A structure and energy dissipation efficiency of relativistic   reconfinement shocks
  We present a semi-analytical hydrodynamical model for the structure of reconfinement shocks formed in astrophysical relativistic jets interacting with external medium. We take into account exact conservation laws, both across the shock front and in the zone of the shocked matter, and exact angular relations. Our results confirm a good accuracy of the approximate formulae derived by Komissarov & Falle (1997). However, including the transverse pressure gradient in the shocked jet, we predict an absolute size of the shock to be about about twice larger. We calculate the efficiency of the kinetic energy dissipation in the shock and show a strong dependence on both the bulk Lorentz factor and opening angle of the jet. 
Krzysztof Nalewajko and Marek Sikora (Nicolaus Copernicus Astronomical   Center)