  In this paper we complete the set of diagnostic tools for synchrotron
emitting sources presented by Del Zanna et al. (Astron. Astrophys. 453, 621,
2006) with the computation of inverse Compton radiation from the same
relativistic particles. Moreover we investigate, for the first time, the
gamma-ray emission properties of Pulsar Wind Nebulae in the light of the
axisymmetric jet-torus scenario. The method consists in evolving the
relativistic MHD equations and the maximum energy of the emitting particles.
The particle energy distribution function is split in two components: the radio
one connected to a relic population born at the outburst of the supernova and
the other associated to the wind population continuously accelerated at the
termination shock and emitting up to the gamma-ray band. We consider the
general Klein-Nishina cross section and three different photon targets: the
nebular synchrotron photons, far-infrared thermal ones and the cosmic microwave
background. The overall synchrotron spectrum is fitted assuming an excess of
injected particles and a steeper power law with respect to previous models. The
TeV emission has the correct shape but is in excess of the data. This is due to
the nebular magnetic field structure as obtained by the simulations. The
jet-torus morphology is visible in high-resolution gamma-ray synthetic maps
too. We present a preliminary exploration of time variability in the X and
gamma-ray bands.
