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We investigate the acceleration of particles by Alfv ́en waves via the second-order Fermi process in the lobes of giant radio galaxies. Such sites are candidates for the accelerators of ultra-high-energy cosmic rays (UHECR). We focus on the nearby Fanaroff–Riley type I radio galaxy Centaurus A. This is motivated by the coincidence of its position with the arrival direction of several of the highest energy Auger events. The conditions necessary for consistency with the acceleration time-scales predicted by quasi-linear theory are reviewed. Test particle calculations are performed in fields which guarantee electric fields with no component parallel to the local magnetic field. The results of quasi-linear theory are, to an order of magnitude, found to be accurate at low turbulence levels for non-relativistic Alfven waves and at both low and high turbulence levels in the mildly relativistic case. We conclude that for pure stochastic acceleration via Alfv ́en waves to be plausible as the generator of UHECR in Cen A, the baryon number density would need to be several orders of magnitude below currently held upper limits.
O'Sullivan, S., Reville, B. and Taylor, A. Stochastic particle acceleration in the lobes of giant radio galaxies. Monthly Notices of the Royal Astronomical Society Volume 400, Issue 1, pages 248–257, November 2009 doi: 10.1111/j.1365-2966.2009.15442.x