A 3D finite element model simulating tearing modes and their measurements in ASDEX Upgrade

Abstract Tearing modes (TM) are a significant challenge for the operation of large tokamak devices as they cause confinement degradation, can lead to a disruption and are part of the disruption process itself. Detecting and characterising tearing modes is basis for both, improved understanding of their evolution as well as adequate countermeasures. The most harmful tearing mode has the toroidal mode number n = 1, which, due to toroidal coupling, usually consists of different helicities, referred to as poloidal harmonics. Determining the poloidal harmonics requires modelling the magnetic measurements with different challenges for rotating and locked modes. Rotating modes produce frequency-dependent shielding currents in conducting structures that modify the perturbation field. Locked modes require pick-up coils measuring mainly the radial perturbation field component <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mtext>r</mml:mtext> </mml:msub> </mml:mrow> </mml:math> , of which there are far fewer than Mirnov coils in ASDEX Upgrade. The agreement between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>B</mml:mi> <mml:mtext>r</mml:mtext> </mml:msub> </mml:mrow> </mml:math> coils and Mirnov coils in a model description can be validated in the low frequency range, where all coils observe the modes and shielding currents are important. We employ a three-dimensional finite element method model to calculate the expected magnetic measurements of the perturbation field produced by an n = 1 tearing mode with a single helicity and frequency. The TMs are represented by helical perturbation currents at the corresponding resonant surfaces while the rest of the plasma is treated as vacuum. We show that, besides the vacuum vessel and the passive stabilisation loop, it is crucial to include other in-vessel components of ASDEX Upgrade. The poloidal composition of an n = 1 TM is determined by the linear superposition of modelled TMs with single helicities that best matches the measurements by a poloidal array of Mirnov coils. The resulting amplitudes and phases of the poloidal harmonics give simulated measurements that are found to be in agreement with their measured values for all coil types.