Why does the power cable have to be Superconducting? Many Power lines on earth exceed 30 miles.
How thick would a standard copper cable have to be to transmit several gigawatts without melting? A meter thick? More? A cable that thick would be too heavy to be supported up to stratospheric height by balloon.
I have read Rocheworld, Dr. Robert Forward. Had a two stage sail to decelerate. That is not necessary, A magnetic sail, such as Mini Magnetosphereic propulsion, could act as a parachute to slow into orbit around the destination star. This should reduce the required range of the laser and reduce the mass of the spacecraft.
From tens of thousands of km/s? Let's say you are going at 20,000 km/s and decelerate at a constant 4 g's. It will take about five billion km to come to a stop, and I don't much like the crew's chances of enduring higher acceleration than that for several days on end (three days at 4 g's). Stellar magnetospheres for a Sol-like or smaller star are kind of weak till you get within a few billion km, and by the time you get close enough that there's much to brake against, you are close enough that you'd have to use bone-crunching deceleration to stop. You're going to have to brake more slowly, and do it against the interstellar medium for a few weeks before arrival.
Also there were several chemically fueled Landers with propellant in the payload to Rocheworld. The point is that mass can be reduced.
You can probably lighten the landers by using a different propulsion method on them, but you really do want to retain the capacity for several landings, since you spend all the time and effort to reach the target solar system. For example, all of the larger-than-Luna-sized bodies that were landed upon in
Rocheworld had atmospheres denser than Mars, so some aerobraking could have been used and saved 70-80% of the descent fuel.
On the other hand, we ARE talking about a closed-loop ecosystem, with complete food production included, to support twenty humans, so there are limits to how small we can make the core starship. Maybe half the mass of Dr. Forward's ship?
It is also not necessary to reach 20% of the speed of light. 5% c will make the trip to Rigil Kentaurus, in under a Century. 10% light speed would allow travel to any of the 25 closest stars (other than the sun) in under 120 years.
If we are not using any hibernation or other human-lifespan-extending methods, then if you want the crew that arrives to be the same crew that departs from Earth (instead of their grandkids, who may not have the equivalent quality of training from their parents that can be had from NASA, MIT, etc., and who more importantly will have no personal reference points for living outside of their starship), and you want them to not be geriatric when they do, then the reasonable limit on travel time is about fifty years of shipboard time.
