Resonant interaction of a charged particle with a slow electromagnetic wave

The problem of the motion of a relativistic charged particle in a homogeneous magnetic field and in the field of a slow oblique electromagnetic wave is stated using a Hamiltonian formulation. The conditions of the occurrence of strong stochasticity due to the overlap of the Cerenkov and adjacent cyclotron resonances are investigated. By using the method proposed by Dunnet et al. (1958), approximate motion integrals are introduced which provide a way to estimate the magnitude of individual resonances and to construct an approximate phase portrait of the system.