Abstract
We investigate the dynamics of a relativistic electron in a strongly nonlinear plasma wave in terms of classical mechanics by taking into account the action of the radiative reaction force. The two limiting cases are considered. In the first case where the energy of the accelerated electrons is low, the electron makes many betatron oscillations during the acceleration. In the second case where the energy of the accelerated electrons is high, the betatron oscillation period is longer than the electron residence time in the accelerating phase. We show that the force of radiative friction can severely limit the rate of electron acceleration in a plasma accelerator.
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