Modified guiding-center equations are derived for particles experiencing a small-amplitude electromagnetic wave of arbitrary polarization. The resulting differential equations contain the first-order wave amplitude explicitly and are relativistically correct. A simple characteristic equation is obtained for the particle trajectory in energy and magnetic-moment phase space for cases where the Doppler frequency shift for drifts perpendicular to the magnetic field is negligible. Two examples are given to illustrate the behavior of particle trajectories in momentum space.
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T.D. Rognlien (1983) studied this question.
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