Change in the energy of a charged particle moving in the field of a slow electromagnetic wave

A differential equation is obtained that describes the change in the energy of a charged particle in the field of a slow wave (with phase velocity not equal to unity) as a function of the distance traversed. Analysis of this equation yields the amplitude and period of the change in the particle's energy.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 97–102, February, 1981.