  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.
