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Recent observations of greatly amplified magnetic fields ($\delta B/B\sim100$) around supernova shocks are consistent with the predictions of thenon-linear theory of particle acceleration (NLT), if the field is generatedupstream of the shock by cosmic ray induced streaming instability. The highacceleration efficiencies and large shock modifications predicted by NLT needhowever to be mitigated to confront observations, and this is usually assumedto be accomplished by some form of turbulent heating. We show here thatmagnetic fields with the strength inferred from observations have an importantdynamical role on the shock, and imply a shock modification substantiallyreduced with respect to the naive unmagnetized case. The effect appears as soonas the pressure in the turbulent magnetic field becomes comparable with thepressure of the thermal gas. The relative importance of this unavoidable effectand of the poorly known turbulent heating is assessed. More specifically weconclude that even in the cases in which turbulent heating may be of someimportance, the dynamical reaction of the field cannot be neglected, as insteadis usually done in most current calculations.

Dynamical effects of self-generated magnetic fields in cosmic ray modified shocks