  A simple model for sequential multiphoton ionization by ultra-intense x-rays
is presented. The derived scaling of the ion yield with pulse energy
quantitatively reproduces the experimental data, which shows that the ion yield
increases according to the "power law" behavior typical of multiphoton
ionization, followed by saturation at high pulse energies. The calculated
average time interval between ionizations for producing ions at a certain
charge state is found to be proportional to the pulse duration and independent
of all other x-ray pulse parameters. This agrees with previous studies where
the kinetic energy of fragment ions with a given charge state produced by
intense x-ray ionization of molecules was found to be independent of the pulse
energy, but to increase with smaller pulse duration due to the smaller time
interval between ionizations.
