  Thermal instability in an electron-ion magnetized plasma, which is relevant
in the intragalactic medium (IGM) of galaxy clusters, solar corona, and other
two-component plasma objects is investigated. We apply the multicomponent
plasma approach when the dynamics of all species is considered separately
through the electric field perturbations. General expressions for the dynamical
variables obtained in this paper can be applied for a wide range of
astrophysical and laboratory plasmas also containing neutrals and dust grains.
We assume that background temperatures of electrons and ions are different and
include the energy exchange in the thermal equations for the electrons and ions
along with the collisional momentum exchange in the equations of motion. We
take into account the dependence of collision frequency on the density and
temperature perturbations. The cooling-heating functions are taken for both
electrons and ions. A condensation mode of thermal instability has been studied
in the fast sound speed limit. A new dispersion relation including the
different electron and ion cooling-heating functions and other effects
mentioned above has been derived and its simple solutions for growth rates in
the limiting cases have been found. We have shown that the perturbations have
an electromagnetic nature. The crucial role of the electric field perturbation
along the background magnetic field in the fast sound speed limit has been
demonstrated. We have found that at conditions under consideration, the
condensation must occur along the magnetic field while the transverse scale
sizes can be both larger and smaller than the longitudinal ones. The results
obtained can be useful for interpretation of observations of dense cold regions
in astrophysical objects.
