  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.
