  The ionization equation of state (IEOS) for a cloud of the dust particles in
the low-pressure gas discharge under microgravity conditions is proposed. IEOS
relates pairs of the parameters specific for the charged components of dusty
plasma. It is based on the modified collision enhance collection model adapted
for the Wigner--Seitz cell model of the dust cloud. This model takes into
account the effect of ion--atom collisions on the ion current to the dust
particles and assumes that the screening length for the ion--particle
interaction is of the same order of magnitude as the radius of the
Wigner--Seitz cell. Included effect leads to a noticeable decrease of the
particle charge as compared to the previously developed IEOS based on the
orbital motion limited model. Assuming that the Havnes parameter of the dusty
plasma is moderate one can reproduce the dust particle number density measured
in experiments and, in particular, its dependence on the gas pressure. Although
IEOS includes no fitting parameters, it can ensure a satisfactory precision in
a wide range of dusty plasma parameters. Based on the developed IEOS, the
threshold relation between the dusty plasma parameters for onset of the lane
formation in binary dusty plasmas is deduced.
