  Laser-accelerated lightsails enable new types of missions that are very
different from the Breakthrough Starshot mission to the Centauri system that
aims to send 1 gram of payload at 0.2 c. The present work widens the mission
design space to 0.1 mg to 100 kt payload and 0.0001-0.99 c cruise velocity.
Drawing up to 5 GW directly from the grid (to augment power drawn from local
energy storage) turns out to be the key to making small missions affordable: It
collapses the accelerating laser's capital cost by up to 5 orders of magnitude,
enabling new possibilities such as a 10 kg Solar system cubesat that
accelerates to 0.001 c (63 au/yr) using a 77 m sail and \$610M laser, costing
\$58M worth of energy per mission.
  Trajectory equations describing lightsail acceleration are derived in closed
form and used instead of numerical integration. Consequently, analyses have
progressed from single point designs to whole performance maps comprised of
thousands of cost-optimized point designs. The performance maps reveal
qualitatively different regimes characterized by the particular constraint that
drives cost, and these driving constraints change depending on mission payload
mass and cruise velocity.
  The performance maps also reveal a family of cost-optimal missions that
accelerate at Earth gravity: The heaviest such mission is a 7.4 km diameter 100
kt vessel (equivalent to 225 International Space Stations) that is accelerated
for 21 days to achieve 0.07 c, reaching the Centauri system within a human
lifetime. While unthinkable at this time, the required 380 PW peak radiated
power (twice terrestrial insolation) might be generated by space solar power or
fusion within a few centuries. Regardless, it is now possible to contemplate
such missions using laser-accelerated lightsails.
