Inductive acceleration of ultra-high energy cosmic rays

Ultra high energy cosmic rays (UHECRs) are charged particles that have energy in excess of 1018 eV and are mostly of extra-galactic origin. Their astrophysical origin and the acceleration mechanisms are still unknown, 50 years after their discovery and 100 years after cosmic rays in general were first identified. Lower energy cosmic rays (CRs), up to approximately 1015 eV ( the knee ) are of galactic origin, presumably accelerated in supernova remnants. The UHECRs above the ankle at 1018 eV can\u27t be contained by the Galactic magnetic field and are thus extragalactic. Considerable progress in CR research has recently been stimulated by the construction and the successful operation of the Pierre Auger observatory. Among the key yearly results is the correlation of the arrival directions of the UHECRs with the large scale structure, though the precise nature of the acceleration sites remains unknown. Noteworthy, a large number of UHECRs come from the direction of Cen A, the nearest AGN. The most commonly suggested mechanism of CR acceleration, initially due to Fermi, suggests that particles gain energy stochastically, by experiencing multiple scatterings off magnetohydrodynamic turbulence. Thus, the rate of the acceleration is low. In this work we investigate an alternative novel mechanism, specific to the UHECRs. We point out that relativistic outflows carrying large scale magnetic field have large inductive potential and may accelerate protons to ultra-high energies. We suggest that magnetized jets of Active Galactic Nuclei (AGN) can accelerate UHECRs via regular energy gain in the inductive electric fields. Cyclotron motion of a CR particle in a sheared magnetic field may become unstable for sufficiently large Larmor radii, comparable with the shear scales. As an unbound particle crosses the jet, it gains the inductive potential square root(L/c), where L is the Poynting luminosity of a jet. Key features of the mechanism are that (i) highest rigidity cosmic rays are accelerated most efficiently; (ii) maximum possible acceleration rate does reach the inverse relativistic gyro-frequency. In this work we study the kinetic motion of the UHECRs in realistic electromagnetic configurations of astrophysical jets. The key issue is the condition for particle motion to become unstable: large energy gains require stronger magnetic fields, which reduce the Larmor radius and make the motion more stable (bound). We find that large energy gains, more than an order of magnitude, are indeed possible for generic profiles of the magnetic field and the velocity shear inside the jet. On the other hand, the CRs that gained the full jet potential are typically beamed along the jet direction – this poses a problem, e.g., in the case of Cen A, whose jets are directed at large angles to the line of sight