Probing non-linear MHD stability of the EDA H-mode in ASDEX Upgrade

Abstract

Regimes of operation in tokamaks that are devoid of large ELMs have to be better understood to extrapolate their applicability to reactor-relevant devices. This paper describes non-linear extended MHD simulations that use an experimental equilibrium from an EDA H-mode in ASDEX Upgrade. Linear ideal MHD analysis indicates that the operational point lies slightly inside of the stable region. The non-linear simulations with the visco-resistive extended MHD code, JOREK, sustain non-axisymmetric perturbations that are linearly most unstable with toroidal mode numbers of ${n=\{6\dots9\}}$, but non-linearly higher and lower $n$ become driven and the low-n become dominant. The poloidal mode velocity during the linear phase is found to correspond to the expected velocity for resistive ballooning modes. The perturbations that exist in the simulations have somewhat smaller poloidal wavenumbers (${k_\theta\sim0.1~\mathrm{to}~0.5~\mathrm{cm^{-1}}}$) than the experimental expectations for the quasi-coherent mode in EDA, and cause non-negligible transport in both the heat and particle channels. In the transition from linear to non-linear phase, the mode frequency chirps down from approximately 35~kHz to 13~kHz, which corresponds approximately to the lower end of frequencies that are typically observed in EDA H-modes in ASDEX Upgrade.

Non-linear MHD investigations of high-confinement regimes without type-I ELMs in ASDEX Upgrade and JT-60SA

“…strongly localised to the LFS, and display characteristics typical of resistive ballooning nature. Namely, the mode velocity and changes to the linear growth rates resulting from variations in local resistivity [37,41]. In contrast, for the QH-mode linearly dominant is an n = 2 kink-peeling mode, which grows at a slower rate than the resistive PB modes that dominate the other two regimes.…”

“…The operational point with respect to the ideal linear MHD PB boundary is shown in figure 2(right). From the MISHKA-1 analysis, it is clear that the operational point lies close to the n ∼ 14 ballooning boundary, however this neglects the stabilising influence of diamagnetic and ExB flows [41].…”

“…The simulations performed based on the experimental discharge described in section 2.3 are described in detail in [41] and contextualised in this section to portray them with respect to the simulations of QH-mode and small ELMs at low triangularity described in the previous two sections. The non-axisymmetric simulations include all toroidal modes between n = 0 and 13 and show linear growth of modes dominated by n = {6 .…”

MHD simulations of formation, sustainment and loss of quiescent H-mode in the all-tungsten ASDEX Upgrade

“…The exact impact of running with such larger resistivity onto the dynamics of the non-axisymmetric perturbations cannot be determined without running dedicated simulations. However, since the instabilities that are linearly unstable for the present simulations hold the mode structure of Kink-Peeling Modes (KPMs) rather than ballooning modes, the effect of resistivity is not foreseen to be as important as it is for [10,36].…”

“…For ψ N = 0.95 this leads to an experimental resistivity of 1.1 × 10 −7 Ω m while the resistivity in the simulation in that location is 9.9 × 10 −7 Ω m. The resistivity in the pedestal region is thus taken to be about a factor of 10 larger than in the experiment. In contrast to JOREK simulations that investigate small-ELMs or the enhanced D-alpha H-mode in AUG which manage to simulate the non-linear MHD activity at realistic resistivity [10,36], these QH-mode simulations probe experimental conditions at lower pedestal resistivity (roughly by a factor of 10 with respect to the aforementioned references) which make it much more complicated to consider realistic resistivity values. The exact impact of running with such larger resistivity onto the dynamics of the non-axisymmetric perturbations cannot be determined without running dedicated simulations.…”