Heat flux effects on the dispersion relation for geodesic modes in rotating plasmas

Abstract

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.

Quasilinear and nonlinear dynamics of energetic-ion-driven Alfvénic eigenmodes

“…The papers published during the graduate studies are listed in Refs. [40,41,98,99,100,101,102] where f is the distribution function; ⌫ ? and ⌧ 1 s are the 90 pitch angle scattering rate and the inverse slowing down time, which are given by 1 This is a robust expression in the sense that the criterion u 2 < T /m does not need to be checked.…”