  The kinetic Boltzmann equation is used to model the non-equilibrium
ionization phase that initiates the evolution of atomic clusters irradiated
with single pulses of intense vacuum ultraviolet radiation. The duration of the
pulses is < 50 fs and their intensity in the focus is < 10^{14} W/cm^2. This
statistical model includes various processes contributing to the sample
dynamics at this particular radiation wavelength, and is computationally
efficient also for large samples. Two effects are investigated in detail: the
impact of the electron heating rate and the effect of the plasma environment on
the overall ionization dynamics. Results on the maximal ion charge, the average
ion charge and the average energy absorbed per atom estimated with this model
are compared to the experimental data obtained at the free-electron-laser
facility FLASH at DESY. Our analysis confirms that the dynamics within the
irradiated samples is complex, and the total ionization rate is the resultant
of various processes. In particular, within the theoretical framework defined
in this model the high charge states as observed in experiment cannot be
obtained with the standard heating rates derived with Coulomb atomic
potentials. Such high charge states can be created with the enhanced heating
rates derived with the effective atomic potentials. The modification of
ionization potentials by plasma environment is found to have less effect on the
ionization dynamics than the electron heating rate. We believe that our results
are a step towards better understanding the dynamics within the samples
irradiated with intense VUV radiation.
