Abstract Details
Abstracts
Author: Howard R Wilson
Requested Type: Poster
Submitted: 2023-03-31 01:51:39
Co-authors: M. Anastopoulos, T. Cote, B. Ford, C.C. Hegna, P.B. Snyder, L. Thompson
Contact Info:
University of York
Heslington
York, YO10 5DD
UK
Abstract Text:
The steep pressure and current gradients of the tokamak pedestal plasma are often limited by ideal MHD peeling-ballooning instabilities. These drive edge localised modes (ELMs), which would damage the structures in future tokamaks, if uncontrolled. One approach to control ELMs is to apply 3D magnetic perturbations (MPs), but a predictive theoretical model for their impact on stability remains a research challenge. The approach presented here builds on the principles of high toroidal mode number, n, ballooning theory [1]. A ballooning mode couples many poloidal Fourier harmonics, labelled m, each radially localised about its rational surface where m=nq, with q the safety factor. The close proximity of rational surfaces ensures that all poloidal harmonics have the same radial dependence, and to leading order in a 1/n expansion one obtains a second order differential equation for this dependence, called the ballooning equation. At next order, the radial variation of the equilibrium breaks the ballooning symmetry, and determines how the Fourier harmonics couple to form the ballooning mode. In the pedestal, the coupling to the harmonics resonant outside the plasma violates this ballooning approximation, and one has to solve the full 2D system using a code like ELITE. We review our 3D stability theory, which (guided by ballooning theory) assumes the dominant effect of the MP is to adjust the amplitudes of the poloidal Fourier harmonics, including coupling of different n modes, without changing their radial shapes. The radial structures for all harmonics are derived from the toroidally symmetric equilibrium using ELITE, and then a 3D variational principle is used to derive the coefficients that scales each of them. Previous results using model equilibria are reviewed, and progress towards assessing the stability of realistic DIII-D equilibria [2] with MPs applied is summarised.
[1] M Anastopoulos, et al Nucl Fus 60 (2020) 106003
[2] S Gu, et al Nucl Fus 62 (2022) 076031
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