Earlier quoted context omitted.
It isn't possible without a magic reactionless drive; it might even require a zero-energy drive since the kinetic energy is huge and needs to come from somewhere. The rocket equation kills you. A reasonable fusion rocket would require an enormous (like an entire planet worth) to continuously accelerate to relativistic speeds. Antimatter drives are the only option and still require large amounts of reaction mass since…
Well the obvious solution would be to figure out a mechanism to capture the particles that bombard your ship and figure out a way to turn those particles into thrust so you don’t need to take a bunch of fuel with you, which I get it, is another hard problem to solve, but maybe not impossible. We have done some incredible things before.
[1] https://www.sciencedirect.com/science/article/pii/S009457652...