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Successive merging of plasmoids and fragmentation in flare current sheet and their X-ray and radio signatures

Based on our recent MHD simulations, first, a concept of the successive merging of plasmoids and fragmentation in the current sheet in the standard flare model is presented. Then, using a 2.5-D electromagnetic particle-in-cell model with free boundary conditions, these processes were modelled on the kinetic level of plasma description. We recognized the plasmoids which mutually interacted and finally merged into one large plasmoid. Between interacting plasmoids further plasmoids and current sheets on smaller and smaller spatial scales were formed in agreement with the fragmentation found in MHD simulations. During interactions (merging - coalescences) of the plasmoids the electrons were very efficiently accelerated and heated. We found that after a series of such merging processes the electrons in some regions reached the energies relevant for the emission in the hard X-ray range. Considering these energetic electrons and assuming the plasma density 10^9-10^10 cm^{-3} and the source volume as in the December 31, 2007 flare (Krucker at al. 2010, ApJ 714, 1108), we computed the X-ray spectra as produced by the bremsstrahlung emission process. Comparing these spectra with observations, we think that these processes can explain the observed above-the-loop-top hard X-ray sources. Furthermore, we show that the process of a fragmentation between two merging plasmoids can generate the narrowband dm-spikes. Formulas for schematic fractal reconnection structures were derived. Finally, the results were discussed.