Nonlinear resonances generate large-scale convection cells in phase space

It is well known that resonance phenomena can destroy adiabatic invariance and cause chaos and mixing. In the present Rapid Communication, we show that a nonlinear wave-particle resonant interaction may do the opposite-generate large-scale coherent structures in phase space. The combined action of the drift due to nonlinear scattering on resonance and trapping (capture) into resonance creates a convection cell-like structure, where the areas of particle acceleration and deceleration are macroscopically separated. At the same time, nonlinear scattering also creates a diffusion that cause mixing on and between the energy levels.