What's the Most Stable Shape for an Interstellar Lightsail?

"We considered different shapes of sail: a) spherical (coincides with parabolic for small sizes) as most appropriate for final configuration of nanocraft en route; b) conical; c) flat (simplest) (will be seen to be unstable so that even spinning of craft does not help)."

"The nanocraft driven by intense laser beam pressure acting on its Lightsail is sensitive to the torques and lateral forces reacting on the surface of the sail. These forces influence the orientation and lateral displacement of the spacecraft, thus affecting its dynamics. If unstable the nanocraft might even be expelled from the area of laser beam. The most dangerous perturbations in the position of nanocraft inside the beam and its orientation relative to the beam axis are those with direct coupling between rotation and displacement (“spin-orbit coupling”)."

"We found that a parachute-shaped sail riding on a Gaussian laser beam is unstable... We show in our paper that a sail shaped as a spherical shell (like a large ping-pong ball) can ride in a stable fashion on a laser beam that is shaped like a cylinder (or 3-4 lasers that establish a nearly circular illumination)."