Enhanced radial velocity and damping rate of Geodesic Acoustic Modes in the presence of a temperature gradient

摘要

Introduction Geodesic acoustic modes (GAMs) represent the oscillating part of the Zonal Flow (ZF) and are generated by toroidal curvature effects through the coupling of the electric field (m,n)=0,0 mode and the (1,0) pressure perturbations. GAMs are strongly involved in the energy transport and in the turbulence suppression. In fact GAM oscillations contribute to the transfer of energy from the ZF to the pressure perturbation [1]. Moreover, GAMs can radially propagate the ZF with important consequences on the energy transport. However, to the present the radial propagation of the GAM is not well understood and several aspects need to be elucidated. Although most of experiments show a radial propagation outwards the tokamak device, some observations show an inward radial propagation of GAMs [2]. Moreover, it is unclear whether this velocity is constant or exhibits variations in the experiments and in particular the role of temperature gradient requires to be investigated. The linear theory of GAM velocity due to finite ion Larmor radius has been well developed in recent years predicting a group velocity v_g ∝ω_Gk_rρ~2_i for a GAM with a wavenumber k_r and a frequency ω_G. However, only a qualitative agreement with the experimental results has been obtained. Experimental results show a velocity much larger than that predicted by linear theory. Consequently in order to explain the gap between theory and experiments the research focuses on nonlinear aspects [3]. Although GAMs are a natural part of the turbulent system, it is nevertheless very useful to further investigate their linear behavior, in order to be able to judge how turbulence and GAMs influence each other. Recently, by studying the linear behavior of GAM in the presence of a temperature gradient a new damping mechanism has been identified [4] -the so called Phase-mixing Landau damping (PL)-mechanism- and discussed in Ref.s [4, 5,6]. The local dependence of GAM frequency on the plasma parameters, such as