Exact Motion of a Charged Particle in an Arbitrary Plane Wave Propagating along a Constant Homogeneous Magnetic Field

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Abstract
The classical relativistic equations of motion are solved for a charged particle moving in an arbitrary plane electromagnetic wave propagating along a constant homogenous magnetic field. The solutions are expressed by (proper time) evolution tensor factors, operating upon the initial value quantities. The calculations are performed in terms of tensor-component matrices. Elliptically polarized waves are then considered. At resonance frequency an expression for the increase in the kinetic energy is obtained. This expression shows that the kinetic energy increases indefinitely, and that the energy exchange is caused by the field component rotating in the same direction as the particle.