Particle acceleration at shocks in relativistic jets

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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.