Inhomogeneous models for plerions: the surface brightness profile of the Crab Nebula

We extend the homogeneous model for the synchrotron emission from plerions to allow more realistic predictions of the surface brightness distribution at different frequencies. Abandoning the assumption of a uniform particle d istribution, we assume that particles are injected into the synchrotron neb ula only in the vicinity of the pulsar. Their distribution is then determin ed by MHD propagation in a magnetic field of spatially constant but time-de pendent intensity. This highly simplified model reproduces the integrated s pectrum and the synchrotron surface brightness profile of the Crab Nebula a t radio frequencies. However, when applied to higher frequencies, it undere stimates the extension of the emitting region, suggesting that particle dif fusion with respect to the magnetic field lines must occur.