[pdonis]

> I've always had trouble understanding why the nuclear reactors weren't powering their own pumps.

They do in normal operation, but they can't (obviously) if they're shut down. That's what the backup generators are for, to power the pumps so coolant flow is maintained for decay heat removal if the reactor has to shut down. Newer reactor designs don't require pumps to keep running after shutdown for decay heat removal; but those designs didn't exist when the Fukushima reactor was built.