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Supernova Remnants (SNRs) shocks are believed to accelerate charged particlesand to generate strong turbulence in the post-shock flow. From high-energyobservations in the past decade, a magnetic field at SNR shocks largelyexceeding the shock-compressed interstellar field has been inferred. We outlinehow such a field amplification results from a small-scale dynamo processdownstream of the shock, providing an explicit expression for the turbulenceback-reaction to the fluid whirling. The spatial scale of the $X-$ray rims andthe short time-variability can be obtained by using reasonable parameters forthe interstellar turbulence. We show that such a vortical field saturation isfaster than the acceleration time of the synchrotron emitting energeticelectrons.

Vortical field amplification and particle acceleration at rippled shocks