Plasma expansions in terms of self-similar solutions

Simple analytical models are presented for hydrodynamic expansion of laser-produced plasma governed by the nonlinear heat conduction. To neatly describe the fluid systems, we put forward new self-similar solutions, which are very useful to completely reveal the essential behavior of the underlying physics. The targets are assumed to have a limited mass. The physical picture significantly contrasts with that well described by the orthodox self-similar solution for a semi-infinite planar rarefaction wave. The ion energy spectrum obtained by the model reproduces well experimental results obtained under different geometrical conditions. It is strictly shown that the hydrodynamic system of an accelerating foil admits a new self-similar solution describing the nonstationary ablation process, through which the payload mass decreases to burn out at the end. The system is appropriately solved as a novel eigenvalue problem such that the acceleration and the heat conductivity are restrictive with each other under the self-similar evolution.