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Modulational instability of geodesic-acoustic-mode packets

Part of: Invited Contributions from the 20th European Fusion Theory Conference

Published online by Cambridge University Press:  10 January 2025

D. Korger Open the ORCID record for D. Korger [Opens in a new window] ,
E. Poli Open the ORCID record for E. Poli [Opens in a new window] ,
A. Biancalani Open the ORCID record for A. Biancalani [Opens in a new window] ,
A. Bottino Open the ORCID record for A. Bottino [Opens in a new window] ,
O. Maj Open the ORCID record for O. Maj [Opens in a new window]  and
J.N. Sama Open the ORCID record for J.N. Sama [Opens in a new window]
D. Korger*
Affiliation:
Max Planck Institute for Plasma Physik, D-85748 Garching, Germany Ulm University, D-89081 Ulm, Germany
E. Poli
Affiliation:
Max Planck Institute for Plasma Physik, D-85748 Garching, Germany
A. Biancalani
Affiliation:
Léonard de Vinci Pôle Universitaire, Research Center, F-92916 Paris La Défense, France
A. Bottino
Affiliation:
Max Planck Institute for Plasma Physik, D-85748 Garching, Germany
O. Maj
Affiliation:
Max Planck Institute for Plasma Physik, D-85748 Garching, Germany
J.N. Sama
Affiliation:
Institut Jean Lamour UMR 7198, Université de Lorraine-CNRS, F-54011 Nancy, France
*
†Email address for correspondence: david.korger@ipp.mpg.de
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Abstract

Isolated, undamped geodesic-acoustic-mode (GAM) packets have been demonstrated to obey a (focusing) nonlinear Schrödinger 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 analysed analytically and numerically using the NLSE model. The predictions of the NLSE are compared with 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 radial spectral components $k_r$. 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.

Keywords

plasma simulationplasma nonlinear phenomenaplasma confinement
Type
Research Article
Information
Journal of Plasma Physics , Volume 91 , Issue 1 , February 2025 , E17
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Copyright
Copyright © The Author(s), 2025. Published by Cambridge University Press

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