Well, you have to start somewhere. In this case I had to decide on a power level, and the ammo.. and just started calculating from there.

1/2" ball bearing ammo

160J

Some caps scavenged from dumpster: 560uF 450V

Internet sourced efficiency expectation: 6%

24 stages. 33" long barrel. 6" tall. It will be bulky but it's shaping up to be possible.. I'm not ready to share my spreadsheet of massive calculations but at this point I've got it spilling out inductance goals for each coil stage.

Where it gets interesting is the power system. Higher voltage will pack more punch, so I'm shooting for 900V. A custom boost converter is in order to step up the battery voltage to and adjustable output of up to 900V, and it's going to be spending the whole time in current limit pumping up a purely capacitive load. 

The battery pack I have lined up are some LiPO4 cells strung up to 48V. 10A continuous, 100A for less than 30s. So right there I'm looking at 480W continuous 4800W peak. So, obviously we won't be using a flyback out of a disposable camera. This will have some meat to it.

I plan on handling those batteries with kid gloves, it will have it's own separate power handler for current limit, undervoltage limit/shutdown, thermal limit/shutdown, and charging. 

Charging will come from the AC when it's plugged in. The AC will be limited to 1500W/15A, so again another current limiting. Where they all tie in will be a sort of soft buss where each system is just putting in what it can while watching it's own back.