Space-time evolution of electron-beam driven electron holes and their effects on the plasma

We report here further results from the three-dimensional particle-in-cell simulations of the electron-beam driven electron holes. We focus here on (i) the transformation of oscillatory waves driven by the electron-beam instability into electron holes, (ii) the continued evolution and propagation of electron holes after their formation, including merging of electron holes, and (iii) the effects of the evolution on the plasma density and ion velocity distribution function. We find that initially electron-beam modes with perpendicular wave numbers k^ = 0 and as well as k^ ≠ 0 are driven resonantly below the electron plasma frequency of the target plasma. The modes interact nonlinearly and modulate each other both in space and time, producing wave structures with finite perpendicular scale lengths. Nonlinear evolution of such wave structures generates the electron holes in the simulations. Initially, a large number of electron holes form in the plasma. Their merging yields continuously a decreasing number of electron holes. The propagation velocity of the electron holes evolves dynamically and is affected by their merging. At late times only a few electron holes are left in the simulation and they decay by emitting low-frequency electrostatic whistler waves just above the lower hybrid (LH) frequency vlh . These waves, which are long structures parallel to the ambient magnetic field B0 and quite short transverse to B0, are associated with similar structures in the plasma density, producing density filaments. It turns out that electron-beam driven plasmas, in general, develop such filaments at some stage of the evolution of the beam-driven waves. In view of the excitation of the LH waves near vlh, which could resonate with the ions, an analysis shows that it is possible to heat transversely the ions in a time scale of a few seconds in the auroral return current plasma, in which electron holes and transversely heated ions have been simultaneously observed.