  Diagnostics based on the polarization properties of the synchrotron emission
can provide precious information on both the ordered structure and the random
level of the magnetic field. While this issue has been already analysed in the
radio, the polarization data recently obtained by the mission IXPE have shown
the need to extend this analysis to the X-rays. While our immediate target are
young SNRs, the scope of this analysis is wider. We aim at extending the
analysis to particle energy distributions more complex than a power law, as
well as to investigate a wider range of cases involving a composition of
ordered and random magnetic fields. Since only in a limited number of cases an
analytical approach is possible, we have devised to this purpose an optimised
numerical scheme, and we have directly used it to investigate particle energy
distributions in the form of a power law with an exponential, or
super-exponential cutoff. We have also considered a general combination of a
ordered field plus an anisotropic random component. We have shown that the
previously derived analytic formulae, valid for power-law distributions, may be
good approximations of the polarization degree also in the more general case
with a cutoff, as typically seen in X-rays. We have explicitly analysed the
young SNRs SN 1006, Tycho and Cas A. In particular, for SN 1006, we have proved
the consistency between the radio and X-ray polarization degrees, favouring the
case of predominantly random field, with an anisotropic distribution. In
addition, for the power-law case, we have investigated the effect of a
compression on both ordered and random magnetic field components, aimed at
describing the mid-age radio SNRs. This work allows a more efficient
exploitation of radio and X-ray measurements of the synchrotron polarization,
and is addressed to present observations with IXPE as well as to future
projects.
