32ND I NTERNATIONAL COSMIC RAY CONFERENCE,BEIJING 2011 UHECR Acceleration around Filaments of Cosmological Structure Formation M. A. MALKOV 1 , R.Z. SAGDEEV 2 AND P.H. DIAMOND 1 1 CASS and Department of Physics, University of California, San Diego, La Jolla, CA 92093 2 University of Maryland, College Park, Maryland 20742-3280, USA mmalkov@ucsd.edu Abstract: A mechanism for proton acceleration to ∼ 10 21 eV 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 the E × B drift with the accretion flow. The energy gain in the drift regime is limited by the conservation of the adiabatic invariant p 2 ⊥ /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 cp max = 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 ∼ 10 19.5 eV 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 ∼ 10 21 eV . Keywords: ultra high energy cosmic rays, particle acceleration, accretion, astrophysical fluid dynamics Introduction To identify the UHECR sources it is neces- sary to test the putative extragalactic accelerators for their capability to accelerate protons beyond 10 20 eV. Possible sites of the UHECR acceleration are the cosmic structure formation shocks. Remarkably, the diffusive shock accel- eration mechanism falls short by one order of magnitude to produce particles in such shocks with the highest energy observed, i.e. a few 10 20 eV [4, 1]. Below we demonstrate that protons accelerated in the struc- ture formation shocks to ∼ 10 19.5 eV can be boosted to 10 21 eV inside the same accretion flow. The suggested mechanism accelerates particles much faster than the DSA, thus sustaining against losses. It operates in plasmas ac- creting on to the gravitating dark matter (DM) filaments. Filaments, along with pancakes and knots are important el- ements of the cosmic structure formation which was estab- lished in a number of simulations (e.g., [5]). Accretion flow According to the the ΛCDM simulations, the gravitationally interacting dark matter (DM) particles aggregate to form a structure which then gravitationally drives conducting gas with the frozen in magnetic field. The matter accrets onto sheets, filaments and nodes and is thus organized in a “cosmic web” of massive nodes con- nected by filaments along which the matter flows towards nearby nodes. The rest of the space can be considered as low density, low magnetic field “voids”, e.g. [5]. Turning to the particle acceleration in such structures, we focus on a single filament with two nodes at its ends (a ’dumbbell’), Fig.1. Strong flow compression near the knots creates magnetic mirrors that confine energetic particles in the field-filament direction. A rarefied plasma accrets onto the filament from the surrounding void and stream then to- wards the nodes, while partially the plasma accrets onto the nodes directly from the void. It is not unreasonable to as- sume that, at least in some cases, the field is well aligned with the filament [3]. Particle acceleration in filaments Consider a DM fila- ment of radius R f that accrets intergalactic gas in radial di- rection. We specify the magnetic field B as B =(0, 0, −B) with B (r) depending only on r =  x 2 + y 2 , the distance to the filament axis (z-axis), while particle motion in z- direction is constrained by magnetic mirrors near the fil- ament end nodes, so that the dynamics of accelerated par- ticles is nearly perpendicular to B, i.e. p ‖ ≪ p ⊥ ≈ p. The equations of motion in the polar coordinates (r , ϑ ) on the (x, y) plane read