Analysis and simulation of BGK electron holes

Recent observations from satellites crossing regions of magnetic-field-alig ned electron streams reveal solitary potential structures that move at spee ds much greater than the ion acoustic/thermal velocity. The structures appe ar as positive potential pulses rapidly drifting along the magnetic field, and are electrostatic in their rest frame. We interpret them as BGK electro n holes supported by a drifting population of trapped electrons. Using Lapl ace transforms, we analyse the behavior of one phase-space electron hole. T he resulting potential shapes and electron distribution functions are self- consistent and compatible with the field and particle data associated with the observed pulses. In particular, the spatial width increases with increa sing amplitude. The stability of the analytic solution is tested by means o f a two-dimensional particle-in-cell simulation code with open boundaries. We consider a strongly magnetized parameter regime in which the bounce freq uency of the trapped electrons is much less than their gyrofrequency. Our i nvestigation includes the influence of the ions, which in the frame of the hole appear as an incident beam, and impinge on the BGK potential with cons iderable energy. The nonlinear structure is remarkably resilient.