Asymptotic state of nonlinear Landau damping in one-dimensional plasma

TL;DR

This paper investigates the long-term behavior of nonlinear Landau damping in one-dimensional plasma, revealing that the asymptotic state is a multi-wave BGK structure with multiple vortices in phase space.

Contribution

It extends the dispersion relation to the complex plane and compares it with nonlinear simulations to characterize the asymptotic state of plasma.

Findings

Asymptotic state is a multi-wave BGK structure.

Multiple vortices in phase space are observed.

The frequency-wavenumber spectrum shows multiple peaks.

Abstract

In this work, the asymptotic state of nonlinear Landau damping in one-dimensional plasma has been examined using a quasi-linear model and a second-order symplectic integrator. The dispersion relation of the plateau distribution function for the steady-state solution of the quasi-linear mode is extended to the complex plane and compared with the nonlinear simulation. We determine that the asymptotic state of the collisionless plasma is a multi-wave BGK structure. This structure is characterized by multiple vortices in phase space, which correspond to distinct peaks in the frequency-wavenumber ({\omega}, k) spectrum of the electric field