Numerical Analysis of the Hydrodynamic Behavior of Ion-beam-heated Uranium Targets for Equation-of-state Studies under Extreme Conditions

The equation of state (EOS) of fissile materials under extreme thermodynamic conditions is of great importance to assess the safety of nuclear energy systems related to extremely severe nuclear accidents and intentional nuclear terrorism. In this study, for a simple, safe, and precise measurement of these properties, we propose an experimental setup in which a small amount of fissile material sample is homogeneously heated by an intense short-pulsed heavy-ion beam, and subsequent hydrodynamic motion is examined. As an example, we investigated the response of a slab of uranium foam (density = 5% of solid density) to a pulsed 23Na+ beam with a duration of 2 ns and peak irradiation flux of 5 GW/mm2. The target thickness and incident beam energy were adjusted to 80 μm and 1.5 MeV/u, respectively, for the beam-energy deposition to occur almost at the top of the Bragg peak and inhomogeneity in the stopping power to be ±2.5%. The hydrodynamic motion of the target during and after irradiation was calculated with a one-dimensional radiation hydrodynamic code. To calculate beam-energy deposition in the target, we used density- and temperature-dependent projectile stopping data obtained with a finite-temperature Thomas-Fermi target atomic model and degeneracy-dependent dielectric response functions. The numerical results showed that the target was almost isometrically heated up to ≈ 105 K well before the rarefaction wave reached the center of the target, and fairly homogeneous temperature and density distributions were obtained at the end of the pulse duration. We discuss the feasibility of experimental EOS studies, such as the evaluation of pressures at off-Hugoniot conditions as a function of internal energy from the measurements of the target expansion velocity.