  Nonthermal 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, beyond the realm of quasilinear theory. The
present description tracks the momentum of the particle through a sequence of
frames in which the electric field vanishes, in the spirit of the original
Fermi scenario. It 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. Those
velocity gradients are subject to strong intermittency: they are spatially
localized and their strengths obey power law 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, the momentum distribution, which is here captured
through an analytical random walk model, displays extended power law tails with
soft-to-hard evolution in time, in general agreement with recent kinetic
numerical simulations. Extensions to this description and possible avenues of
exploration are discussed.
