Erlangen 2026 – scientific programme
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P: Fachverband Plasmaphysik
P 14: Magnetic Confinement V
P 14.4: Talk
Thursday, March 19, 2026, 12:05–12:30, KH 02.016
Toward a nonlinear Schrödinger equation for the description of geodesic-acoustic-modes in tokamaks — •David Korger1, Emanuele Poli1, Fulvio Zonca2, Matteo Valerio Falessi2, Riccardo Stucchi1, Alberto Bottino1, and Thomas Hayward-Schneider1 — 1Max-Planck-Institut für Plasmaphysik, Garching, 85748, Germany — 2Center for Nonlinear Plasma Science and C.R. ENEA Frascati, C.P. 65, 00044 Frascati, Italy
The geodesic-acoustic-mode (GAM) is a plasma oscillation observed in fusion reactors with toroidal geometry and is recognized to be the nonstationary branch of the zonal flows (ZFs). Prior studies have established that as a direct consequence of nonlinear gyrokinetic theory, the GAM dynamics is well described by an equation of Schrödinger type - i. e., an equation whose linear contribution is exactly of the same form as the linear Schrödinger equation, while the nonlinear dynamics necessitates an integro-differential expression.
The presented work takes a closer look into the nonlinear contributions by deriving approximate, but well-defined analytic expressions from the (exact) integro-differential operators. At the lowest order of accuracy, prior numerical studies anticipate the retrieval of a cubic nonlinear Schrödinger equation. This may come unexpected since nonlinear interactions usually have a quadratic structure, such as e. g. the E×B-nonlinearity. The third power is found to stem from an interaction of quadratic structures generated by the GAMs (with oscillation frequencies that are either zero or twice the GAM frequency) with the GAM itself. Analytic results are compared to gyrokinetic simulations.
Keywords: Gyrokinetic Theory; Geodesic-Acoustic-Mode; Tokamak; Nonlinear Dynamics; Zonal Flows