Wave-particle interaction at double resonance.

This paper is devoted to studying wave-particle interaction at "double resonance" condition, i.e., when two waves interact resonantly with the same group of charged particles. A theoretical Hamiltonian model and a symplectic numerical code are built to describe the three-dimensional interactions of wave spectra with resonant electrons in a magnetized plasma. Related simulations on the evolution of two waves of close parallel phase velocities interacting resonantly with particles' fluxes have been performed, which reveal some common features which do not depend on the kind of waves, instabilities, and particles' distributions: after the stage of linear instability, when the waves' amplitudes saturate due to particle trapping, a nonlinear process takes place which is characterized by a quasiperiodical exchange of energy between the waves, depending in particular on the value of the mismatch between the waves' resonant velocities. In order to explain such observations, a simple Hamiltonian model describing the interaction of two different waves of close resonant velocities with a periodical train of bunches of trapped particles moving synchronously has been built. It allows one to describe the nonlinear characteristics of this process as well as to estimate analytically its time scale and shows a good agreement with the numerical simulation results.