Inductive acceleration of UHECRs in sheared relativistic jets

(Abridged)Relativistic outflows carrying large scale magnetic fields have large inductive potential and may accelerate protons to ultra high energies. We discuss a novel scheme of Ultra-High Energy Cosmic Ray (UHECR) acceleration due to drifts in magnetized, cylindrically collimated, sheared jets of powerful active galaxies (with jet luminosity $\geq 10^{46}$ erg s$^{-1}$). We point out that a positively charged particle carried by such a plasma is in an unstable equilibrium if ${\bf B} \cdot \nabla \times {\bf v}< 0$, so that kinetic drift along the velocity shear would lead to fast, {\it regular} energy gain. We show that if a seed of pre-accelerated particles with energy below the ankle $\leq 10^{18}$ eV is present, these particles can be boosted to energies above $ 10^{19}$ eV. A key feature of the mechanism is that the highest rigidity particles are accelerated most efficiently implying the dominance of light nuclei for energies above the ankle in our model: from a mixed population of pre-accelerated particle the drift mechanism picks up and boosts protons preferably. In addition, after a particle traversed large fraction of the available potential, its Larmor radius becomes of the order of the jet thickness. In this case, {\it the maximum possible acceleration rate of inverse relativistic gyro-frequency is achieved} and a particle finally become unconfined and leave the jet.