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 hohlraum 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.
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