On the dispersion of geodesic acoustic modes
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AVES AND INSTABILITIES IN PLASMA
On the Dispersion of Geodesic Acoustic Modes1 A. I. Smolyakova, b, M. F. Bashirc, A. G. Elfimovd, M. Yagie, and N. Miyatoe a Department b
of Physics and Engineering Physics, University of Saskatchewan, Saskatoon, Saskatchewan, Canada National Research Centre Kurchatov Institute, pl. Akademika Kurchatova 1, Moscow, 123182 Russia c Department of Physics, COMSATS Institute of Information Technology, Lahore, Pakistan d Institute of Physics, University of São Paulo, São Paulo, Brazil e Japan Atomic Energy Agency, Obuchi, Rokkasho, Aomori, Japan e-mail: [email protected] Received November 6, 2015
Abstract—The problem of dispersion of geodesic acoustic modes is revisited with two different methods for the solution of the kinetic equation. The dispersive corrections to the mode frequency are calculated by including the m = 2 poloidal harmonics. Our obtained results agree with some earlier results but differ in various ways with other previous works. Limitations and advantages of different approaches are discussed. DOI: 10.1134/S1063780X16050172
1. INTRODUCTION Geodesic acoustic modes (GAMs) are the linear modes supported by plasma compressibility in toroidal geometry. GAMs derive their name from the effect of the averaged geodesic curvature providing the restoring force. Within the ideal MHD model [1], GAMs dispersion relation has a simple form ω2 = 2c s2 / R 2 + c s2 / ⎛⎜⎝ q 2 R 2 ⎞⎟⎠ , where c s2 = γ p0 / ρ 0 is the ideal MHD sound velocity. Over the last decade, it has gradually been realized that together with zonal flows, GAMs represent an important ingredient of drift wave turbulence in a tokamak. Drift-wave fluctuations are coupled to low-frequency zonal flows and finite frequency GAMs via toroidal effects and nonlinear Reynolds stress [2, 3]. GAMs and zonal flows rotational modes suppress the small scale fluctuations via shearing and energy sink thus creating complex interactions between drift wave turbulence, zonal flows, and GAMs [4–6]. The direct effect of GAMs on anomalous transport is not clear at the moment; however, there are significant experimental evidence indicating coupling and mutual effects of turbulent fluctuations and GAMs. In addition to their role in regulation of anomalous transport, it has been suggested that GAM can also be useful for plasma diagnostic purposes [7]. Large body of the current work investigates GAM coupling to Alfvén and drift modes (see, e.g., [8–12] and references therein). Yet, already in 1973, A.B. Mikhailovskii pointed out that the theory of drift waves in toroidal systems has to be developed taking 1 The article is published in the original.
into account the averaged curvature, magnetic well, and electromagnetic effects [13]. Using two-fluid theory, in that paper, he developed the theory of drift instabilities that include GAMs, Alfvén effects, magnetic well, and magnetic shear, as well as ion finiteLarmor-radius (FLR) effects. Such general electromagnetic perturbations in toroidal systems with averaged magnetic well are described
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