When the parameters of electron - extreme power laser interaction enter the regime of dominated radiation reaction, the electron dynamics changes qualitatively. The adequate theoretical description of this regime becomes crutially important with the use of the radiation friction force either in the Lorentz-Abraham-Dirac form, which possess unphysical runaway solutions, or in the Landau-Lifshitz form, which is a perturbation valid for relatively low electromagnetic wave amplitude. The goal of the present paper is to find the limits of the Landau-Lifshitz radiation force applicability in terms of the electromagnetic wave amplitude and frequency. For this a class of the exact solutions to the nonlinear problems of charged particle motion in the time-varying electromagnetic field is used.Comment: 14 pages, 5 figure
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