Low-frequency magnetohydrodynamics and geodesic acoustic modes in toroidally rotating tokamak plasmas

Abstract

This paper analyses low-frequency magnetohydrodynamic (MHD) modes, especially the geodesic acoustic modes (GAMs), in toroidal plasmas with large aspect ratio and circular cross section, including the effects of toroidal plasma rotation. A system of equations describing MHD modes with frequency of the order of the sound frequency in such plasmas is derived from the Frieman–Rotenberg equation, using a technique where the plasma perturbation \U0001d6cf and the perturbed magnetic field Q are expanded separately in the inverse aspect ratio ε = r/R, where r and R denote the minor and major radii of the plasma torus, respectively. The large-scale, ideal MHD properties of the GAM induced by toroidal rotation (Wahlberg 2008 Phys. Rev. Lett. 101 115003) are thereafter analysed in more detail employing this system of equations. It is shown that both the axisymmetric GAMs existing in rotating plasmas are localized on a specific magnetic surface only to leading order in ε, and that a ‘halo’ consisting of finite components of both \U0001d6cf and Q with dominant poloidal mode numbers m = ±2 appears outside this magnetic surface to higher orders in ε.