The Evolution of Shocks in Blazar Jets
  We consider the shock structures that can arise in blazar jets as a consequence of variations in the jet flow velocity. There are two possible cases: (1) A double shock system consisting of both a forward and reverse shock (2) A single shock (either forward or reverse) together with a rarefaction wave. These possibilities depend upon the relative velocity of the two different sections of jet. Using previously calculated spherical models for estimates of the magnetic field and electron number density of the emission region in the TeV blazar Markarian 501, we show that this region is in the form of a thin disk, in the plasma rest frame. It is possible to reconcile spectral and pair opacity constraints for MKN 501 for Doppler factors in the range of 10--20. This is easiest if the corrections for TeV absorption by the infrared background are not as large as implied by recent models. 
G.V. Bicknell and S.J. Wagner