Analysis and simulation of BGK electron holes

Abstract. Recent observations from satellites crossing regions of magnetic-field-aligned electron streams reveal solitary potential structures that move at speeds much greater than the ion acoustic/thermal velocity. The structures appear as positive potential pulses rapidly drifting along the magnetic field, and are electrostatic in their rest frame. We interpret them as BGK electron holes supported by a drifting population of trapped electrons. Using Laplace transforms, we analyse the behavior of one phase-space electron hole. The 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 increasing amplitude. The stability of the analytic solution is tested by means of a two-dimensional particle-in-cell simulation code with open boundaries. We consider a strongly magnetized parameter regime in which the bounce frequency of the trapped electrons is much less than their gyrofrequency. Our investigation 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 considerable energy. The nonlinear structure is remarkably resilient