You don't need to "capture" asteroids. You mine them in place and build heavy industry and everything you need in-situ. It's a hell of a lot easier to launch a new vessel off an asteroid than Earth. For some reason, people always think we'll be bringing these resources back to the surface of the Earth. That's wasteful, why do we want to throw them back into a gravity well?

We don't even need fancy fusion tech or anything for this to work, regular fission reactors can power things just fine. And the bonus is, you don't have to worry about where you put the waste. Just designate another asteroid in a clear orbit where it's most likely to not hit anything else for the next ten thousand years as a dumping ground, and mark it on the maps.