You actually don't need to actively supply current -- it just keeps going round and round, and you can't "short" it out because the path of least resistance will always be the superconducting winding.
You also can't open a switch to stop the current because it's basically a giant inductor, it really wants to keep the magnetic field (and current) constant. Meaning if you suddenly disconnected the winding, it would arc across the gap (continuously, for quite a while until the stored energy was spent).
So what they do is vent/boil off the liquid helium which is keeping the magnet cold, such that it's no longer superconducting and the current will die off. You can't reclaim the helium, hence you need a fresh refill to chill down the magnet again.
You also can't open a switch to stop the current because it's basically a giant inductor, it really wants to keep the magnetic field (and current) constant. Meaning if you suddenly disconnected the winding, it would arc across the gap (continuously, for quite a while until the stored energy was spent).
So what they do is vent/boil off the liquid helium which is keeping the magnet cold, such that it's no longer superconducting and the current will die off. You can't reclaim the helium, hence you need a fresh refill to chill down the magnet again.