We give a rigorous solution that describes, in the laboratory reference frame, the dynamics of charged particles moving in the field of a fast or slow transverse electromagnetic wave with an arbitrary field strength. We determine the size of the interaction region where the particles effectively exchange energy with the field, and determine the dependence of the frequency of oscillations of passing and captured particles on the wave's field strength. We also formulate the conditions in which the particles are accelerated by the wave and the conditions in which the particles give up some of their energy to the wave. Finally, we show that even in a which the particles give up some of their energy to the wave. Finally, we show that even in a large energy spread to short-wave radiation can be highly efficient.
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