Gradients of Synchrotron Polarization: Tracing 3D distribution of
  magnetic fields
  We describe a new technique for probing galactic and extragalactic 2D and 3D
magnetic field distribution using gradients of polarized synchrotron emission.
The fluctuations of magnetic field are elongated along the ambient magnetic
field. Therefore, the field variations are maximal perpendicular to the
B-field. This allows tracing B-field with synchrotron polarization gradients
(SPGs). We demonstrate that the Faraday depolarization allows to map 3D B-field
structure by. The depolarization ensures that the polarization gradients sample
the regions close to the observer with the sampling depth controlled by the
frequency of radiation. We also analyze the B-field properties along the
line-of-sight by applying the gradient technique to the wavelength derivative
of synchrotron polarization. This Synchrotron Derivative Polarization Gradients
(SDPGs) technique can recover the 3D vectors of the underlying B-fields. The
new techniques are different from the Faraday tomography as they provide a way
to map the 3D distribution of B-fields components perpendicular to the line of
sight. In addition, we find that the alignment of gradients of polarization
with the synchrotron polarization can be used to separate the contribution of
the foreground from the polarization of cosmological origin. We notice that the
same alignment is also present for the dust polarization.
