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

An analytical study of charged particle dynamics in the presence of an elliptically polarized electromagnetic wave and a uniform axial magnetic field is presented. It is found that a charged particle resonantly gains energy for gω0/ω′=±1, ω0, and ω′, 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=±1, respectively, correspond to right and left-handedness of polarization. An explicit solution of the governing equation is also 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.