Formation of power law spectra of energetic electrons during multiple X line magnetic reconnection with a guide field

In this paper, with a two-dimensional particle-in-cell simulation model, we study the formation of power-law spectra of energetic electrons in multiple X line magnetic reconnection with a strong guide field. The processes of both magnetic reconnection and electron acceleration can be separated into two stages. In the first stage, two X lines appear at the border and center of the simulation domain, and then, two magnetic islands are formed. In this stage, electrons are accelerated mainly by parallel electric fields, and a power-law spectrum of energetic electrons is generated with the appearance of the second X line. In the second stage, the two magnetic islands are merged into one big island. Besides parallel electric fields, the Fermi mechanism also plays an important role in the production of energetic electrons, and its contribution is comparable to that of parallel electric fields when the electron energy is sufficiently large. In this stage, the generated power-law spectrum of energetic electrons be...