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 cha rged particle driven by a circularly polarized electromagnetic wave and a c onstant magnetic field, The explicit expressions of particle position and v elocity are obtained For certain initial conditions. The results are of int erest to the interaction of the high-power laser with the magnetized plasma , electromagnetically pumped free-electron laser with a guide magnetic fiel d, propagation of electromagnetic wave signals through a re-entry plasma sh eath in the presence of a strong magnetic held, and magnetic confinement pl asmas.