Dynamics and instability of electron phase-space tubes

Two-dimensional simulations of beam-driven turbulence in the auroral ionosphere have shown the formation and instability of phase-space tubes. These tubes are a generalization of electron phase-space holes in a one-dimensional plasma. In a strongly magnetized plasma, such tubes vibrate at frequencies below the bounce frequency of the trapping potential. A theory for these vibrations yields quantitative agreement with kinetic simulations. Furthermore, the theory predicts that the vibrations can become unstable when resonantly coupled to electrostatic whistlers-also in agreement with simulations.