Radiation hydrodynamics simulations of shock imaging with a betatron x-ray source at BELLA

The feasibility of high-resolution imaging of the evolution of high-energy-density hydrodynamic experiments using new laser-plasma accelerator radiation sources at the BELLA Laser is studied using CRASH, a radiation hydrodynamic simulation code. The BELLA facility features a Joule-class, femtosecond laser, which can produce a brilliant high-flux betatron x-ray source with 2--3 $\mu $m spot, well-suited to probe hydrodynamic instability experiments. CRASH simulations show that the dynamics produced by the 1 J laser with a 200 ps pulse length in a \textasciitilde 40 $\mu $m spot size (irradiance of 4e14 W cm$^{\mathrm{-2}})$ can launch a shock in a water stream. Changes in the phase of the x-ray beam in the material are to be recorded, allowing for greater sensitivity to small density variations compared to measurements of amplitude. Synthetic radiographs from a 3D simulation are used to illustrate the nature of the shock front development. Simulations were conducted across a range of accessible backlight energies, of which the 4-keV result is the most useful. The results from these simulations demonstrate the applicability of the BELLA laser to diagnose shock waves in high-energy-density systems.