Back in Ye Olde Days of the Space Age, the 1960s, various NASA & Aerospace Industry researchers studied Interstellar Travel in terms of idealised rockets. Fusion rockets were studied and their maximum performance computed based on known reactions – the best single-reaction fusion energy release comes from the D+3He reaction, which can produce an ideal exhaust velocity of 0.0893c. Assuming a mass-ratio of, at most, 10,000 and a 40 year ship-board trip-time, the maximum range is 16.75 ly and the top-speed 0.3896c. Of course to achieve a mass-ratio of 10,000 the fusion rocket was assumed to be multiply staged – four stages with mass-ratios of 10, or thereabouts.
That’s one-way performance. Returning to Earth would result in a halved top-speed and an 80 year trip-time, one-way. What if that can be improved?
In “Avatar” the ISV “Venturestar” uses “Polypropulsion” to do a round-trip to Alpha Centauri in a reasonable trip-time and reasonable total propellant requirement. First, a laser fired from a generator in the Solar System propels the ISV to 0.7c. Then, approaching Alpha Centauri, the ship fires up its antimatter/matter annihilation drive and brakes. To return to Earth the procedure reverses. The advantage is that the Rocket Equation’s limitations – the multiplication of mass-ratios to increase velocities linearly – is bypassed for half the overall mission. This results in a square-root reduction of the total propellant needed e.g. if the one-velocity change mass-ratio was 10, then the total mass-ratio would be 10,000 (104) for four engine firings. With polypropulsion that’s reduced to just 100 (102), and just 20 if the ISV can refuel at destination.
Let’s look at a pure-deuterium fusion rocket, since we don’t presently have matter/antimatter producing generators. According to (controversial) work with “Cold Fusion” or ‘pycnonuclear reactions’, in which deuterium forms super-dense clusters inside a metal matrix and fusion occurs due to an energy injection, typically electrical, there seems to be a process which allows deuterium to fuse totally into helium-4. Normal thermonuclear reactions with deuterium require multiple steps to get helium-4 – D+D —> 3He (50%) and 3T (50%), then protons and deuterons (2D) fuse with those fusion products to eventually produce 4He. If, a big if, there’s some way of bypassing the intermediate, then theoretically D+D —> 4He should liberate 0.64% of its mass-energy. That’s a 4He nucleus shooting off at 0.112955c and so would allow higher performance from a fusion rocket.
How high? If we assume that 100 mass-ratio from the old fusion-studies, then that’s a top speed of tanh(ln(100)*0.112955)c = 0.47784c. Because of time-dilation the trip appears to happen at 0.544c, thus if we factor in the acceleration time, assumed a constant 1 gee, then a one-way trip-time (ship-board) of 40 years gets us 21.478 ly. Accelerating a bit harder at 1.5 gee gets 21.57 ly, while accelerating at a low 0.1 gee means a range of just 18.957 ly.
With Polypropulsion we can use our 10,000 mass-ratio to do all the hard work of deccelerating and accelerating at the destination since we have no facilities there. Thus we can do a round-trip in half the time of the scenario in which we carry gas for all stages of the journey. If magnetic or plasma sails prove effective, then we could reduce the propellant required to just what’s needed to brake at low-speeds (when sails peter out) and accelerating back up to speed. That might reduce the mass-ratio to just ~200 for the extreme case considered here.
Of course if the 40 year trip-time is for the round-trip, then the maximum distance is half the above, ~10.8 ly in the 1.5 gee case, roughly here to Epsilon Eridani.