  We address the occurrence of narrow planetary rings and some of their
structural properties, in particular when the rings are shepherded. We consider
the problem as Hamiltonian {\it scattering} of a large number of
non-interacting massless point particles in an effective potential. Using the
existence of stable motion in scattering regions in this set up, we describe a
mechanism in phase space for the occurrence of narrow rings and some
consequences in their structure. We illustrate our approach with three
examples. We find eccentric narrow rings displaying sharp edges, variable width
and the appearance of distinct ring components (strands) which are spatially
organized and entangled (braids). We discuss the relevance of our approach for
narrow planetary rings.
