We use 2D and 3D hybrid (kinetic ions - fluid electrons) simulations to
investigate particle acceleration and magnetic field amplification at
non-relativistic astrophysical shocks. We show that diffusive shock
acceleration operates for quasi-parallel configurations (i.e., when the
background magnetic field is almost aligned with the shock normal) and, for
large sonic and Alfv\'enic Mach numbers, produces universal power-law spectra
proportional to p^(-4), where p is the particle momentum. The maximum energy of
accelerated ions increases with time, and it is only limited by finite box size
and run time. Acceleration is mainly efficient for parallel and quasi-parallel
strong shocks, where 10-20% of the bulk kinetic energy can be converted to
energetic particles, and becomes ineffective for quasi-perpendicular shocks.
Also, the generation of magnetic turbulence correlates with efficient ion
acceleration, and vanishes for quasi-perpendicular configurations. At very
oblique shocks, ions can be accelerated via shock drift acceleration, but they
only gain a factor of a few in momentum, and their maximum energy does not
increase with time. These findings are consistent with the degree of
polarization and the morphology of the radio and X-ray synchrotron emission
observed, for instance, in the remnant of SN 1006. We also discuss the
transition from thermal to non-thermal particles in the ion spectrum
(supra-thermal region), and we identify two dynamical signatures peculiar of
efficient particle acceleration, namely the formation of an upstream precursor
and the alteration of standard shock jump conditions.Comment: 21 pages, 14 figures, Minor changes reflecting the version accepted
to Ap