Electromagnetic Particle-in-Cell Simulations of Electron Holes Formed During the Electron Two-Stream Instability

Previous electrostatic particle-in-cell (PIC) simulations have pointed out that elec- tron phase-space holes (electron holes) can be formed during the nonlinear evolution of the electron two-stream instability. The parallel cuts of the parallel and perpendicular electricfield have bipolar and unipolar structures in these electron holes, respectively. In this study, two-dimensional (2D) electromagnetic PIC simulations are performed in the x- y plane to investigate the evolution of the electron two-stream instability, with the emphasis on the magnetic structures associated with these electron holes in di®erent plasma conditions. In the simulations, the background magnetic field (B_o = B_o ~ ex) is along the x direction. In weakly magnetized plasma (­e <ω_pe, where ­e and !pe are the electron gyrofrequency and electron plasma frequency, respectively), several 2D electron holes are formed. In these 2D electron holes, the parallel cut of the fluctuating magneticfield ±Bx and ±Bz has unipolar structures, while the flctuating magneticfield ±By has bipolar structures. In strongly magnetized plasma (­e >ω_pe), several quasi-1D electron holes are formed. The electrostatic whistler waves with streaked structures of Ey are excited. The fluctuating mag- netic field δBx and δBz also have streaked structures. The fluctuating magneticfield δBx and δBy are produced by the current in the z direction due to the electric field drift of the trapped elec- trons, while the fluctuating magneticfield δBz can be explained by the Lorentz transformation of a moving quasielectrostatic structure. The influences of the initial temperature anisotropy on the magnetic structures of the electron holes are also analyzed. The electromagnetic whistler waves are found to be excited in weakly magnetized plasma. However, they do not have any significant effects on the electrostatic structures of the electron holes.