Multi-dimensional radiative effects in supercritical shock waves

In supercritical shock waves, the radiation emitted by the shock front preheats and ionizes the medium ahead of the shock wave creating a radiative precursor. These radiative shocks have been recently created in high energy density laser experiments. In this article we investigate the structure of the radiation field generated in high Mach number shock waves (supercritical shock waves) which have a finite extension R in the direction perpendicular to the shock wave propagation. A simple analytical model allows us to calculate how the radiation field decreases with R for a medium with an homogeneous radiation emission in volume. We then perform a 3-dimensional radiative transfer calculation of the radiation field created by a stationary shock wave, and compare the predicted radiative energy density and flux with 1-dimensional calculations. We find that the variation of the radiation field with R follows the trend given by the analytical calculation. Finally, we perform radiative-hydrodynamical calculations to investigate further the variation of the radiation field with R and to estimate the decrease of the velocity of the radiative precursor with R. (authors)