Electric field generation by the electron beam filamentation instability: filament size effects

Abstract

The filamentation instability (FI) of counter-propagating beams of electrons is modelled with a particle-in-cell simulation in one spatial dimension and with a high statistical plasma representation. The simulation direction is orthogonal to the beam velocity vector. Both electron beams have initially equal densities, temperatures and moduli of their non-relativistic mean velocities. The FI is electromagnetic in this case. A previous study of a small filament demonstrated that the magnetic pressure gradient force (MPGF) results in a nonlinearly driven electrostatic field. The probably small contribution of the thermal pressure gradient to the force balance implied that the electrostatic field performed undamped oscillations around a background electric field. Here, we consider larger filaments, which reach a stronger electrostatic potential when they saturate. The electron heating is enhanced and electrostatic electron phase space holes form. The competition of several smaller filaments, which grow simultaneously with the large filament, also perturbs the balance between the electrostatic and magnetic fields. The oscillations are damped but the final electric field amplitude is still determined by the MPGF.