Two-dimensional electron phase-space holes in space plasmas

Two-dimensional(2D) electrostatic particle-in-cell simulations were performed to investigate the nonlinear evolution of electron bi-stream instability in weakly(Ωe=0.5ωpe,where Ωe and ωpe are the electron cyclotron frequency and electron plasma frequency,respectively) and strongly(Ωe=2ωpe) magnetized plasma.The results show that nearly monochromatic electrostatic waves are firstly excited,then these waves coalesce with adjacent waves.At last one or several solitary waves are formed,which corresponds to electron phase-space holes.In weakly magnetized plasma,these holes have two-dimensional structures,which are isolated in both directions parallel and perpendicular to the background magnetic field.In strongly magnetized plasma,these electron holes have quasi-one-dimensional structures.The parallel extent is limited while the perpendicular extent is unlimited.However,the amplitude of the electric fields is varied along the perpendicular direction.In both cases,in these holes,the parallel cut of the parallel electric field(Ex) exhibits bipolar structures while the perpendicular electric field Ey is unipolar.The results are consistent with observations in auroral region.We also find that electrostatic whistler waves are unstable in strongly magnetized plasma,which can destroy the electrostatic solitary structures.