Abstract
The interactions of a relativistic free electron with a pulsed electromagnetic (EM) plane wave in the presence of constant magnetic fields are studied using the well-known constants of motion. The goal is to determine the energy gained by the electron after the wave has passed. For a constant magnetic field along the axis of the wave, a general solution for the energy gain as a function of the vector potential describing the EM plane wave is obtained. Solutions for magnetic fields transverse to the axis of the wave are sought in the limit where the cyclotron frequency is much less than the wave frequency and are examined using several different profiles for the wave amplitude. For this case, an adiabatic invariant is found that shows that there is no energy gain when an EM plane wave comes and goes with a profile that is slowly varying in time with respect to the cyclotron motion.
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