Nonlinear electrostatic oscillations in a cold magnetized electron-positron plasma

TL;DR

This study investigates nonlinear electrostatic oscillations in a cold magnetized electron-positron plasma, revealing how magnetic fields influence phase mixing and introducing new nonlinear solutions with potential relevance to laboratory and astrophysical plasmas.

Contribution

The paper demonstrates that pure electrostatic modes exhibit delayed phase mixing in magnetized e-p plasmas and constructs a unique nonlinear wave solution unaffected by phase mixing, expanding understanding of plasma nonlinearities.

Findings

Magnetic field delays phase mixing compared to unmagnetized plasma.

Pure electrostatic oscillations undergo phase mixing nonlinearly.

A nonlinear wave at upper-hybrid frequency is constructed without phase mixing signatures.

Abstract

We study the spatio-temporal evolution of the nonlinear electrostatic oscillations in a cold magnetized electron-positron (e-p) plasma using both analytics and simulations. Using a perturbative method we demonstrate that the nonlinear solutions change significantly when a pure electrostatic mode is excited at the linear level instead of a mixed upper-hybrid and zero-frequency mode that is considered in a recent study. The pure electrostatic oscillations undergo phase mixing nonlinearly. However, the presence of the magnetic field significantly delays the phase-mixing compared to that observed in the corresponding unmagnetized plasma. Using 1D PIC simulations we then analyze the damping of the primary modes of the pure oscillations in detail and infer the dependence of the phase-mixing time on the magnetic field and the amplitude of the oscillations. The results are remarkably different from those found for the mixed upper-hybrid mode mentioned above. Exploiting the symmetry of the e-p plasma we then explain a generalized symmetry of our non-linear solutions. The symmetry allows us to construct a unique nonlinear solution up to the second order which does not show any signature of phase mixing but results in a nonlinear wave traveling at upper-hybrid frequency. Our investigations have relevance for laboratory/astrophysical e-p plasmas.