Nonlinear excitation of low-n harmonics in reduced magnetohydrodynamic simulations of edge-localized modes

TL;DR

This study uses nonlinear reduced MHD simulations to show that low-n harmonics, especially n=1, grow significantly during ELMs, with a simple model explaining energy transfer among harmonics and their spatial structure changes.

Contribution

The paper introduces a quadratic coupling model that explains the nonlinear growth and spatial evolution of low-n harmonics during ELMs in reduced MHD simulations.

Findings

Low-n harmonics grow to energies comparable with dominant harmonics during nonlinear evolution.

A simple model based on second order nonlinear interactions reproduces the spectrum evolution.

The spatial structure of n=1 harmonic shifts from core to edge during nonlinear growth.

Abstract

Nonlinear simulations of the early ELM phase based on a typical type-I ELMy ASDEX Upgrade discharge have been carried out using the reduced MHD code JOREK. The analysis is focused on the evolution of the toroidal Fourier spectrum. It is found that during the nonlinear evolution, linearly subdominant low-n Fourier components, in particular the n = 1, grow to energies comparable with linearly dominant harmonics. A simple model is developed, based on the idea that energy is transferred among the toroidal harmonics via second order nonlinear interaction. The simple model reproduces and explains very well the early nonlinear evolution of the toroidal spectrum in the JOREK simulations. Furthermore, it is shown for the n = 1 harmonic, that its spatial structure changes significantly during the transition from linear to nonlinearly driven growth. The rigidly growing structure of the linearly barely unstable n = 1 reaches far into the plasma core. In contrast, the nonlinearly driven n = 1 has a rigidly growing structure localized at the plasma edge, where the dominant toroidal harmonics driving the n = 1 are maximal and in phase. The presented quadratic coupling model might explain the recent experimental observation of strong low-n components in magnetic measurements [Wenninger et al., Non-linear magnetic perturbations during edge localized modes in TCV dominated by low n mode components, submitted to Nuclear Fusion].