One thing I've wondered about with respect to bustard ramjets: they work by collecting hydrogen from the quite rarified interstellar medium and fusing it for energy release.

Collection of hydrogen for fusion means that collected hydrogen atoms need to be in close proximity with one another for fusion to occur.

This in turn means that interstellar hydrogen, essentially at rest with respect to the ramjet-equipped spaceship ploughing through the medium, has to be accelerated pretty much from the rest frame to the velocity of the ship as part of the collection process. This acceleration of hydrogen to ship velocity requires energy.

At what ship velocity would more energy be expended collecting hydrogen than it would yield in ship reference frame when fused? This would seem to be an upper limit for Bussard-type propulsion systems.

It's the same with jet engines, for similar reasons. (Although in practice your maximum speed is largely dictated by "melting the engine is considered shortsighted".)

The theoretical upper-bound exhaust velocity of a Bussard ramjet is something like ~0.12c, assuming you start with 4 hydrogen and end with 1 helium. As such, the theoretical upper-bound speed limit relative to the interstellar medium of a Bussard ramjet is also ~0.12c. In actuality, it will be quite a bit lower, as quite a lot of the energy is carried off in the form of energetic photons and neutrinos.

Personally? A Bussard ramjet will never work, even assuming we get the scoop part figured out. The lower bound on how fast it has to go before it can start working and the upper bound on how fast it can go are too close. Not to mention the Lawson criterion for hydrogen burning (4xH -> He), or, alternatively, the problem of containment of the catalyst and the beta-decay steps of the CNO cycle.

If you crunch the numbers, it turns out the bad news is a Bussard ramjet won't work as an engine.

The good news is, it will work as a brake. That takes care of the deceleration half of your delta-V requirement, which is better news than it sounds: thanks to the rocket equation, it doesn't just halve your required mass fraction of fuel, it square-roots it.

Assuming proton-proton fusion, the speed limit is about 12% c, relative to the interstellar medium (http://www.projectrho.com/public_html/rocket/slowerlight.php). That depends, however, on the assumption that the initial kinetic energy of the incoming hydrogen is completely wasted- that the ramjet does not have "regenerative braking", so to speak, that can recover some of the pre-existing kinetic energy. That's a pretty reasonable assumption from an engineering point of view, but physics theoretically allows us to do better.