal tubing that fits the case mouth relatively closely.  Design it with maybe 400 hz or higher frequency.  That will put some heat on it     


On passing around your garbage can lid capacitor parts, everything is a matter of references in electrical power.  As long as they are isolated, the charge will remain.  We used to work 480 volts hot all the time early in my career.   After a few people publicized their research on 480 volts ionizing the atmosphere in short circuit situations, everyone decided that might not be such a good idea anymore  . Working 120/208/240 volt circuits hot isn't a big deal unless you get grounded. If you are nervous and your hands get wet and sweaty, the risk goes up exponentially    There are people who work in 110,000 volt transmission lines hot.  It is just a matter of isolating the high voltage potential and not making a circuit to another phase or ground.

When I was a 1st year apprentice I drew a static arc about an inch long off a 13,800 volt line.  I decide I didn't like that stuff 

Wayne, Odd that doesn't say AC or DC, but since it looks like they control the power by varying the voltage, it must be AC.

Rebel:       You absolutely can build a case annealer for a Weller soldering gun.  Caliber specific.  Hardest part is finding nuts.  Any heavy copper wire will do.