  Observations of young supernova remnants (SNRs) in X-rays and gamma-rays have
provided conclusive evidence for particle acceleration to at least TeV
energies. Analysis of high spatial resolution X-ray maps of young SNRs has
indicated that the particle acceleration process is accompanied by strong
non-adiabatic amplification of magnetic fields. If Fermi acceleration is the
mechanism producing the energetic cosmic rays (CRs), the amplified magnetic
field must be turbulent and CR-driven instabilities are among the most probable
mechanisms for converting the shock ram pressure into the magnetic turbulence.
The development and evolution of strong magnetic turbulence in the
collisionless plasmas forming SNR shells are complicated phenomena which
include the amplification of magnetic modes, anisotropic mode transformations
at shocks, as well as the nonlinear physics of turbulent cascades. Polarized
X-ray synchrotron radiation from ultra-relativistic electrons accelerated in
the SNR shock is produced in a thin layer immediately behind the shock and is
not subject to the Faraday depolarization effect. These factors open
possibilities to study some properties of magnetic turbulence and here we
present polarized X-ray synchrotron maps of SNR shells assuming different
models of magnetic turbulence cascades. It is shown that different models of
the anisotropic turbulence can be distinguished by measuring the predominant
polarization angle direction. We discuss the detection of these features in
Tycho's SNR with the coming generation of X-ray polarimeters such as the
Imaging X-ray Polarimetry Explorer (IXPE).
