We will discuss a statistical description of synchrotron fluctuations arising
from magnetized turbulence. We demonstrate that the synchrotron intensity
fluctuations are anisotropic with enhanced correlations present along the
direction of the magnetic field. This anisotropy is dominated by the quadrupole
component with the ratio between quadrupole and monopole parts being sensitive
to the compressibility of underlying turbulence. We show how the
structure of correlations reflects what turbulent modes are present.
We shall also discuss synchrotron polarization fluctuations in the presence
of Faraday rotation. Several measures that can be used to obtain the spectral
slopes and correlation scales of both the underlying magnetic turbulent gas
responsible for the emission and the spectrum of the Faraday rotation
fluctuations are introduced. Our results are relevant for quantitative studies of
magnetic turbulence in our galaxy and beyond using synchrotron emission as
well as separation of synchrotron foreground emission from
cosmological signals, namely CMB or highly redshifted HI emission.
We expect applications of our techniques both with existing synchrotron
data sets as well as with big forthcoming data sets from LOFAR and SKA.