Turbulent acceleration of electrons by large-amplitude magnetohydrodynamic waves in solar flares

Context. Solar flares appear as a sudden local enhancement of the emission of electromagnetic waves from the radio to the γ-ray range on the Sun. This radiation is primarily generated by energetic electrons. In addition, these electrons play an important role, since they carry a substantial part of the energy released during a flare. Thus, the generation of highly energetic electrons during flares is one of the basic questions in flare physics. The flare is generally understood as a manifestation of magnetic reconnection in the corona. Several mechanisms of particle acceleration during flares are discussed. Observations and numerical simulations show that a strong magnetohydrodynamic (MHD) turbulence appears in the outflow region of the reconnection site. We consider this turbulence as an ensemble of large-amplitude steepened MHD waves. Aims. We studied the interaction of electrons with such a wave structure to determine whether the interaction accelerates the electrons. Methods. The properties of the large-amplitude steepened MHD waves are described in terms of simple MHD waves. The interaction of an electron with such a wave structure was treated with a mechanism equivalent to the well-known diffusive shock acceleration. Results. The multiple interactions of an electron with a large-amplitude steepened MHD waves lead to its continuous acceleration to high energies. The resulting differential electron flux consists of a thermal and a non-thermal component, the latter of which is governed by a power law. The spectral index depends on the density compression within the wave. The stronger the turbulence, the stronger the density compression, and the lower the spectral index. Thus, strong (e.g. GOES M- or X-class) flares are accompanied by strong MHD turbulence in the outflow region of the reconnection site and by a large number of highly relativistic electrons, which are required to account for the solar hard X- and γ-ray radiation. Conclusions. Strong MHD turbulence in the outflow region of the magnetic reconnection site is able to accelerate electrons to highly relativistic energies.