Nonlinear resonances generate large-scale vortices in the phase space in plasma systems.

It is well-known that the resonance phenomena can destroy the adiabatic invariance and cause chaos and mixing. In the present paper we show that the nonlinear wave-particle resonant interaction may cause the emergence of large-scale coherent structures in the phase space. The combined action of the drift due to nonlinear scattering on resonance and trapping (capture) into resonance create a vortex-like structure, where the areas of particle acceleration and deceleration are macroscopically separated. At the same time, nonlinear scattering also creates a diffusion that causes mixing and uniformization in around the vortex.