Nonlinear particle acceleration at nonrelativistic shocks

I will review the theory of diffusive shock acceleration (DSA) with an emphasis on the role of escaping particles. There is convincing evidence that supernova remnant shocks can produce cosmic rays (CRs) with high efficiency and the most likely acceleration mechanism is DSA. If the acceleration is efficient, nonlinear effects will be important and, in DSA, these effects include a modification of the shock structure from the backpressure of CRs, an amplification of the ambient magnetic field above simple compression, and the production of a sizable flux of the highest energy CRs which escape upstream. Since all of these processes are strongly coupled, semi-analytical or fully numerical techniques are required to describe the important nonlinear effects. I will show some recent Monte Carlo results where the escaping particle flux is calculated explicitly and where the particle diffusion coefficient is determined in self-generated magnetic turbulence. These results will be compared to other models of nonlinear DSA. (author)