The filamentation instability driven by warm electron beams: Statistics and electric field generation

TL;DR

This study uses PIC simulations to analyze the filamentation instability driven by warm electron beams, revealing the roles of electric and magnetic forces in filament growth, saturation, and electric field generation.

Contribution

It provides a detailed comparison of 1D and 2D simulation results, highlighting the saturation mechanism and the importance of magnetic pressure gradients in electric field formation.

Findings

Filament size increases linearly over time.

Electrostatic and magnetic forces are equally important at saturation.

Magnetic pressure gradients drive the electrostatic fields.

Abstract

The filamentation instability of counterpropagating symmetric beams of electrons is examined with 1D and 2D particle-in-cell (PIC) simulations, which are oriented orthogonally to the beam velocity vector. The beams are uniform, warm and their relative speed is mildly relativistic. The dynamics of the filaments is examined in 2D and it is confirmed that their characteristic size increases linearly in time. Currents orthogonal to the beam velocity vector are driven through the magnetic and electric fields in the simulation plane. The fields are tied to the filament boundaries and the scale size of the flow-aligned and the perpendicular currents are thus equal. It is confirmed that the electrostatic and the magnetic forces are equally important, when the filamentation instability saturates in 1D. Their balance is apparently the saturation mechanism of the filamentation instability for our initial conditions. The electric force is relatively weaker but not negligible in the 2D simulation, where the electron temperature is set higher to reduce the computational cost. The magnetic pressure gradient is the principal source of the electrostatic field, when and after the instability saturates in the 1D simulation and in the 2D simulation.