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 (B₀ = B₀e_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 > _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.