Microphysics of Diffusive Shock Acceleration: Impact on the Spectrum of Accelerated Particles

Diffusive shock acceleration at collisionless shocks remains the most likely process for accelerating particles in a variety of astrophysical sources. While standard prediction strong is that spectrum accelerated universal, $f(p)\propto p^{-4}$, numerous phenomena affect this simple conclusion. In general, non-linear dynamical reaction leads to concave spectrum, steeper than $p^{-4}$ momenta below few tens GeV/c and harder high energies. However, effects become important presence magnetic field amplification, which turn higher values maximum momentum $p_{max}$. It was recently discovered self-generated perturbations enhance particle scattering, when advected downstream, move same direction as background plasma, so effective compression factor decreases becomes steeper. We investigate implications excitation non-resonant streaming instability on these spectral deformations, dependence steepening velocity role played by injection momentum.