Particle acceleration and turbulence in cosmic Ray shocks: possible pathways beyond the Bohm limit

Abstract

Diffusive shock acceleration is discussed in terms of its potential to accelerate cosmic rays (CR) to 1018 eV (beyond the “knee,” as observations suggest) and in terms of the related observational signatures (spectral features). One idea to reach this energy is to resonantly generate a turbulent magnetic field via accelerated particles much in excess of the background field. We identify difficulties with this scenario and suggest two separate mechanisms that can work in concert with one another leading to a significant acceleration enhancement.The first mechanism is based on a nonlinear modification of the flow ahead of the shock supported by particles already accelerated to some specific (knee) momentum. The particles gain energy by bouncing off converging magnetic irregularities frozen into the flow in the shock precursor and not so much by re‐crossing the shock itself. The acceleration rate is determined by the gradient of the flow velocity and turns out to be formally independent of the particle mean free path. The velocity gradient is set by the knee‐particles. The acceleration rate of particles above the knee does not decrease with energy, unlike in the linear acceleration regime. The knee (spectrum steepening) forms because particles above it are effectively confined to the shock only if they are within limited domains in the momentum space, while other particles fall into “loss‐islands”, similar to the “loss‐cone” of magnetic traps. This also maintains the steep velocity gradient and high acceleration rate.The second mechanism is based on the generation of Alfven waves at the gyroradius scale at the background field level, with a subsequent transfer to longer scales via interaction with strong acoustic turbulence in the shock precursor. The acoustic turbulence in turn, may be generated by Drury instability or by parametric instability of the Alfven (A) waves.