  The relaxation of temperatures and velocities of the components of a
quasi-equilibrium two-component homogeneous completely ionized plasma is
investigated on the basis of a generalization of the Chapman-Enskog method
applied to the Landau kinetic equation. The generalization is based on the
functional hypothesis in order to account for the presence of kinetic modes of
the system. In the approximation of a small difference of the component
temperatures and velocities, it is shown that relaxation really exists (the
relaxation rates are positive). The proof is based on the arguments that are
valid for an arbitrary two-component system. The equations describing the
temperature and velocity kinetic modes of the system are investigated in a
perturbation theory in the square root of the small electron-to-ion mass ratio.
The equations of each order of this perturbation theory are solved with the
help of the Sonine polynomial expansion. Corrections to the known Landau
results related to the distribution functions of the plasma and relaxation
rates are obtained. The hydrodynamic theory based on these results should take
into account a violation of local equilibrium in the presence of relaxation
processes.
