# Theory of Edge Localized Mode Suppression by Static Resonant Magnetic Perturbations in the DIII-D Tokamak

## TL;DR

This paper develops an analytic model to quickly simulate and understand how static resonant magnetic perturbations suppress edge localized modes in the DIII-D tokamak, building on previous nonlinear MHD simulations.

## Contribution

It simplifies existing nonlinear MHD models into an analytic form enabling rapid simulation of RMP-induced ELM suppression in DIII-D.

## Key findings

- Analytic model reproduces key features of ELM suppression
- Model predicts ELM suppression thresholds accurately
- Provides physical insight into RMP penetration mechanism

## Abstract

The plasma response to an externally generated, static, n=2, resonant magnetic perturbation (RMP) in the pedestal region of DIII-D discharge #158115 is investigated. In this particular discharge, the resonant amplitudes of the RMP are modulated in a cycloidal manner at a frequency of 1 Hz. Adopting the plausible hypothesis that mode penetration at the top of the pedestal is a necessary and sufficient condition for the RMP-induced suppression of edge localized modes (ELMs), recent cylindrical, nonlinear, reduced-magnetohydrodynamical (MHD) simulations performed by Hu, Nazikian, et al., (2019) can account, in a quantitative fashion, for the density-pump out and RMP-induced ELM suppression threshold observed in DIII-D discharge #158115. The primary aim of this paper is to employ analytic theory to further simplify the model of Hu, Nazikian, et al., in such a manner that a complete simulation of RMP-induced ELM-suppression in a DIII-D H-mode discharge can be performed in a matter of minutes of real time. A secondary aim is to gain a more exact understanding of the physical mechanism that underlies RMP-induced ELM suppression in the DIII-D tokamak.