  Supernova Remnants (SNRs) shocks are believed to accelerate charged particles
and to generate strong turbulence in the post-shock flow. From high-energy
observations in the past decade, a magnetic field at SNR shocks largely
exceeding the shock-compressed interstellar field has been inferred. We outline
how such a field amplification results from a small-scale dynamo process
downstream of the shock, providing an explicit expression for the turbulence
back-reaction to the fluid whirling. The spatial scale of the $X-$ray rims and
the short time-variability can be obtained by using reasonable parameters for
the interstellar turbulence. We show that such a vortical field saturation is
faster than the acceleration time of the synchrotron emitting energetic
electrons.
