Dynamics and instability of electron phase-space tubes

Two-dimensional simulations of beam-driven turbulence in the auroral ionosp here have shown the formation and instability of phase-space tubes. These t ubes are a generalization of electron phase-space holes in a one-dimensiona l plasma. In a strongly magnetized plasma, such tubes vibrate at frequencie s below the bounce frequency of the trapping potential. A theory for these vibrations yields quantitative agreement with kinetic simulations. Furtherm ore, the theory predicts that the vibrations can become unstable when reson antly coupled to electrostatic whistlers-also in agreement with simulations .