Hydrodynamics of exploding foil x-ray lasers

Abstract

An accurate simple model for the hydrodynamics of laser heated exploding foils is presented. Particular emphasis is given to applications in the design of soft x-ray lasers. The model predicts the conditions in the foil plasma (e.g., temperature, density, and scale length), given the experimental parameters (e.g., optical laser intensity, laser pulse duration, target thickness, and target composition). The simple model is based on an isothermal, homogeneous expansion similarity solution of the ideal hydrodynamic equations. Both analytical and numerical solutions of the similarity equations are studied. The numerical solutions agree closely with computational hydrodynamic simulations at times of interest—after the laser burns through the foil. Analytic solutions for constant intensity laser irradiation provide useful power-law scaling relations between the input laser and target parameters and the plasma variables. The simple model is a powerful design tool that reproduces the essential results of more expensive and time-consuming simulations over a large and important range of parameter space.