  We analyze the stochastic acceleration of particles inside a fully developed
turbulent plasma. It is well known that large-amplitude magnetic fluctuations
and coherent structures in such an environment obey a fractal scaling, and our
specific aim is to study for the first time the effects of the fractality of
these environments on stochastic acceleration. We have shown that an injected
Maxwellian energy distribution is heated and forms a high energy tail in a very
short time. Using standard parameters for the low solar corona, the injected
Maxwellian distribution of electrons gets heated from the initial 100 eV to 10
KeV, and the power-law index of the high energy tail is about -2.3-4.0. The
high energy tail starts around 100 keV, and reaches 10 MeV. The index of the
power-law tail depends on the system size, and it is in good agreement with
observed values for realistic system sizes. The heating and acceleration
process is very fast (\sim 2 s). The reason why the acceleration time is so
short is that the particles are trapped within small scale parts of the fractal
environment, and their scattering mean free path reduces drastically. The
presence of small scale activity also pulls easily particles from the thermal
pool, so there is no need for a seed population. The mean square displacement
in space and energy is superdiffusive for the high energy particles.
