  Particle transport, acceleration and energisation are phenomena of major
importance for both space and laboratory plasmas. Despite years of study, an
accurate theoretical description of these effects is still lacking. Validating
models with self-consistent, kinetic simulations represents today a new
challenge for the description of weakly-collisional, turbulent plasmas. We
perform two-dimensional (2D) hybrid-PIC simulations of steady-state turbulence
to study the processes of diffusion and acceleration. The chosen plasma
parameters allow to span different systems, going from the solar corona to the
solar wind, from the Earth's magnetosheath to confinement devices. To describe
the ion diffusion, we adapted the Nonlinear Guiding Center (NLGC) theory to the
2D case. Finally, we investigated the local influence of coherent structures on
particle energisation and acceleration: current sheets play an important role
if the ions Larmor radii are on the order of the current sheets size. This
resonance-like process leads to the violation of the magnetic moment
conservation, eventually enhancing the velocity-space diffusion.
