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

Abstract Regimes of operation in tokamaks that are devoid of large edge localised modes have to be better understood to extrapolate their applicability to reactor-relevant devices. This paper describes non-linear extended magnetohydrodynamic (MHD) simulations that use an experimental equilibrium from an enhanced D-alpha (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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mo fence="false" stretchy="false">{</mml:mo> <mml:mn>6</mml:mn> <mml:mo>…</mml:mo> <mml:mn>9</mml:mn> <mml:mo fence="false" stretchy="false">}</mml:mo> </mml:mrow> </mml:math> , 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 ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mi>k</mml:mi> <mml:mi>θ</mml:mi> </mml:msub> <mml:mo>∼</mml:mo> <mml:mn>0.1</mml:mn> </mml:math> – <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>0.5</mml:mn> <mml:mtext> </mml:mtext> <mml:mrow> <mml:mi mathvariant="normal">c</mml:mi> <mml:msup> <mml:mi mathvariant="normal">m</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> ) 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.