Modulational instability of Geodesic-Acoustic-Mode packets

TL;DR

This study investigates the modulational instability of geodesic-acoustic-mode packets using nonlinear Schrödinger equation analysis and gyrokinetic simulations, revealing damping effects that can stabilize certain instabilities.

Contribution

It provides a comparative analysis of NLSE predictions and gyrokinetic simulations, highlighting the impact of damping and radial dependence on GAM packet stability.

Findings

GAM packets can undergo modulational instability as predicted by NLSE.

Damping mechanisms, especially Landau damping, significantly influence the instability.

Discrepancies between NLSE and gyrokinetic results are due to radial dependence and damping effects.

Abstract

Isolated, undamped geodesic-acoustic-mode (GAM) packets have been demonstrated to obey a (focusing) nonlinear Schr\"odinger equation (NLSE) [E. Poli, Phys. Plasmas 2021]. This equation predicts susceptibility of GAM packets to the modulational instability (MI). The necessary conditions for this instability are analyzed analytically and numerically using the NLSE model. The predictions of the NLSE are compared to gyrokinetic simulations performed with the global particle-in-cell code ORB5, where GAM packets are created from initial perturbations of the axisymmetric radial electric field $E_r$. An instability of the GAM packets with respect to modulations is observed both in cases in which an initial perturbation is imposed and when the instability develops spontaneously. However, significant differences in the dynamics of the small scales are discerned between the NLSE and gyrokinetic simulations. These discrepancies are mainly due to the radial dependence of the strength of the nonlinear term, which we do not retain in the solution of the NLSE, and to the damping of higher spectral components. The damping of the high-$k_r$ components, which develop as a consequence of the nonlinearity, can be understood in terms of Landau damping. The influence of the ion Larmor radius $\rho_i$ as well as the perturbation wavevector $k_{\text{pert}}$ on this effect is studied. For the parameters considered here the aforementioned damping mechanism hinders the MI process significantly from developing to its full extent and is strong enough to stabilize some of the (according to the undamped NLSE model) unstable wavevectors.