Shock modification by cosmic-ray-excited turbulences

In cosmic-ray-mediated shocks large amplitude Alfvén waves are believed to be generated by accelerated cosmic ray particles. The enhanced magnetic pressure shared by these waves is non-negligible in the momentum and energy balances across the shock transition region. Accordingly the shock Rankine-Hugoniot condition is further modified, and the compression ratio across the shock departs from the classical values of 4 (nonrelativistic) and 7 (relativistic). We argue that in the 'grand equipartition' limit, namely equipartition among the waves, the background plasma, and the cosmic ray particles, the compression ratio recovers to the value of 4, and the corresponding spectral index of cosmic ray particles also comes back to the canonical value of 2.