Critical self-organization of astrophysical shocks

There are two distinct regimes of the first order Fermi acceleration at shocks. The first is a linear (test particle) regime in which most of the shock energy goes into thermal and bulk motion of the plasma. The second is an efficient regime when it goes into accelerated particles. Although the transition region between them is narrow, we identify the factors that drive the system to a {\it self-organized critical state} between those two. Using an analytic solution, we determine this critical state and calculate the spectra and maximum energy of accelerated particles.