  We extend Pacini & Salvati's model for the synchrotron emission from plerions
to allow more realistic predictions of the surface brightness profiles of the
Crab Nebula at radio, optical and X-ray frequencies. Abandoning the assumption
of a uniform particle distribution, we assume that particles are injected into
the synchrotron nebula only in the vicinity of the pulsar. Their distribution
is then determined, to zeroth order, by MHD propagation in an azimuthal
magnetic field of spatially constant but time-dependent intensity. A good
agreement with observations across the electromagnetic spectrum is obtained if
the finite extension of the particle injection region and particle diffusion
with respect to the azimuthal field lines are taken into account.
