Nonlinear electrostatic oscillations in a cold magnetized electron-positron plasma

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 one dimensional particle-in-cell simulations, we then analyze the damping of the primary mode 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 mode study mentioned earlier. 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 the upper-hybrid frequency. Our investigations have relevance for laboratory/astrophysical e-p plasmas. Published by AIP Publishing.