Jones and Kang (2005a) present initial simulation results for the time evolution of CR modified plane parallel shocks in magneto-hydro-dynamical flows. The simulations utilize very efficient 'Coarse Grained finite Momentum Volume' (CGMV) transport scheme (Jones and Kang, 2005b). The simulations aim to explore nonlinear feedback among the particles, the wave turbulence, and the bulk flows. The calculations incorporate self-consistent treatment of the momentum-dependent CR diffusion- convection equation and, as it assumed by Jones and Kang (2005a), will soon be coupled with wave action equations for resonantly scattering Alfven and fast mode waves, also treated through the CGMV scheme.

Jones and Kang (2005a) note that the physics of strong, CR modified shocks is complex and nonlinear; through diffusive shock acceleration, CR can capture a major portion of the energy flux through the shocks, greatly modifying the shock dynamics and structures in the process (e.g., Webb et al., 1986; Baring et al., 1993; Frank et al., 1995; Berezhko and Volk, 2000; Bell and Lucek, 2001). CR

propagation in and around the shocks is mediated by the presence of the large-scale magnetic field and by resonant scattering on MHD waves, which are usually considered as Alfven wave turbulence. Most, but not all, theoretical treatments of CR modified shocks assume a fixed CR scattering or diffusion law, and commonly the dynamical roles of the wave turbulence and the large scale magnetic field are ignored. On the other hand, a key feature of diffusive shock acceleration is that the relevant wave turbulence is strongly amplified by streaming CR near the shock (Bell, 1978). As a consequence, it can contribute a significant pondermotive force on the bulk plasma flow, and its dissipation upstream of the classical gas sub-shock structure can preheat the upstream plasma, which also modifies the character of the shock transition. Lucek and Bell (2000), for example, have argued that the streaming instability can enhance the scattering waves so much that the scattering length is orders of magnitude less than expressed by Bohm diffusion using the upstream magnetic field. This has led several authors to argue that CR acceleration can be much more rapid than usually described (e.g., Bell and Lucek, 2001; Ptuskin and Zirakashvili, 2003). Furthermore, the scattering turbulence is likely to be anisotropic, which, among other things, can mean that the effective motion of the scattering centers will not match the motion of the bulk plasma, as usually assumed. For instance, Alfven waves amplified by the streaming instability may be expected to propagate with respect to the bulk plasma along the large scale magnetic field at approximately the Alfven speed. Since the Alfven speed variations normal to the shock structure are not the same as the gas speed variations, this may modify the properties of diffusive shock acceleration through the shock (McKenzie and Volk, 1982; Jones, 1993). It is clearly important to carry out theoretical studies of the diffusive shock acceleration that can incorporate the physical processes just outlined. Jones and Kang (2005a) conclude that recent advances in MHD turbulence theory require a broadened outlook on scattering processes in CR modified shocks. The paper of Jones and Kang (2005a) reports initial steps in an effort to do just that.

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