Inductive acceleration of UHECRs in sheared relativistic jets

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 ⩾1046⩾1046 erg s−1). We point out that a positively charged particle carried by such a plasma is in an unstable equilibrium if B·∇×v<0B·∇×v<0, so that kinetic drift along the velocity shear would lead to fast, regular   energy gain. This can be achieved in an axially inhomogeneous jet through gradient drift induced by propagation of inertial Alfvén waves along the jet. We show that if a seed of pre-accelerated particles with energy below the ankle ⩽1018eV is present, these particles can be boosted to energies above 1019eV. A key feature of the mechanism is that the highest rigidity (ratio of energy to charge) 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, the maximum possible acceleration rate of inverse relativistic gyro-frequency is achieved   and a particle finally become unconfined and leave the jet. The power-law spectrum of the resulting UHE particles flattens with time and asymptotically may become ∝E-2∝E-2. The real injection spectrum depends on the distribution of pre-accelerated particles inside a jet and, in case of contribution from many sources, on the distribution of total potential drop.We also point out that astrophysical schemes based on DC-type acceleration (by electric field parallel to or larger than magnetic field) cannot have potentials larger than ∼1015V and thus fell short by many orders of magnitude to produce UHECRs.