Geodesic acoustic modes with poloidal mode couplings ad infinitum

TL;DR

This paper develops a comprehensive model of geodesic acoustic modes (GAMs) incorporating all poloidal mode couplings, revealing their impact on GAM dispersion and matching experimental observations.

Contribution

It introduces a novel infinite chain model for GAMs with all poloidal mode couplings, providing new insights into their dispersion and experimental frequency profiles.

Findings

High poloidal mode couplings are significant at larger radial wave numbers.

The model's roots match experimentally observed GAM frequencies in Tore Supra.

The infinite chain reduces to a renormalized bi-nodal chain for analysis.

Abstract

Geodesic acoustic modes (GAMs) are studied, for the first time, including all poloidal mode $(m)$ couplings using drift reduced fluid equations. The nearest neighbor coupling pattern, due to geodesic curvature, leads to a semi-infinite chain model of the GAM with the mode-mode coupling matrix elements proportional to the radial wave number $k_{r}$. The infinite chain can be reduced to a renormalized bi-nodal chain with a matrix continued fractions. Convergence study of linear GAM dispersion with respect to $k_{r}$ and the $m$-spectra confirms that high m couplings become increasingly important with $k_{r}$. The radially sorted roots overlap with experimentally measured GAM frequency profile in low collisionality shots in Tore Supra thus explaining the reduced frequency of GAM in Tore Supra.