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

Abstract

Nonlinear simulations of the early edge-localized mode (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 ¼ 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 ¼ 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 ¼ 1 reaches far into the plasma core. In contrast, the nonlinearly driven n ¼ 1 has a rigidly growing structure localized at the plasma edge, where the dominant toroidal harmonics driving the n ¼ 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," Nucl. Fusion (submitted)]. [http://dx.

Recent progress in the quantitative validation of JOREK simulations of ELMs in JET

“…In cases with higher resistivity and viscosity, nonlinear coupling in the early phase of the ELM is frequently observed, as in [17,18]. However, the theoretical resistivity is set by the Spitzer value, and a higher viscous coefficient would stabilise the ballooning modes, which is the reason for the present choice of η and μ.…”

“…The MHD model used for the present paper is similar to that used in previous ELM studies [14][15][16][17][18]. It is a five-field reduced MHD model for the variables ψ (poloidal magnetic flux), Φ (electric potential), v ∥ → (parallel velocity), ρ (density), T (total temperature), including the two-fluid diamagnetic effects.…”

Velocimetry analysis of type-I edge localized mode precursors in ASDEX Upgrade

“…Linear simulations of peeling-ballooning modes predict high toroidal mode numbers n [3], while the experimentally observed structure are at low toroidal mode numbers [4,5]. Nonlinear reduced MHD simulations can explain the growth of low n toroidal mode numbers by an inverse cascade mechanism [6,7], which is a purely nonlinear feature. Furthermore nonlinear electromagnetic gyrokinetic simulations show that depending on β = p/(B 2 /2µ 0 ) (with plasma pressure p and magnetic field strength B) different instabilities dominate the linear growth phase [8].…”

A 3-D MHD equilibrium description of nonlinearly saturated ideal external kink/peeling structures in tokamaks

“…phase so that n 1 structures become dominant (Wenninger et al 2013) that are further buttressed with linear to nonlinear simulations undertaken with the JOREK code (Krebs et al 2013;Liu et al 2015). On the right-hand side of figure 6, we see that for the smaller J BS /I t = 0.307 edge bootstrap current case, the m/n = 6/4 Fourier component of B is dominant at the plasma boundary, with subdominant m/n = 7/4, 5/4 and 9/4 structures also appearing.…”