We report a newly found two-stage mechanism of electron acceleration near X-lines of 3D collisionless guide-field magnetic reconnection in the nonrelativistic regime typical, e.g., for stellar coronae. We found that after electrons are first pre-accelerated during the linear growth of reconnection, they become additionally accelerated in the course of the nonlinear stage of 3D guide-field magnetic reconnection. This additional acceleration is due to the filamentation of electric and magnetic fields caused by streaming instabilities. In addition to enhanced parallel electric fields, the filamentation leads to additional curvature-driven electron acceleration in the guide-field direction. As a result, part of the accelerated electron spectra becomes a power law with a spectral index of?~?1.6 near the X-line. This second stage of acceleration due to nonlinear reconnection is relevant for the production of energetic electrons in, e.g., thin current sheets of stellar coronae.
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