  We describe results from time-dependent numerical modeling of the
collisionless reverse shock terminating the pulsar wind in the Crab Nebula. We
treat the upstream relativistic wind as composed of ions and electron-positron
plasma embedded in a toroidal magnetic field, flowing radially outward from the
pulsar in a sector around the rotational equator. The relativistic cyclotron
instability of the ion gyrational orbit downstream of the leading shock in the
electron-positron pairs launches outward propagating magnetosonic waves.
Because of the fresh supply of ions crossing the shock, this time-dependent
process achieves a limit-cycle, in which the waves are launched with
periodicity on the order of the ion Larmor time. Compressions in the magnetic
field and pair density associated with these waves, as well as their
propagation speed, semi-quantitatively reproduce the behavior of the wisp and
ring features described in recent observations obtained using the Hubble Space
Telescope and the Chandra X-Ray Observatory. By selecting the parameters of the
ion orbits to fit the spatial separation of the wisps, we predict the period of
time variability of the wisps that is consistent with the data. When coupled
with a mechanism for non-thermal acceleration of the pairs, the compressions in
the magnetic field and plasma density associated with the optical wisp
structure naturally account for the location of X-ray features in the Crab. We
also discuss the origin of the high energy ions and their acceleration in the
equatorial current sheet of the pulsar wind.
