Geodesic acoustic modes with poloidal mode coupling ad infinitum

Geodesic acoustic mode (GAM) is studied 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 fraction. 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. Theoretical predictions were compared against the experimental observations on GAM frequency profiles in Tore Supra shots showing that the radially sorted theoretical roots down shift to overlap with experimental GAM frequency profile for low collisionality shot in the radial wave number range 0.1< kr < 0.15. This is proposed as a possible resolution of the GAM frequency reduction in Tore Supra compared with the previous theories. (author)