Particle Diffusion and Acceleration by Shock Waves in Magnetized Filamentary Turbulence

We expand the off-resonant scattering theory for particle diffusion in magnetized current filaments that can be typically compared to astrophysical jets, including active galactic nucleus jets. In a high plasma β region where the directional bulk flow is a free-energy source for establishing turbulent magnetic fields via current filamentation instabilities, a novel version of quasi-linear theory to describe the diffusion of test particles is proposed. The theory relies on the proviso that the injected energetic particles are not trapped in the small-scale structure of magnetic fields wrapping around and permeating a filament but deflected by the filaments, to open a new regime of the energy hierarchy mediated by a transition compared to the particle injection. The diffusion coefficient derived from a quasi-linear type equation is applied to estimating the timescale for the stochastic acceleration of particles by the shock wave propagating through the jet. The generic scalings of the achievable highest energy of an accelerated ion and electron, as well as of the characteristic time for conceivable energy restrictions, are systematically presented. We also discuss a feasible method of verifying the theoretical predictions. The strong, anisotropic turbulence reflecting cosmic filaments might be the key to the problem of the acceleration mechanism of the highest energy cosmic rays exceeding 100 EeV (1020 eV), detected in recent air shower experiments.