An exact solution of the relativistic equation of motion of a charged particle driven by a circularly polarized electromagnetic wave and a constant magnetic field

An exact solution is found for the relativistic equation of motion of a charged particle driven by a circularly polarized electromagnetic wave and a constant magnetic field, The explicit expressions of particle position and velocity are obtained For certain initial conditions. The results are of interest to the interaction of the high-power laser with the magnetized plasma, electromagnetically pumped free-electron laser with a guide magnetic field, propagation of electromagnetic wave signals through a re-entry plasma sheath in the presence of a strong magnetic field, and magnetic confinement plasmas.