  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.
