  We propose a new mechanism which explains the existence of enormously sharp
edges in the rings of Saturn. This mechanism is based on the synchronization
phenomenon due to which the epicycle rotational phases of particles in the
ring, under certain conditions, become synchronized with the phase of external
satellite, e.g. with the phase of Mimas in the case of the outer B ring edge.
This synchronization eliminates collisions between particles and suppress the
diffusion induced by collisions by orders of magnitude. The minimum of the
diffusion is reached at the center of the synchronization regime corresponding
to the ratio 2:1 between the orbital frequency at the edge of B ring and the
orbital frequency of Mimas. The synchronization theory gives the sharpness of
the edge in few tens of meters that is in agreement with available
observations.
