  We analyze the transport properties of charged particles (ions and electrons)
interacting with randomly formed magnetic scatterers (e.g.\ large scale local
``magnetic fluctuations'' or ``coherent magnetic irregularities'' usually
present in strongly turbulent plasmas), using the energization processes
proposed initially by Fermi in 1949. The scatterers are formed by large scale
local fluctuations ($\delta B/B \approx 1$) and are randomly distributed inside
the unstable magnetic topology. We construct a 3D grid on which a small
fraction of randomly chosen grid points are acting as scatterers. In
particular, we study how a large number of test particles are accelerated and
transported inside a collection of scatterers in a finite volume. Our main
results are: (1) The spatial mean-square displacement $<(\Delta r)^2>$ inside
the stochastic Fermi accelerator is superdiffusive, $<(\Delta r)^2> \sim
t^{a_{r}},$ with $a_r \sim 1.2-1.6$, for the high energy electrons with kinetic
energy $(W)$ larger than $1 MeV$, and it is normal ($a_r=1$) for the heated low
energy $(W< 10 keV)$ electrons. (2) The transport properties of the high energy
particles are closely related with the mean-free path that the particles travel
in-between the scatterers ($\lambda_{sc}$). The smaller $\lambda_{sc}$ is, the
faster the electrons and ions escape from the acceleration volume. (3) The mean
displacement in energy $<\Delta W> \sim t^{a_{W}}$ is strongly enhanced inside
the acceleration volume $(a_W=1.5- 2.5)$ for the high energy particles compared
to the thermal low energy particles ($a_W=0.4$), i.e.\ high energy particles
undergo an enhanced systematic gain in energy.(4) The mean-square displacement
in energy $<W^2>$ is superdiffusive for the high energy particles and normal
for the low energy, heated particles.
