UHECR Acceleration in Dark Matter Filaments of Cosmological Structure Formation

A mechanism for proton acceleration to ∼ 1021eV is suggested. It may operate in accretion flows onto thin dark matter filaments of cosmic structure formation. The flow compresses the ambient magnetic field to strongly increase and align it with the filament. Particles begin the acceleration by E × B drifting with the accretion flow. The energy gain in the drift regime is limited by the conservation of the adiabatic invariant p⊥/B(r). Upon approaching the filament, the drift turns into the gyro-motion around the filament so that the particle moves parallel to the azimuthal electric field. In this ’betatron’ regime the acceleration speeds up to rapidly reach the electrodynamic limit cpmax = eBR for an accelerator with magnetic field B and the orbit radius R (Larmor radius). The periodic orbit becomes unstable and the particle slings out of the filament to the region of a weak (uncompressed) magnetic field, which terminates the acceleration. To escape the filament, accelerated particles must have gyro-radii comparable with the filament radius. Therefore, the mechanism requires pre-acceleration that is likely to occur in structure formation shocks upstream or nearby the filament accretion flow. Previous studies identify such shocks as efficient proton accelerators to a firm upper limit ∼ 1019.5eV placed by the catastrophic photo-pion losses. The present mechanism combines explosive energy gain in its final (betatron) phase with prompt particle release from the region of strong magnetic field. It is this combination that allows protons to overcome both the photo-pion and the synchrotron-Compton losses and therefore attain energy ∼ 1021eV . A customary requirement on accelerator power to reach a given Emax, which is placed by the accelerator energy dissipation ∝ E2 max/Z0 due to the finite vacuum impedance Z0, is lifted by the cyclic operation of the accelerator.