  The non-thermal acceleration of particles in magnetohydrodynamic (MHD)
turbulence plays a central role in a wide variety of astrophysical sites. This
physics is addressed here in the context of a strong turbulence, composed of
coherent structures rather than waves, outside the realm of quasilinear theory.
The present description tracks the momentum of the particle along its history
through a sequence of (non-inertial) frames in which the electric field
vanishes, in the spirit of the original Fermi scenario. It thus connects the
sources of energy gain (or loss) to the gradients of the velocity of the
magnetic field lines, in particular the acceleration and the shear of their
velocity flow projected along the field line direction, as well as their
compression in the transverse plane. Momentum diffusion coefficients associated
to these different contributions are expressed as a function of the power
spectrum of those velocity fluctuations. Importantly, those velocity gradients
are subject to intermittency: they are spatially localized and their strengths
obey powerlaw distributions, as demonstrated through direct measurements in the
incompressible MHD simulation of the Johns Hopkins University database. This
intermittency impacts the acceleration process in a significant way, which
opens up prospects for a rich phenomenology, in particular non-thermal spectra
with extended powerlaw tails. Those findings generally agree with recent
kinetic numerical simulations. Extensions to this description and possible
avenues of exploration are discussed.
