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 have to absorb the energy to throw it out the back, or use a laser.
You need a hydrogen 'scoop' and fusion. If you can accelerate to 0.01c, you can collect enough hydrogen for 1000 MW fusion power from 32 km2 (6 km diameter) scoop area. Faster you fly, more you get. You can accelerate until interstellar particles start to do real damage.
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.
Theoretically it works, yes, though not nearly as well as initially thought. The engineering and the required materials, however, are still questionable and way beyond our current understanding of physics and material science.
It's a similar story for solar sails, unfortunately, though progress is being made in that area. Personally, I think that's the only realistic way of interstellar travel given our current knowledge of physics and engineering.
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 have to absorb the energy to throw it out the back, or use a laser.