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 ξ 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 ξ and Q with dominant poloidal mode numbers m = ±2 appears outside this magnetic surface to higher orders in ε.

Generalised zonal modes in stationary axisymmetric plasmas

“…While standard gyrokinetic models struggle with these features, the MHD results of Ref. [5] appear to agree with experimental measurements of GAMs using magnetic probes. Also, perhaps little known is the effect that equilibrium toroidal plasma rotation (e.g.…”

“…In Section III where static (non-rotating) plasmas are considered, it will be shown that zonal modes are exactly electrostatic, and there are no flows across magnetic flux surfaces. While full electromagnetic calculations have been made for GAMs and zonal modes [5], analysis of the continuum mode frequencies in rotating plasma are recovered on setting ξ ψ p = ξ p · ∇ψ = 0 and δB = 0 in Eq. (13).…”

“…In Ref. [5] the electromagnetic global structure of these two modes was allucidated, both for cases of n = 0 and for non-axisymmetric modes. In the limit of vanishing toroidal rotation the zonal mode coincides with the zero frequency non-axisymmetric modes identified by Goedbloed in Ref.…”

Flow shear stabilization of rotating plasmas due to the Coriolis effect

“…In integrated form the effect first appeared in an analysis of the internal kink mode [5] where it was grouped with inertial terms and was denoted as "flutter." The effect also surfaced in more recent analyses [6,7]. In Ref.…”

Response to “Comment on ‘Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks’ ” [Phys. Plasmas 19, 064701 (2012)]

“…A large piece of the Comment is devoted to the proposition to go out of use in MHD the conventional sonic Mach number used in II and in a lot of papers by the other authors (see, e.g., Refs. [4][5][6][7]. Although this subject is rather general and has no specific relation to the commented paper II, there is a sense to note the following.…”