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Instability of phase space tubes

An approximate analytical model is developed to study the instability of phase space tubes (holes extended perpendicular to B) in a 2-D magnetized plasma. This instability has been observed in long-duration kinetic simulations of the two-stream instability that produce bipolar electric field structures comparable to those observed in the auroral ionosphere. The tubes are shown to possess stable vibrational modes that become unstable when resonantly coupled to an electrostatic whistler with parallel wavelength long compared to the width of the tube.