Self-similar ablative flow of nonstationary accelerating foil due to nonlinear heat conduction

Ablating plasma flow of an accelerating foil driven by nonlinear heat conduction is investigated theoretically. It is shown that the hydrodynamic system admits a new self-similar solution describing the nonstationary ablation process, through which the payload mass decreases to burn out at the end. In contrast to previous analyses based on stationary flow, the present solution provides a practical physical picture with a finite peak density and a distinct vacuum boundary at the front. The system is solved as a novel eigenvalue problem such that the acceleration and the heat conductivity are restrictive with each other under the self-similar evolution. Scaling laws are obtained to describe the temporal evolution for the shell acceleration and such ablation performances as the mass ablation rate and the ablation pressure.