## What is it about?

This article presents a global reduced model for slab-like microtearing modes (MTM) in the H-mode pedestal, which reproduces distinctive features of experimentally observed magnetic fluctuations, such as chirping and discrete frequency bands at non-contiguous mode numbers. Our model, importantly, includes the global variation of the diamagnetic frequencies, which is necessary to reproduce the experimental observations. The key insight underlying this model is that MTM instability is enabled by the alignment of a rational surface with the peak in the profile of the diamagnetic frequency. Conversely, MTMs are strongly stabilized for toroidal mode numbers for which these quantities are misaligned. This property explains the discrete fluctuation bands in several DIII-D and JET discharges, which we survey using our reduced model in conjunction with global gyrokinetic simulations. A fast yet accurate reduced model for MTMs enables rapid interpretation of magnetic fluctuation data from a wide range of experimental conditions to help assess the role of MTM in the pedestal.

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## Why is it important?

This paper introduces the slab-like MTM (SLiM) model for predicting and interpreting pedestal magnetic fluctuations. The model is motivated by the recent discovery that (1) MTMs are responsible for a prominent class of edge magnetic fluctuations, and (2) the alignment of rational surfaces with the peak in the electron diamagnetic frequency governs the stability of these modes resulting in sensitive selection of unstable toroidal mode numbers. We define a criterion for the critical toroidal mode number below which this sensitive n-number selection can occur: $n_{crit}=\frac{\rho_{tor}}{2\hat{s}q\mu_{crit}}$, $\mu_{crit}$ is the radial stability boundary where MTM will become stable outside of it ($\mu$ is defined at Fig. \ref{fig:Ome_8percents}). The SLiM model encompasses two modes of operation: (1) a reduced model for global slab MTM, which has been shown to qualitatively reproduce global GENE results by identifying the stabilization of toroidal mode numbers, and (2) a heuristic approach for rapidly identifying stable toroidal mode numbers based on the location of their rational surfaces (the offset stabilization illustrated in Fig.~\ref{fig:demo}). In combination with sparse application of global gyrokinetic simulations and local gyrokinetic simulations for curvature-driven MTM, this provides a rigorous yet efficient approach to predicting and interpreting edge magnetic fluctuations. The major applications as SLiM so far are: \begin{itemize} \item Matching the frequency with an experiment using SLiM and complemented with local linear simulations for high mode number MTM. \item Determining the poloidal mode numbers of unstable MTM's. \item Adapting the equilibrium by constraining the safety factor on the pedestal. \end{itemize} We have surveyed four discharges for which the concept of offset stabilization was successfully applied to magnetic spectrograms. The growing number of such analyses demonstrates the explanatory power of the concept of offset stabilization. Three of these studies have been described in previous publications. We review these and, in some cases, extend the analysis. We also present a new analysis of DIII-D discharge 174819. For this discharge, there are two frequency bands which can be experimentally identified as $n=3,5$. Using the SLiM model to guide minor modifications to the q profile, we can precisely reproduce these mode numbers and frequencies with global linear gyrokinetic simulations. Perhaps surprisingly we can even construct a scenario wherein the $n=3$ mode is unstable while $n=6$ is stable (despite the fact that they share the same rational surface). Additionally, we characterize the rate of stabilization with offset distance (distance between a rational surface and the peak). Moreover, we demonstrate that this is an intrinsically global effect that cannot be captured by a local flux tube approach. The SLiM model performs well across different Tokamak devices. The rational surfaces located at the peak of $\omega_{*,e}$ with an integer multiple of its mode numbers explained the discrete band of the spectrogram. Under such an approach, simulations' high sensitivity of magnetic profile has been explained. The SLiM model will provide information on the potential instability that was observed experimentally. By utilizing SLiM, one can obtain more information regarding the safety factor in the pedestal region which provides a route to very precise equilibrium reconstructions of the pedestal. Future work (ongoing) will entail a more extensive survey of magnetic fluctuations on DIII-D using the SLiM model.

## Read the Original

This page is a summary of: A survey of pedestal magnetic fluctuations using gyrokinetics and a global reduced model for microtearing stability, Physics of Plasmas, April 2022, American Institute of Physics,

DOI: 10.1063/5.0084842.

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