April 15-17

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Author: Gerrit J. Kramer
Requested Type: Pre-Selected Invited
Submitted: 2019-02-22 14:10:39

Co-authors: B.J. Tobias, A. Turnbull, E.M. Bass

Contact Info:
PPPL
P.O.box 451
Princeton, NJ   08543
USA

Abstract Text:
A surprising observation from the Electron Cyclotron Emission Imaging (ECE-I) diagnostic is that the Alfven eigenmode (AE) wave fronts are radially curved. Simulations with gyro-kinetic and gyro-Landau fluid codes are able to reproduce the measured frequency behavior and yield radial phase variations. However, codes do not consistently agree with each other or experiment on the direction of phase variation. Although the results of these simulations are impressive in describing the experiments, the physical mechanism that is responsible for the radial wavefront curvature is difficult to be traced in these large-scale simulations and the physical mechanism behind the curvature remains somewhat opaque.

We show that for non-linearly saturated AEs this wavefront curvature is consistent with a spatial mismatch between the drive and damping: the mode has to transport the power gained at the location of the drive to the damping region where the power is dissipated. This radial energy transport is setup by the wavefront curvature as is deduced from the Poynting flux induced by the mode.

The Poynting flux is calculated from ideal MHD whereby the ansatz for the radial displacement of the mode is modified by an additional phase factor that is consistent with experiments. From the radial displacement, the fluctuating electric and magnentic fields are obtained and used to calculate the power flow from the Poynting vector. Without a radial phase factor, the mode-induced power flow is mainly along the field lines. But including the radial phase factor generates very strong radial power flows.

For non-linearly saturated AEs, Poynting's theorem can then be used to extract the regions where the wave gains and where it dissipates power. A stability analysis with the NOVA-k code shows that regions of positive Poyting-flux divergence are associated with fast-ion mode drive, while regions of negative Poynting-flux divergence are associated with mode (ion Landau) damping.

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