We have calculated the cosmic ray(CR) acceleration at young remnants from Type Ia supernovae expanding into a uniform interstellar medium(ISM). Adopting quasi-parallel magnetic fields, gasdynamic equations and the diffusion convection equation for the particle distribution function are solved in a comoving spherical grid which expands with the shock. Bohm-type diffusion due to self-excited Alfven waves, drift and dissipation of these waves in the precursor and thermal leakage injection were included. With magnetic fields amplified by the CR streaming instability, the particle energy can reach up to 1016Z eV at young supernova remnants(SNRs) of several thousand years old. The fraction of the explosion energy transferred to the CR component asymptotes to 40-50 % by that time. For a typical SNR in a warm ISM, the accelerated CR energy spectrum should exhibit a concave curvature with the power-law slope flattening from 2 to 1.6 at E ≳ 0.1 TeV.

Clusters of galaxies are storage rooms of cosmic rays. They confine the hadronic component of cosmic rays over cosmological time scales due to diffusion, and the electron component due to energy losses. Hadronic cosmic rays can be accelerated during the process of structure formation, because of the supersonic motion of gas in the potential wells created by dark matter. At the shock waves that result from this motion, charged particles can be energized through the first order Fermi process. After discussing the most important evidences for non-thermal phenomena in large scale structures, we describe in some detail the main issues related to the acceleration of particles at these shock waves, emphasizing the possible role of the dynamical backreaction of the accelerated particles on the plasmas involved.

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc ≳ 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that 10-4 - 10-3 of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The CR acceleration efficiency increases with shock Mach number, but it asymptotes to ~50% in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks (Ms ≲ 5), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to ~ 1015 eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that 10-4 - 10-3 of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies ~ 50%, regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

In order to explore the cosmic ray acceleration at the cosmological shocks, we have performed numerical simulations of one-dimensional, plane-parallel, cosmic ray (CR) modified shocks with the newly developed CRASH (Cosmic Ray Amr SHock) numerical code. Based on the hypothesis that strong Alfven waves are self-generated by streaming CRs, the Bohm diffusion model for CRs is adopted. The code includes a plasma-physics-based 'injection' model that transfers a small proportion of the thermal proton flux through the shock into low energy CRs for acceleration there. We found that, for strong accretion shocks with Mach numbers greater than 10, CRs can absorb most of shock kinetic energy and the accretion shock speed is reduced up to 20%, compared to pure gas dynamic shocks. Although the amount of kinetic energy passed through accretion shocks is small, since they propagate into the low density intergalactic medium, they might possibly provide acceleration sites for ultra-high energy cosmic rays of E > 10 18eV. For internal/merger shocks with Mach numbers less than 3, however, the energy transfer to CRs is only about 10-20% and so nonlinear feedback due to the CR pressure is insignificant. Considering that intracluster medium (ICM) can be shocked repeatedly, however, the CRs generated by these weak shocks could be sufficient to explain the observed non-thermal signatures from clusters of galaxies.

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.

Cosmic-ray acceleration, although physically important in many astrophysical contexts, is difficult to incorporate into numerical models,. because it involves microphysics that is generally far from thermodynamic equilibrium, and also because the length and time scales for that physics typically range over many orders of magnitude, reflecting the huge range of particle rigidities that must be represented. The most common accelerator models are stochastic in nature and involve nonequilibrium plasma properties that are also often poorly understood. Still, nature clearly finds a way to produce simple, robust and almost scale-free energy distributions for the cosmic-rays. Their importance has inspired a number of approaches to examining the production and transport of cosmic-ray particles in numerical simulations. I offer here a brief comparison of some of the methods that have been introduced.