Some Advanced Antimatter and Fusion Rocket Designs

I'm a big fan of The Expanse, both the books by James S.A. Corey and the Amazon Prime TV show based on the books. In the series, an advanced fusion rocket design enables reasonably fast travel throughout the solar system (days between planets, not months). 

Are such rockets possible? In a word, yes, and there are many different designs. For details, see Engine List 3 on the Atomic Rockets site. The content is moderately technical, but not beyond the reading level of anyone who's been reading a lot of what we used to call "hard" science fiction. I would have devoured this stuff when I was 16.

Here's the introduction to the antimatter rockets section.

These are various rocket engines trying to harness the awesome might of antimatter. While the fuel is about as potent as you can get, trying to actually use the stuff has many problems.

Generally your spacecraft has metric tons of propellant, and a few micrograms antimatter fuel. The exceptions are the antimatter beam-core and positron ablative engines.

Nanograms of antimatter fuel are injected into some matter. The energy release is used to heat the propellant, which flies out the exhaust nozzle to create thrust.

Antimatter rockets have analogous exhaust velocity limits to nuclear thermal rockets. The higher the engine heat, the higher the exhaust velocity, which is a good thing. Unfortunately once the heat level reaches the liquefaction point, the engine melts. Which is a bad thing. This limits the maximum exhaust velocity.

And yes, there is a discussion of the rockets used in The Expanse that's worth reading if you enjoy the show. (Sorry, no direct link, but it's about halfway down the lengthy page).