Spectral universality of strong shocks accelerating charged particles

As a rule, the shock compression controls the spectrum of diffusively accelerated particles. We argue that this is not so if the backreaction of these particles on the shock structure is significant. We present a self-similar solution in which the accelerated particles change the flow structure near the shock so strongly that the total shock compression may become arbitrarily large. Despite this, the energy spectrum behind the shock is close to E^{-3/2} independently of anything at all.