# Plasma electron hole oscillatory velocity instability

## TL;DR

This paper introduces a new instability in electron holes caused by their interaction with passing ions, leading to oscillations, wave emissions, and density perturbations, supported by theoretical analysis and PIC simulations.

## Contribution

It presents a novel theoretical framework for electron hole-ion interactions and validates it with high-fidelity PIC simulation results.

## Key findings

- Electron hole velocity oscillations become unstable under certain conditions.
- Unstable oscillations emit ion-acoustic waves and cause hole decay.
- Theoretical predictions match PIC simulation observations.

## Abstract

In this paper, we report a new type of instability of electron holes (EHs) interacting with passing ions. The nonlinear interaction of EHs and ions is investigated using a new theory of hole kinematics. It is shown that the oscillation in the velocity of the EH parallel to the magnetic field direction becomes unstable when the hole velocity in the ion frame is slower than a few times the cold ion sound speed. This instability leads to the emission of ion-acoustic waves from the solitary hole and decay in its magnitude. The instability mechanism can drive significant perturbations in the ion density. The instability threshold, oscillation frequency and instability growth rate derived from the theory yield quantitative agreement with the observations from a novel high-fidelity hole-tracking Particle-In-Cell (PIC) code.