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The electrostatic geodesic mode oscillations are investigated in rotating large aspect ratio tokamak plasmas with circular isothermal magnetic surfaces. The analysis is carried out within the magnetohydrodynamic model including heat flux to compensate for the non-adiabatic pressure distribution along the magnetic surfaces in plasmas with poloidal rotation. Instead of two standard geodesic modes, three geodesic continua are found. The two higher branches of the geodesic modes have a small frequency up-shift from ordinary geodesic acoustic and sonic modes due to rotation. The lower geodesic continuum is a new zonal flow mode (geodesic Doppler mode) in plasmas with mainly poloidal rotation. Limits to standard geodesic modes are found. Bifurcation of Alfvén continuum by geodesic modes at the rational surfaces is also discussed. Due to that, the frequency of combined geodesic continuum extends from the poloidal rotation frequency to the ion-sound band that can have an important role in suppressing plasma turbulence.

A two fluid model with parallel viscosity is employed to derive the dispersion relation for electromagnetic geodesic acoustic modes (GAMs) in the presence of drift (diamagnetic) effects. Concerning the influence of the electron dynamics on the high frequency GAM, it is shown that the frequency of the electromagnetic GAM is independent of the equilibrium parallel current but, in contrast with purely electrostatic GAMs, significantly depends on the electron temperature gradient. The electromagnetic GAM may explain the discrepancy between the f ∼ 40 kHz oscillation observed in TCABR [Yu. K. Kuznetsov et al., Nucl. Fusion 52, 063044 (2012)] and the former prediction for the electrostatic GAM frequency. The radial wave length associated with this oscillation, estimated presently from this analytical model, is λ r ∼ 25 cm, i. e., an order of magnitude higher than the usual value for zonal flows (ZFs).

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Abstract. The MHD theory of the effect of toroidal and poloidal rotations on the dynamics of Zonal Flows -ZFs and Geodesic Acoustic Modes -GAMs in axisymmetric magnetic confinement configurations is revisited. The MHD model has an arbitrariness regarding the energy conservation equation and previous works on the effect of rotation on ZFs and GAMs adopted an adiabatic law, or other simplifying assumptions, to treat this problem. However, in fusion grade plasmas, the heat transport along the magnetic field lines is rather fast and, therefore, a somewhat more appropriate model is to assume isothermal flux surfaces. This implies to take into account the heat transport equation in the model and, in the presence of rotation, this leads to an increase in the degree of the dispersion relation for these modes, giving rise to a low-frequency third branch of these modes. This has been previously obtained by Elfimov, Galvão and Sgalla [1] employing a model of circular flux surfaces from the outset. In this paper, the theoretical development is generalized by using flux coordinates, following the method of Ilgisonis et al [2]. This allows a better assessment of the applicability of the results and to investigate the relevance of the low frequency mode in non-circular tokamaks. Specific results for the TCABR tokamak are presented. IntroductionGeodesic acoustic modes (GAMs) are plasma eigenmodes characterized by a perturbed electric field constrained to oscillate only in the radial direction (i.e., m = n = 0, where m and n are the poloidal and toroidal mode numbers, respectively) and by a perturbed density that varies with the first order poloidal harmonic, m = ±1. GAMs, whose existence was predicted in the 1960s [1], are stable oscillations over magnetic surfaces. Their generation mechanism is based on the effect of the (radial) perturbed electric field, constant and perperdicular to the magnetic surfaces, which induces a poloidal flow over the surface due to the drift velocity, E × B. In a toroidal magnetic surface, the geodesic curvature of the field lines gives rise to a restoring force against that flux, thus inducing an oscillatory motion. GAMs are the branch of nonzero frequency of the same dispersion relation associated with zonal flows (ZFs), which are zero-frequency modes.The nonlinear process behind the existence of the GAMs could be described as follows. Density and temperature gradients trigger drift micro-instabilities, which give rise to a turbulent spectrum of fluctuations with large convective cells that cause the anomalous transport. After certain thresholds, the correlation between the same fluctuations triggers GAMs and ZFs by means of the Reynolds stress tensor and other parametric mechanisms. Sheared flows, associated with these modes, tend to tear the convective cells, thus reducing the anomalous transport.