Particle Acceleration in an Evolving Network of Unstable Current Sheets

We study the acceleration of electrons and protons interacting with localized, multiple, small-scale dissipation regions inside an evolving, turbulent active region. The dissipation regions are unstable current sheets (UCSs), and in their ensemble they form a complex, fractal, evolving network of acceleration centers. Acceleration and energy dissipation are thus assumed to be fragmented. A large-scale magnetic topology provides the connectivity between the UCSs and in this way determines the degree of possible multiple acceleration. The particles travel along the magnetic field freely without losing or gaining energy until they reach a UCS. In a UCS, a variety of acceleration mechanisms are active, with the end result that the particles depart with a new momentum. The stochastic acceleration process is represented in the form of continuous-time random walk, which allows one to estimate the evolution of the energy distribution of the particles. It is found that under certain conditions, electrons are heated and accelerated to energies above 1 MeV in much less than 1 s. Hard X-ray and microwave spectra are calculated from the electrons' energy distributions, and they are found to be compatible with the observations. Ions (protons) are also heated and accelerated, reaching energies up to 10 MeV almost simultaneously with the electrons. The diffusion of the particles inside the active region is extremely fast (anomalous superdiffusion). Although our approach does not provide insight into the details of the specific acceleration mechanisms involved, its benefits are that it relates acceleration to the energy release, it well describes the stochastic nature of the acceleration process, and it can incorporate the flaring large-scale magnetic topology, potentially even its temporal evolution.