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The late time asymptotics of the physical solutions to the Lorentz-Diracequation in the electromagnetic external fields of simple configurations -- theconstant 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 externalelectromagnetic fields admitting a two-parametric symmetry group, which includeas a particular case the above mentioned field configurations, are obtained.General properties of the total radiation power of a charged particle areestablished. In particular, for a circularly polarized wave and constantuniform crossed fields, the total radiation power in the asymptotic regime isindependent of the charge and the external field strength, when expressed interms of the proper-time, and equals a half of the rest energy of a chargedparticle divided by its proper-time. The spectral densities of the radiationpower formed on the late time asymptotics are derived for a charged particlemoving in the external electromagnetic fields of the simple configurationspointed above.

Radiation of de-excited electrons at large times in a strong electromagnetic plane wave