Turbulence Particle Acceleration and UHECR

The standard model to produce non-thermal particles is the particle acceleration at shocks. However, the photon spectra in high-energy objects, such as blazars, frequently show very hard feature, which seems inconsistent with the standard shock acceleration theory. The alternative model is the particle acceleration by turbulence. If we adopt a hard-sphere-like acceleration, in which the acceleration timescale is independent of the particle energy, the electron energy distribution becomes consistent with blazar photon spectra. Adopting this model to the deceleration phase of gamma-ray burst jets, ultra high-energy cosmic-rays can be produced. The resultant spectrum is harder than other models, so that the secondary neutrino production in their propagation is relatively suppressed. As a candidate of the hard-sphere acceleration mechanism, we propose the acceleration by large scale compressible MHD waves, where the transit time damping (TTD) is a key mechanism. We find that the acceleration efficiency is higher than previously considered.