  The modern Free-Electron-Lasers generate a highly intense polarized radiation
which initiate a sequence of ionization and decay events. Their probability
depends on the polarization of each state as function of time. Its complete
accounting is limited by the fact that a state can be formed in various ways.
Here we present the equivalent of rate equations for population that completely
accounts polarization of radiation and formulated in terms of the statistical
tensors. To illustrate our approach we theoretically consider sequential
photoionization of krypton by an intense extreme ultraviolet femtosecond pulse
for the photon energies below the 3d-shell excitation threshold. The
calculations of the ion yields, photoelectron spectra and ionic polarization
for various photon fluence are presented and role of polarization is discussed.
