Stochastic Turbulent Acceleration in a Fractal Environment

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. 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 (∼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 easily pulls 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.