Transverse instability of magnetized electron holes

We study a transverse instability of the nonlinear equilibria known as elec tron phase-space holes in the presence of a magnetic field. The instability is intrinsically two dimensional and is determined by the dynamics of the trapped electrons. It depends on hole amplitudes, ambient magnetic fields, and the perpendicular velocity spread. The long-standing hole stability pro blem in multiple dimensions can be characterized by the gyro-to-bounce freq uency ratio A low ratio associated with a small perpendicular velocity spre ad results in a disintegration of the positive potential spikes.