One-dimensional particle simulation of the filamentation instability: electrostatic field driven by the magnetic pressure gradient force

TL;DR

This study uses one-dimensional particle-in-cell simulations to analyze the filamentation instability in counter-propagating electron beams, revealing the electrostatic field's role driven by magnetic pressure gradients in filament dynamics.

Contribution

It demonstrates that the electrostatic field oscillates around the magnetic pressure gradient force during nonlinear filamentation, providing new insights into filament confinement and overlap mechanisms.

Findings

Electrostatic force oscillates around magnetic pressure gradient force.

Electrostatic and magnetic forces have comparable strength.

Electrostatic field influences filament density and overlap.

Abstract

Two counter-propagating cool and equally dense electron beams are modelled with particle-in-cell (PIC) simulations. The electron beam filamentation instability is examined in one spatial dimension, which is an approximation for a quasi-planar filament boundary. It is confirmed, that the force on the electrons imposed by the electrostatic field, which develops during the nonlinear stage of the instability, oscillates around a mean value that equals the magnetic pressure gradient force. The forces acting on the electrons due to the electrostatic and the magnetic field have a similar strength. The electrostatic field reduces the confining force close to the stable equilibrium of each filament and increases it farther away, limiting the peak density. The confining time-averaged total potential permits an overlap of current filaments with an opposite flow direction.