Transverse instability and magnetic structures associated with electron phase space holes

Electron phase space holes (electron holes) are found to be unstable to the transverse instability. Two-dimensional (2D) electromagnetic particle-in-cell simulations are performed to investigate the structures of the fluctuating magnetic field associated with electron holes. The combined actions between the transverse instability and the stabilization by the background magnetic field (B₀=B₀e→_x) lead a one-dimensional electron hole into several 2D electron holes which are isolated in both the x and y directions. The electrons trapped in these 2D electron holes suffer the electric field drift v_E=E×B₀/B02 due to the existence of the perpendicular electric field E_y, which generates the current along the z direction. Then, the unipolar and bipolar structures are formed for the parallel cut of the fluctuating magnetic field along the x and y directions, respectively. At the same time, these 2D electron holes move along the x direction, and the unipolar structures are formed for the parallel cut of the fluctuating magnetic field along the z direction.