The maximum momentum of particles accelerated at cosmic ray modified shocks

Particle acceleration at non-relativistic shocks can be very efficient, leading to the appearance of non-linear effects due to the dynamical reaction of the accelerated particles on the shock structure and to the non-linear amplification of the magnetic field in the shock vicinity. The value of the maximum momentum, p(max), in these circumstances cannot be estimated using the classical results obtained within the framework of test-particle approaches. We provide here the first attempt at estimating p(max) in the cosmic ray modified regime, taking into account the non-linear effects mentioned above.