Given the difficulty and expense of building a reactor, I wonder if it would be cheaper to just start firing it into outer space. I'm guessing we could engineer a nigh indestructible container capable of surviving rocket malfunctions [without leaking]. How many Falcon 9 launches would it take...
It's the same problem as doing nuclear power in space: if the rocket blows up during the launch, or even fails normally and just falls somewhere, it would be VERY VERY bad.