Ebay has some nice 1F 5v caps for pretty cheap I think 3 for 5$ I got
you could put them in series until you get the proper voltage rating and then use extra space to put them in parrallel
say 3 in series to get 15v then with say a 1 ohm solenoid resistance you get 15 amps max, 5 amps a sec later, 2 amps another sec later then less and less
Less resistance will make it more amps for a shorter time, more resitance means less amps for a longer time
and these I saw are pretty small you could probably get 12 on the space of an arduino, so if you added in series and charged them with 60 volts you can get 60 amps thru your 1 ohm resistance, which I would suggest not being around when that happens lol