Captures into resonance and scattering on resonance in dynamics of a charged relativistic particle in magnetic field and electrostatic wave

The dynamics of a relativistic charged particle in a uniform magnetic field and an electrostatic plane wave is studied. For a small-amplitude high-frequency wave, the system is reduced to a two-degree-of-freedom Hamiltonian system with slow and fast variables. In this system, the phenomena of capture into resonance and scattering on the resonance are described. These phenomena determine the long-term dynamics of the particle.