  The process of diffusive acceleration of charged particles in shocked plasmas
is widely invoked in astrophysics to account for the ubiquitous presence of
signatures of non-thermal relativistic electrons and ions in the universe. A
key characteristic of this statistical energization mechanism is the absence of
a momentum scale; astrophysical systems generally only impose scales at the
injection (low energy) and loss (high energy) ends of the particle spectrum.
The existence of structure in the cosmic ray spectrum (the "knee") at around
3000 TeV has promoted contentions that there are at least two origins for
cosmic rays, a galactic one supplying those up to the knee, and even beyond,
and perhaps an extragalactic one that can explain even the ultra-high energy
cosmic rays (UHECRs) seen at 1-300 EeV. Accounting for the UHECRs with familiar
astrophysical sites of acceleration has historically proven difficult due to
the need to assume high magnetic fields in order to reduce the shortest
diffusive acceleration timescale, the ion gyroperiod, to meaningful values. Yet
active galaxies and gamma-ray bursts remain strong and interesting candidate
sources for UHECRs, turning the theoretical focus to relativistic shocks. This
review summarizes properties of diffusive shock acceleration that are salient
to the issue of UHECR generation. These include spectral indices, acceleration
efficencies and timescales, as functions of the shock speed and mean field
orientation, and also the nature of the field turbulence. The interpretation of
these characteristics in the context of gamma-ray burst models for the
production of UHECRs is also examined.

Astrophysics