In this work, we present the results of two-dimensional radiation-hydrodynamics simulations of a hohlraum target whose outgoing radiation is used to produce a homogeneously ionized carbon plasma for ion-beam stopping measurements. The cylindrical hoh
lraum with gold walls is heated by a frequency-doubled ($lambda_l = 526.5$ $mu m$) $1.4$ $ns$ long laser pulse with the total energy of $E_l = 180$ $J$. At the laser spot, the peak matter and radiation temperatures of, respectively, $T approx 380$ $eV$ and $T_r approx 120$ $eV$ are observed. X-rays from the hohlraum heat the attached carbon foam with a mean density of $rho_C = 2$ $mg/cm^3$ to a temperature of $T approx 25$ $eV$. The simulation shows that the carbon ionization degree ($Z approx 3.75$) and its column density stay relatively stable (within variations of about $pm7%$) long enough to conduct the ion-stopping measurements. Also, it is found that a special attention should be paid to the shock wave, emerging from the X-ray heated copper support plate, which at later times may significantly distort the carbon column density traversed by the fast ions.
Remaining within the pure hydrodynamic approach, we formulate a self-consistent model for simulating the dynamic behavior of matter passing through metastable states in the two-phase liquid-vapor region of the phase diagram. The model is based on the
local criterion of explosive boiling, derived by applying the theory of homogeneous bubble nucleation in superheated liquids. Practical application of the proposed model is illustrated with hydrodynamic simulations of a volumetrically uniformly heated planar layer of fused silica SiO2. Implications for experimentally measurable quantities are briefly discussed. A newly developed equation of state, based on the well known QEOS model and capable of handling homogeneous mixtures of elements, was used in the numerical simulations.
