  Collisionless, magnetized turbulence offers a promising framework for the
generation of non-thermal high-energy particles in various astrophysical sites.
Yet, the detailed mechanism that governs particle acceleration has remained
subject to debate. By means of 2D and 3D PIC, as well as 3D (incompressible)
magnetohydrodynamic (MHD) simulations, we test here a recent model of
non-resonant particle acceleration in strongly magnetized
turbulence~\cite{2021PhRvD.104f3020L}, which ascribes the energization of
particles to their continuous interaction with the random velocity flow of the
turbulence, in the spirit of the original Fermi model. To do so, we compare,
for a large number of particles that were tracked in the simulations, the
predicted and the observed histories of particles momenta. The predicted
history is that derived from the model, after extracting from the simulations,
at each point along the particle trajectory, the three force terms that control
acceleration: the acceleration of the field line velocity projected along the
field line direction, its shear projected along the same direction, and its
transverse compressive part. Overall, we find a clear correlation between the
model predictions and the numerical experiments, indicating that this
non-resonant model can successfully account for the bulk of particle
energization through Fermi-type processes in strongly magnetized turbulence. We
also observe that the parallel shear contribution tends to dominate the physics
of energization in the PIC simulations, while in the MHD incompressible
simulation, both the parallel shear and the transverse compressive term provide
about equal contributions.
