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To investigate how magnetic reconnection (MR) accelerates electrons to a power-law energy spectrum in solar flares, we explore the scaling of a kinetic model proposed by Che & Zank (CZ) and compare it to observations. Focusing on thin current sheet MR particle-in-cell (PIC) simulations, we analyze the impact of domain size on the evolution of the electron Kelvin–Helmholtz instability (EKHI). We find that the duration of the growth stage of the EKHI ($t_G\sim {\mathrm{\Omega }}_e^{-1}$) is short and remains nearly unchanged because the electron gyrofrequency Ω_eis independent of domain size. The quasi-steady stage of the EKHI (t_MR) dominates the electron acceleration process and scales linearly with the size of the simulations asL/v_A0, wherev_A0is the Alfvén speed. We use the analytical results obtained by CZ to calculate the continuous temporal evolution of the electron energy spectra from PIC simulations and linearly scale them to solar flare observational scales. For the first time, an electron acceleration model predicts the sharp two-stage transition observed in typical soft–hard–harder electron energy spectra, implying that the electron acceleration model must be efficient with an acceleration timescale that is a small fraction of the duration of solar flares. Our results suggest that we can use PIC MR simulations to investigate the observational electron energy spectral evolution of solar flares if the ratiot_MR/t_Gis sufficiently small, i.e., ≲10%.

Ion beam-driven instabilities in a collisionless space plasma with low β, i.e. low plasma and magnetic pressure ratio, are investigated using particle-in-cell (PIC) simulations. Specifically, the effects of different ion drift velocities on the development of Buneman and resonant electromagnetic (EM) right-handed (RH) ion beam instabilities are studied. Our simulations reveal that both instabilities can be driven when the ion beam drift exceeds the theoretical thresholds. The Buneman instability, which is weakly triggered initially, dissipates only a small fraction of the kinetic energy of the ion beam while causing significant electron heating, owing to the small electron-ion mass ratio. However, we find that the ion beam-driven Buneman instability is quenched effectively by the resonant EM RH ion beam instability. Instead, the resonant EM RH ion beam instability dominates when the ion drift velocity is larger than the Alfvén speed, leading to the generation of RH Alfvén waves and RH whistler waves. We find that the intensity of Alfvén waves decreases with decrease of ion beam drift velocity, while the intensity of whistler waves increases. Our results provide new insights into the complex interplay between ion beams and plasma instabilities in low β collisionless space plasmas.