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Both observational evidence and theoretical considerations from MHDsimulations of jets suggest that the relativistic jets of active galacticnuclei (AGN) are radially stratified, with a fast inner spine surrounded by aslower-moving outer sheath. The resulting relativistic shear layers are a primecandidate for the site of relativistic particle acceleration in the jets of AGNand gamma-ray bursts (GRBs). In this article, we present outcomes ofparticle-in-cell simulations of magnetic-field generation and particleacceleration in the relativistic shear boundary layers (SBLs) of jets in AGNand GRBs. We investigate the effects of inverse Compton cooling on relativisticparticles that are accelerated in the SBLs of relativistic jets including theself-consistent calculation of the radiation spectrum produced by inverseCompton scattering of relativistic electrons in an isotropic external softphoton field. We find that the Compton cooling can be substantial, depending onthe characteristic energy (blackbody temperature and energy density) of theexternal radiation field. The produced Compton emission is highly anisotropicand more strongly beamed along the jet direction than the characteristic$1/\Gamma$ pattern expected from intrinsically isotropic emission in thecomoving frame of an emission region moving along the jet with bulk Lorentzfactor $\Gamma$. We suggest that this may resolve the long-standing problem ofthe Doppler Factor Crisis.

Inverse Compton Emission and Cooling of Relativistic Particles Accelerated at Shear Boundary Layers in Relativistic Jets