Charged particle dynamics in an elliptically polarized electromagnetic wave and a uniform axial magnetic field

An analytical study of the charged particle dynamics in the presence of an elliptically polarized electromagnetic wave and a uniform axial magnetic field, is presented. It is found that for $g\omega_{0}/ \omega' = \pm 1$, maximum energy gain occurs respectively for linear and circular polarization; $\omega_{0}$ and $\omega'$ respectively being the cyclotron frequency of the charged particle in the external magnetic field and Doppler-shifted frequency of the wave seen by the particle, and $g =\pm 1$ respectively correspond to left and right-handedness of the polarization. An explicit solution of the governing equation is presented in terms of particle position or laboratory time, for the specific case of resonant energy gain in a circularly polarized electromagnetic wave. These explicit position- or time-dependent expressions are useful for better insight into various phenomena, viz., cosmic ray generation, microwave generation, plasma heating, and particle acceleration, etc.