  In this paper we present, for the first time, simulated maps of the
circularly polarized synchrotron emission from the Crab nebula, using
multidimensional state of the art models for the magnetic field geometry.
Synchrotron emission is the signature of non-thermal emitting particles,
typical of many high-energy astrophysical sources, both Galactic and
extra-galactic ones. Its spectral and polarization properties allow us to infer
key informations on the particles distribution function and magnetic field
geometry. In recent years our understanding of pulsar wind nebulae has improved
substantially thanks to a combination of observations and numerical models. A
robust detection or non-detection of circular polarization will enable us to
discriminate between an electron-proton plasma and a pair plasma, clarifying
once for all the origin of the radio emitting particles, setting strong
constraints on the pair production in pulsar magnetosphere, and the role of
turbulence in the nebula. Previous attempts at measuring the circular
polarization have only provided upper limits, but the lack of accurate
estimates, based on reliable models, makes their interpretation ambiguous. We
show here that those results are above the expected values, and that current
polarimetric tecniques are not robust enough for conclusive result, suggesting
that improvements in construction and calibration of next generation radio
facilities are necessary to achieve the desired sensitivity.
