Göttingen 2025 – wissenschaftliches Programm
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P: Fachverband Plasmaphysik
P 10: Poster Session I
P 10.52: Poster
Dienstag, 1. April 2025, 16:15–18:15, ZHG Foyer 1. OG
Toward a nonlinear Schrödinger equation description for geodesic-acoustic-modes in tokamaks: Analytic gyrokinetic studies of the nonlinear self-interaction — •David Korger1,2,3, Emanuele Poli1, Fulvio Zonca3, and Matteo Falessi3 — 1Max-Planck-Institut für Plasmaphysik, Garching, 85748, Germany — 2Ulm University, Ulm, 89081, Germany — 3Center 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 Schrödonger 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.
Keywords: Gyrokinetic Theory; Geodesic-Acoustic-Mode; Tokamak; Nonlinear Dynamics