Transverse instability magnetic field thresholds of electron phase-space holes

A detailed comparison is presented of analytical and particle-in-cell simulation investigation of the transverse instability, in two dimensions, of initially one-dimensional electron phase-space hole equilibria. Good quantitative agreement is found between the shift-mode analysis and the simulations for the magnetic field (B) threshold at which the instability becomes overstable (time oscillatory) and for the real and imaginary parts of the frequency. The simulation B threshold for full stabilization exceeds the predictions of shift-mode analysis by 20-30%, because the mode becomes substantially narrower in spatial extent than a pure shift. This threshold shift is qualitatively explained by the kinematic mechanism of instability.