Transverse instability magnetic field thresholds of electron phase-space holes

TL;DR

This paper compares analytical and PIC simulation methods to determine the magnetic field thresholds that stabilize transverse instabilities in electron phase-space holes, revealing quantitative agreement and explaining discrepancies through a kinematic mechanism.

Contribution

It provides a detailed comparison between shift-mode analysis and PIC simulations for magnetic thresholds of transverse instability in electron holes, highlighting the mode narrowing effect.

Findings

Good agreement between analysis and simulations for instability thresholds

Simulation thresholds are 20-30% higher than analytical predictions

Mode narrowing explains the threshold discrepancy

Abstract

A detailed comparison is presented of analytical and particle-in-cell (PIC) 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 to 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.