  The Kuiper belt is a population of icy bodies beyond the orbit of Neptune. A
particularly puzzling and up-to-now unexplained feature of the Kuiper belt is
the so-called `kernel', a concentration of orbits with semimajor axes a~44 AU,
eccentricities e~0.05, and inclinations i<5 deg. Here we show that the Kuiper
belt kernel can be explained if Neptune's otherwise smooth migration was
interrupted by a discontinuous change of Neptune's semimajor axis when Neptune
reached ~28 AU. Before the discontinuity happened, planetesimals located at ~40
AU were swept into Neptune's 2:1 resonance, and were carried with the migrating
resonance outwards. The 2:1 resonance was at ~44 AU when Neptune reached ~28
AU. If Neptune's semimajor axis changed by fraction of AU at this point,
perhaps because Neptune was scattered off of another planet, the 2:1 population
would have been released at ~44 AU, and would remain there to this day. We show
that the orbital distribution of bodies produced in this model provides a good
match to the orbital properties of the kernel. If Neptune migration was
conveniently slow after the jump, the sweeping 2:1 resonance would deplete the
population of bodies at ~45-47 AU, thus contributing to the paucity of the
low-inclination orbits in this region. Special provisions, probably related to
inefficiencies in the accretional growth of sizable objects, are still needed
to explain why only a few low-inclination bodies have been so far detected
beyond ~47 AU.
