Hydrodynamic approach to cosmic ray acceleration

To study the structure and dynamics of a cosmic-ray-plasma system, hydrodynamic approach is a fairly good approximation. In this approach, there are three basic energy transfer mechanisms: work done by the plasma flow against pressure gradients, cosmic ray streaming instability and stochastic acceleration. The interplay between these mechanisms gives a range of structures. We present some results of different version of the hydrodynamic approach, e.g., flow structure, injection, instability, acceleration with and without shocks.