Particle Acceleration in Shearing Flows: Efficiencies and Limits

We examine limits to the efficiency for particle acceleration in shearing flows, showing that relativistic flow speeds are required for efficient gradual shear acceleration. We estimate maximum achievable particle energies for parameters applicable to the relativistic jets of active galactic nuclei. The implications of our estimates is that if large-scale jets are relativistic, then efficient electron acceleration up to several PeV and proton acceleration up to several EeV energies appears feasible. This suggests that shear particle acceleration could lead to a continued energization of synchrotron X-ray emitting electrons, and be of relevance for the production of ultra-high-energy cosmic-ray particles.