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Particle Acceleration in a Model of a Turbulent Reconnecting Plasma: A Fractional Diffusion Approach

High-energy charged particles are produced during solar flares. These may be accelerated by the strong electric fields associated with the magnetic reconnection process which is the source of energy release in flares. A simple model of random acceleration of charged particles due to fragmented electric fields is considered for the case of a turbulent reconnecting plasma in which the fluctuating electric field is highly localized and its magnitude distributed according to power laws. The statistical properties of the acceleration process are expressed in terms of a fractional diffusion equation in velocity space, whose solution displays a power-law tail related only to the statistics of the electric field.