Currently I am working on a paper & presentation for the 100 YSS Symposium in Houston, to be presented by an Icarus colleague. I am examining the effectiveness of using a magnetic-sail to brake to low-speeds in the target system, but part of that is a comparison with a pure fusion rocket. As it is still the most detailed design for an interstellar fusion rocket I am using the performance characteristics of the “Project Daedalus” star-probe. The most economical use of propellant for pure-fusion is to boost up to cruise speed using the 1st Stage, drop the spent stage, then brake using the 2nd Stage after a period of cruising. “Daedalus”, due to its ignition system and the tricky physics of implosion ignited fusion, had two different exhaust velocities for the stages – 1st Stage was 10,600 km/s and 2nd Stage was 9,210 km/s.
A limiting variable on the possible mass-ratio was the mass of the cryogenic tankage required to keep helium-3/deuterium fuel at a chilly 3 K storage temperature. For the 1st Stage the tankage was 2.85% of the fuel mass stored and 4% for the 2nd Stage. As a critical mass-ratio is approached the required mass of propellant goes asymptotic – runs off to infinity. Thus there’s a maximum cruise speed for a single stage using “Daedalus” style storage systems. It works out as 0.1c for the 2nd Stage engine. To achieve that speed requires infinite propellant mass, so it’s not really practical.
A more practical question is the fastest trip to a given destination. Rockets are limited in how quickly they can burn their fuel – Stage 1 burns it at 0.72 kg/s and Stage 2 burns it at 0.0711 kg/s. To achieve higher speeds requires burn-times that are asymptotically rising, when the critical mass-ratio is factored in.
Alpha Centauri is 4.36 light-years away. A two-stage “Daedalus” vehicle can travel there in 68 years at a maximum speed of 0.075c and then brake to a halt at the destination. However the amount of fuel required is about 300,000 tonnes. Going a bit slower – arriving in 71 years – can reduce the fuel required to just 140,000 tonnes. “Daedalus” carried an immense payload by modern standards – 450 tonnes, the equivalent of the International Space Station. The recent paper on boot-strapping a robotic economy on the Moon only required delivery of 41 tonnes to kick-start things. A large exo-solar industrial base could be sent to other star systems in a decent time frame to build, in advance of human arrival, large laser or mass-beam facilities to decelerate a human-carrying star-ship. Such would allow much faster trip-times.