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We present the results of time dependent two-fluid cosmic-ray (CR) mediated MHD shock simulations. The calculations were carried out with a new numerical code for {1-D} ideal MHD. By coupling this code with the CR energy transport equation we can simulate the time dependent evolution of MHD shocks including the acceleration of the CR and their backreaction on the shock structures. In these models the different rates of CR diffusion parallel and perpendicular to the magnetic field are accounted for.
We present results which map the dynamical time-asymptotic shock driven CR acceleration efficiency as a function of the tangential magnetic field strength and upstream angle between the field and the shock normal, $\theta_B$. We have also explored the effect of the plasma $\beta$ on the CR acceleration efficiency. We find that for the efficiency is most strongly reduced for large tangential field components and low $\beta$. In particular it appears to be the tangential field strength and not $\theta_B$ which is the crucial parameter.
We have also explored time dependent properties of the CR mediated MHD shocks, including modifications due to nonlinear generation of downstream magnetic pressure and the introduction of slow mode shocks.
This work was supported in part by NASA, the NSF and the University of Minnesota Supercomputer Institute.
