Cosmic ray acceleration at supergalactic accretion shocks: a new upper energy limit due to a finite shock extension

Accretion flows onto supergalactic-scale structures are accompanied with large spatial scale shock waves. These shocks were postulated as possible sources of ultra-high energy cosmic rays. The highest particle energies were expected for perpendicular shock configuration in the so-called "Jokipii diffusion limit", involving weakly turbulent conditions in the large-scale magnetic field imbedded in the accreting plasma. For such configuration we discuss the process limiting the highest energy that particles can obtain in the first-order Fermi acceleration process due to finite shock extensions to the sides, along and across the mean magnetic field. Cosmic ray outflow along the shock structure can substantially lower (below ~10^18 eV for protons) the upper particle energy limit for conditions considered for supergalactic shocks.