Position and velocity space diffusion of test particles in stochastic electromagnetic fields

The two-dimensional diffusive dynamics of test particles in a random electromagnetic
field is studied. The synthetic electromagnetic fluctuations are generated through randomly placed
magnetised "clouds" oscillating with a frequency ?. We investigate the mean square displacements
of particles in both position and velocity spaces. As ? increases the particles undergo standard
(Brownian-like) motion, anomalous diffusion and ballistic motion in position space. Although in
general the diffusion properties in velocity space are not trivially related to those in position space,
we find that energization is present only when particles display anomalous diffusion in position
space. The anomalous character of the diffusion is only in the non-standard values of the scaling
exponents while the process is Gaussian.