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We propose classical equations of motion for charged particles in an electromagnetic field. These are general formulas for the particle acceleration that take the radiation-induced deceleration into account and contain no second derivatives of the particle velocity. In several particular cases considered, the new equations yield results coinciding with those known in the literature and experimentally verified. We show that in the range of ultrahigh energies, classical electrodynamics does not lead to inherent inconsistencies and in principle allows particle motion with energies exceeding the Pomeranchuk limit.

This paper contains details of calculation of the surface wave excitation by a fast moving charged particle in a thin uniform metal film surrounded by a dielectic medium. Early on the effect was described in the paper arXiv:0911.0565 03 November 2009. It is shown that the Vavilov-Cherenkov like effect for the surface waves could arise for particles whose velocities are ten-and even hundred-times lower than the corresponding velocities in a uniform medium.

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