Resonant wave-particle interaction at the half-integer cyclotron harmonics

A single particle is subjected to the combined action of a static uniform magnetic field and an electromagnetic wave. The equations of motion are solved using the perturbation method up to second order. In the results, two different types of second-order effects appear: (i) the always present non-resonant effects, resulting in a ponderomotive drift and a nonlinear cyclotron frequency shift, and (ii) the resonant effects appearing at the half-integer harmonics of the gyrofrequency and leading to perpendicular heating and diffusion.