  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.
