Context. We investigate the nonlinear evolution of the electron distribution in the presence of the strong inductive electric field in the reconnecting current sheets (RCS) of solar flares. Aims. We aim to study the characteristics of nonthermal electron-beam plasma instability and its influence on electron acceleration in RCS. Methods. Including the external inductive field, the one-dimensional Vlasov simulation is performed with a realistic mass ratio for the first time. Results. Our principal findings are as follows: 1) the Buneman instability can be quickly excited on the timescale of 10-7 s for the typical parameters of solar flares. After saturation, the beam-plasma instabilities are excited due to the non-Maxwellian electron distribution; 2) the final velocity of the electrons trapped by these waves is of the same order as the phase speed of the waves, while the untrapped electrons continue to be accelerated; 3) the inferred anomalous resistance of the current sheet and the energy conversion rate are basically of the same order as those previously estimated, e.g., ``the analysis of Martens''. Conclusions. The Buneman instability is excited on the timescale of 10-7 s and the wave-particle resonant interaction limits the low-energy electrons to be further accelerated in RCS. Key words: turbulence - Sun: magnetic fields - acceleration of particles
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