Particle acceleration at shocks in relativistic jets

The theory of particle acceleration at shock fronts is briefly reviewed, with special emphasis on the production of the particles responsible for the nonthermal emission from blazars. The flat radio/IR spectra of these sources cannot be produced by diffusive acceleration at a simple nonrelativistic shock front propagating in a homogeneous medium. It can, however, be produced by a single unmodified mildly relativistic shock, if the pressure in the shocked gas is provided by the leptonic component, or, independently of the equation of state, by a relativistic shock which is oblique to the magnetic field. The analytic theory of these shocks makes several simplifications, but Monte-Carlo simulations exist which extend the range of validity. Of particular interest is acceleration in a tangled magnetic field. Here, however, the Monte-Carlo simulations have not yet yielded unambiguous results. The "homogeneous" models of blazar emission are discussed, and is it shown that they imply a geometry of the emitting region which is laminar in form, with an aspect ratio of d/R< 3% in the case of Mkn~421. Identifying these with relativistic shock fronts, a model of acceleration is described, which displays characteristic variations in the synchrotron spectral index with intensity.