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Accretion flows onto supergalactic-scale structures are accompanied withlarge spatial scale shock waves. These shocks were postulated as possiblesources of ultra-high energy cosmic rays. The highest particle energies wereexpected for perpendicular shock configuration in the so-called "Jokipiidiffusion limit", involving weakly turbulent conditions in the large-scalemagnetic field imbedded in the accreting plasma. For such configuration wediscuss the process limiting the highest energy that particles can obtain inthe first-order Fermi acceleration process due to finite shock extensions tothe sides, along and across the mean magnetic field. Cosmic ray outflow alongthe shock structure can substantially lower (below ~10^18 eV for protons) theupper particle energy limit for conditions considered for supergalactic shocks.Comment: A&A, accepte

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