meh, 18v cordless drill battery and charger. From harbor freight if you want to go cheap.
I'm guessing you'd want it to pulse the entire time the trigger is pulled.
I know enough to know it's possible with a 555 timer to do the pulsing and a transistor to control the higher voltage/current going to the solenoid.
Too much of a noob to draw you a schematic without spending more time than I'd want on it.