  The late time asymptotics of the physical solutions to the Lorentz-Dirac
equation in the electromagnetic external fields of simple configurations -- the
constant homogeneous field, the linearly polarized plane wave (in particular,
the constant uniform crossed field), and the circularly polarized plane wave --
are found. The solutions to the Landau-Lifshitz equation for the external
electromagnetic fields admitting a two-parametric symmetry group, which include
as a particular case the above mentioned field configurations, are obtained.
General properties of the total radiation power of a charged particle are
established. In particular, for a circularly polarized wave and constant
uniform crossed fields, the total radiation power in the asymptotic regime is
independent of the charge and the external field strength, when expressed in
terms of the proper-time, and equals a half of the rest energy of a charged
particle divided by its proper-time. The spectral densities of the radiation
power formed on the late time asymptotics are derived for a charged particle
moving in the external electromagnetic fields of the simple configurations
pointed above.
