Decay of geodesic acoustic modes due to the combined action of phase mixing and Landau damping

Abstract

Geodesic acoustic modes (GAMs) are oscillations of the electric field whose importance in tokamak plasmas is due to their role in the regulation of turbulence. The linear collisionless damping of GAMs is investigated here by means of analytical theory and numerical simulations with the global gyrokinetic particle-in-cell code ORB5. The combined effect of the phase mixing and Landau damping is found to quickly redistribute the GAM energy in phasespace, due to the synergy of the finite orbit width of the passing ions and the cascade in wave number given by the phase mixing. When plasma parameters characteristic of realistic tokamak profiles are considered, the GAM decay time is found to be an order of magnitude lower than the decay due to the Landau damping alone, and in some cases of the same order of magnitude of the characteristic GAM drive time due to the nonlinear interaction with an ITG mode. In particular, the radial mode structure evolution in time is investigated here and reproduced quantitatively by means of a dedicated initial value code and diagnostics.

Gyrokinetic investigation of the damping channels of Alfvén modes in ASDEX Upgrade

“…[15] (see also Ref. [16,17,18] for the application to Geodesic Acoustic modes, GAMs). To see evidence of this mechanism, the simulations presented in this section have been run with simplified geometries and profiles, without the presence of EPs.…”

Kinetic theory of geodesic acoustic modes in toroidal plasmas: a brief review

“…with the selection rule k = k ′ + k G . Note that equations (41) and (42) are derived using the k ⊥ ρ ti ≪ 1 and 1/q ≪ 1 expansions, while no assumptions on the mode amplitudes are made except the gyrokinetic ordering [52]. As a result, equations (41) and (42) are general, and can be applied to study the nonlinear saturation of DWs [74,134,135].…”

“…Note that equations (41) and (42) are derived using the k ⊥ ρ ti ≪ 1 and 1/q ≪ 1 expansions, while no assumptions on the mode amplitudes are made except the gyrokinetic ordering [52]. As a result, equations (41) and (42) are general, and can be applied to study the nonlinear saturation of DWs [74,134,135]. In this paper, for the sake of simplicity, we will only review the results obtained for the "linear" growing stage of the parametric instability, with the emphasis on the effect of system nonuniformities and kinetic dispersiveness on GAM excitation.…”

“…13. The governing nonlinear equations can be derived from equations (41) and (42), taking δφ d = δφ P + δφ S , with the ballooning mode decomposition for δφ d :…”

Linear gyrokinetic investigation of the geodesic acoustic modes in realistic tokamak configurations

“…Distorting the GAM radial structure and creating higher radial wavenumbers, this process can strongly increase the GAM damping rate [8,25]. A section 4 of our paper is dedicated to the extension of previous works [22,24], which were done treating the electrons as adiabatic, and in circular flux surfaces, to the inclusion of kinetic electrons and realistic tokamak configurations. Finally, the last section of this paper is dedicated to the investigation of a realistic discharge of ASDEX Upgrade, described in Ref.…”