The evolution of the magnetic structures in electron phase‐space holes: Two‐dimensional particle‐in‐cell simulations

Observations have shown that electron phase‐space holes (electron holes) possess regular magnetic structures. In this paper, two‐dimensional (2D) electromagnetic particle‐in‐cell (PIC) simulations are performed in the ( x , y ) plane to study magnetic structures associated with electron holes under different plasma conditions. In the simulations, the background magnetic field ( B 0 = B 0 x ) is along the x direction. The combined actions between the transverse instability and stabilization by the background magnetic field lead to the generation of the electric field E y . Then electrons suffer the electric field drift and produce the current in the z direction, which leads to the fluctuating magnetic field along the x and y directions. Meanwhile, the motion of the electron holes along the x direction and the existence of the electric field E y generate the fluctuating magnetic field along the z direction. In very weakly magnetized plasma (Ω e ≪ ω pe , where Ω e and ω pe are the electron gyrofrequency and electron plasma frequency, respectively.), the transverse instability is very strong and the magnetic structures associated with electron holes disappear quickly. When Ω e is comparable to ω pe , the parallel cut of the fluctuating magnetic field δB x and δB z has unipolar structures in the electron holes, while the parallel cut of fluctuating magnetic field δB y has bipolar structures. In strongly magnetized plasma (Ω e > ω pe ), electrostatic whistler waves with streaked structures of E y are excited. The fluctuating magnetic field δB x and δB z also have streaked structures. The relevance between our simulation results and the magnetic structures associated with electron holes observed in the plasma sheet is also discussed.