Numerical simulations for the design of absolute equation-of-state measurements by laser-driven shock waves

A recently proposed experiment for the absolute measurement of the Equation of State (EOS) of solid materials in the 10-50 Mbar pressure range is analyzed by means of numerical simulations. In the experiment, an intense laser pulse drives a shock wave in a solid target. The shock velocity and the fluid velocity are measured simultaneously by rear side time-resolved imaging and by transverse X-radiography, respectively. An EOS point is then computed by using the Hugoniot equations. The target evolution is simulated by a two-dimensional radiation-hydrodynamics code; ad hoc developed post-processors then generate simulated diagnostic images. The simulations evidence important two-dimensional effects, related to the finite size of the laser spot and to lateral plasma expansion. The first one may hinder detection of the fluid motion, the second results in a decrease of the shock velocity with time (for constant intensity laser pulses). A target design is proposed which allows for the accurate measurement of the fluid velocity; the variation of the shock velocity can be limited by the choice of a suitably time-shaped laser pulse.