Fig. 4: The electron acceleration mechanism.

a The comparison of the time-integrated electron spectrum obtained from two-flow cases and single-flow cases. The energized electrons are observed in three directions showing similar power-law distributions with a spectral index of 3 (dotted black line), when the kinetic turbulence is formed. The systematically shaded region corresponds to the error bar of electron number (Δn/n ~ 20%, where Δn is the electron number error mainly caused by the sensitivity of the image plate). b Simulations show that the evolution of the electron spectrum in the turbulent region, where the background thermal electrons are accelerated to ≥ 100k_BT_e leading to the formation of a power-law distribution with a spectral index of 3.3 (dotted black line). The color bar stands for the time evolution. c History of two typical selected electrons’ kinetic energy as a function of time, one is an accelerated electron (P₁), and the other is a thermal electron (P₂). The acceleration process can be divided into three stages, and the dominant acceleration occurs in the last stage. Panels (d) to (f) show the trajectory of particles during different acceleration stages. The colormaps for (d) to (f) correspond to the distribution of magnetic fields at 4 ns, 10 ns, and 14 ns, respectively. Panel (g) represents the change of the x-coordinate of particle P1 over time, with the red and green crosses indicating points where its average velocity direction undergoes significant changes, representing the locations where reflection occurs. h The average energy gains experienced by electrons in each reflection in panel (g) are plotted.