UHECR Acceleration at Filaments of Cosmological Structure Formation

A mechanism of particle acceleration to $\sim10^{21}eV$ is suggested. It operates in accretion flows around thin DM filaments of cosmic structure formation. The magnetic field is compressed by the flow to become nearly parallel to the filament. Initially, particles $\mathbf{E}\times\mathbf{B}$ drift towards the filament in the azimuthal electric field $\mathbf{E}$. Upon approaching the filament, the particle \emph{drift} changes to a nearly \emph{circular} rotation around the filament, i.e. along the motion electric field. In this ``betatron'' acceleration regime the electrodynamic limit on the particle energy $cp_{max}=eBR$ in an accelerator with the orbit radius $R$ and magnetic field $B$, is reached very rapidly. As soon as $p$ exceeds $p_{max}$, the particle slings out of the filament to the region of a weak (uncompressed) magnetic field and the acceleration is terminated. The mechanism is a re-acceleration that operates on particles with the required initial energy. Particle pre- acceleration is likely to occur in structure formation shocks. Such shocks are efficient proton accelerators to a firm upper limit $\sim10^{19.5}eV$ placed by the catastrophic photo-pion losses. The suggested mechanism, being explosive in its betatron phase, has a potential to overcome the losses and boost protons to $\sim10^{21}eV$.