Structural Stability of a Lightsail for Laser-Driven Interstellar Flight

The structural stability of a lightsail under the laser flux necessary for interstellar flight is studied analytically and numerically. A sinusoidal perturbation is introduced into a two-dimensional thin-film sail to determine if the sail remains stable or if the perturbations grow in amplitude. A reflective material that gives specular reflection of the laser illumination is assumed in determining the resulting loading on the sail, although other reflection models can be incorporated as well. The quasi-static solution of the critical point between shape stability and instability is found by equating the bending moments induced on the sail due to radiation pressure with the restoring moments caused by the strength of the sail and the tension applied at the edges of the sail, permitting analytical expressions for the elastic modulus and boundary tension magnitude to be found as a function of sail properties and the amplitude and wave number of the initial perturbation. These expressions are also derived from a formal variational energy approach. A numerical model of the sail dynamics is developed by discretizing the sail into finite elements. By introducing torsional and rectilinear springs between the elements into the numerical model, a hierarchy of models is produced that can incorporate the effects of bending and applied tension. The numerical models permit the transient dynamics of a perturbed sail to be compared to the analytic results of the quasi-static analysis. The analytic expressions can correctly predict the stability boundary found in the numerical simulations. The stiffness required to make a sail stable against uncontrolled perturbation growth is shown to be unfeasible for known materials. A modest tensioning of the sail (e.g., via an inflatable structure or spinning of the sail) can maintain a stable sail shape under all wavelengths and amplitudes of perturbations.