Theory and numerical modeling of the accelerated expansion of laser-ablated materials near a solid surface

Abstract

A self-similar theory and numerical hydrodynamic modeling is developed to investigate the effects of dynamic source and partial ionization on the acceleration of the unsteady expansion of laser-ablated material near a solid target surface. The dynamic source effect accelerates the expansion in the direction perpendicular to the target surface, while the dynamic partial ionization effect accelerates the expansion in all directions. The vaporized material during laser ablation provides a nonadiabatic dynamic source at the target surface into the unsteady expanding fluid. For studying the dynamic source effect, the self-similar theory begins with an assumed profile of plume velocity, ${u=v/v}_{m}=\ensuremath{\alpha}+(1\ensuremath{-}\ensuremath{\alpha})\ensuremath{\xi},$ where ${v}_{m}$ is the maximum expansion velocity, $\ensuremath{\alpha}$ is a constant, and $\ensuremath{\xi}{=x/v}_{m}t.$ The resultant profiles of plume density and plume temperature are derived. The relations obtained from the conservations of mass, momentum, and energy, respectively, all show that the maximum expansion velocity is inversely proportional to $\ensuremath{\alpha},$ where $1\ensuremath{-}\ensuremath{\alpha}$ is the slope of plume velocity profile. The numerical hydrodynamic simulation is performed with the Rusanov method and the Newton Raphson method. The profiles and scalings obtained from numerical hydrodynamic modeling are in good agreement with the theory. The dynamic partial ionization requires ionization energy from the heat at the expansion front, and thus reduces the increase of front temperature. The reduction of thermal motion would increase the flow velocity to conserve the momentum. This dynamic partial ionization effect is studied with the numerical hydrodynamic simulation including the Saha equation. With these effects, $\ensuremath{\alpha}$ is reduced from its value of conventional free expansion. This reduction on $\ensuremath{\alpha}$ increases the flow velocity slope, decreases the flow velocity near the surface, and reduces the thermal motion of plume, such that the maximum expansion velocity is significantly increased over that found from conventional models. The result may provide an explanation for experimental observations of high-expansion front velocities even at low-laser fluence.