Ionization and Dust Charging in Protoplanetary Disks
  Ionization-recombination balance in dense interstellar and circumstellar
environments is a key factor for a variety of important physical processes,
such as chemical reactions, dust charging and coagulation, coupling of the gas
with magnetic field and development of instabilities in protoplanetary disks.
We determine a critical gas density above which the recombination of electrons
and ions on the grain surface dominates over the gas-phase recombination. For
this regime, we present a self-consistent analytical model which allows us to
exactly calculate abundances of charged species in dusty gas, without making
assumptions on the grain charge distribution. To demonstrate the importance of
the proposed approach, we check whether the conventional approximation of low
grain charges is valid for typical protoplanetary disks, and discuss the
implications for dust coagulation and development of the "dead zone" in the
disk. The presented model is applicable for arbitrary grain-size distributions
and, for given dust properties and conditions of the disk, has only one free
parameter - the effective mass of the ions, shown to have a low effect on
results. The model can be easily included in numerical simulations following
the dust evolution in dense molecular clouds and protoplanetary disks.
