The tokamak, a leading fusion energy platform, requires high confinement modes (H-mode) for economically viable operation. H-mode's high confinement stems from a steep pressure gradient at the plasma edge, forming a pressure pedestal. However, these steep gradients make the plasma edge susceptible to magnetohydrodynamic (MHD) instabilities, resulting in ELMs. These ELMs, filamentary eruptions of particles and energy, pose a significant threat to plasma-facing components in future fusion reactors, potentially causing damage. Resonant magnetic perturbations (RMPs), generated by additional coils, offer an effective method for controlling ELMs while maintaining high confinement. RMPs distort the tokamak's toroidal symmetry, suppressing ELMs in various tokamaks. However, a complete understanding of the underlying physics mechanism remains crucial for accurate predictions and control in future devices. Rational magnetic surfaces, where magnetic field lines close on themselves after an integral number of turns, are key to understanding the plasma's response to RMPs. In the presence of resistivity, magnetic reconnection can alter surface topology, forming magnetic islands. In the tokamak edge, overlapping islands can create a stochastic field. Early explanations suggested that RMPs induce stochasticity, enhancing transport and reducing the pressure gradient, thereby preventing ELM instability. However, this is contradicted by experimental observations of predominantly particle transport changes. MHD theory predicts helical screening currents on rational surfaces, shielding the plasma from perturbations and hindering stochasticity. These currents are especially strong in the H-mode pedestal, suggesting that RMP penetration is more likely in regions with low pressure gradients. A prominent hypothesis for ELM suppression proposes that RMPs penetrate just inside the steep gradient region where the pressure gradient and electron fluid velocity are low. It is suggested that RMPs excite ideal kink modes, which amplify the perturbation and drive magnetic island formation at a rational surface at the pedestal top. This limits pedestal width, preventing ELMs. This hypothesis explains several observations, including windows in ELM suppression, the importance of kink mode-rational surface coupling, and sudden changes in magnetic probe measurements during the ELM-suppressed transition. However, a direct link between pedestal flattening and magnetic islands remained unconfirmed, as this flattening could also result from islands with different mode numbers or turbulent transport.

The literature review extensively covers previous research on ELM suppression techniques in tokamaks, focusing on the use of RMPs. Studies demonstrated the effectiveness of RMPs in mitigating or suppressing ELMs in various tokamak experiments (Evans et al., 2006; Sun et al., 2016; Suttrop et al., 2018; Shousha et al., 2022). Theoretical work explored the mechanisms behind ELM suppression by RMPs, including the role of stochastic magnetic fields and helical screening currents (Nardon et al., 2010; Huijsmans et al., 2015; Sweeney et al., 2020). Different models were proposed, such as the stochastic transport model and the magnetic island hypothesis. These models were validated against experimental observations and numerical simulations (Park et al., 2018; Snyder et al., 2012; Paz-Soldan et al., 2015; Ryan et al., 2015; Nazikian et al., 2015; Wade et al., 2015; Moyer et al., 2017; Hu et al., 2020; Fitzpatrick, 2020; Gu et al., 2019; King et al., 2015; Leuthold et al., 2023; Nazikian et al., 2014). The literature also included studies on the challenges of measuring magnetic islands in the presence of kink modes (Fitzpatrick, 1995; Gude, 2015; Igochine et al., 2017; Yu et al., 2008). Previous attempts to identify helical perturbations using electron cyclotron emission (ECE) measurements were inconclusive (Willensdorfer et al., 2016; Denk et al., 2018). The review highlights the need for a direct experimental confirmation of the magnetic island hypothesis to improve the predictive capability of ELM control strategies.

The experiment was conducted on the ASDEX-Upgrade tokamak, which is well-suited for this type of investigation due to its flexible RMP coil setup and high-resolution ECE diagnostics. The study focused on two consecutive plasma discharges: one with ELM suppression and the other with ELMs. The only difference between the two discharges was the amount of injected deuterium gas. The RMP field was rotated in a controlled manner to probe the magnetic island structure. Electron cyclotron emission (ECE) measurements provided high-resolution electron temperature (Te) profiles, which were used to determine the perturbed magnetic surface geometry. The Te profiles are almost constant along the magnetic field line and allow the identification of short-circuited field lines associated with magnetic islands. The challenge of measuring small magnetic islands amidst dominant ideal kink modes is addressed using a rotating RMP field. The experimental setup involved generating an RMP field with n = 2 toroidal symmetry using saddle coils, while the ECE diagnostic measured Te perturbations. The RMP field's toroidal phase was varied systematically while the plasma parameters were kept constant. The analysis compared the measured Te contours with predictions from the 3D ideal MHD code VMEC (Variational Moments Equilibrium Code). VMEC accurately reproduced the plasma boundary distortion caused by the kink modes. The comparison focused on the amplitude and phase of the n = 2 magnetic surface perturbation around the pedestal top. To identify magnetic islands, the researchers compared measured Te perturbations with predictions from ideal MHD theory using the VMEC code. The presence of a magnetic island was inferred from deviations of the measurements from the ideal MHD predictions, specifically the appearance of a bump structure in the amplitude and a phase jump in the perturbation profiles. To isolate the magnetic island signature, the ideal kink component was subtracted from the measured Te perturbations. A magnetic island was indicated by a phase jump of approximately π in the residual signal. Nonlinear resistive MHD calculations using the JOREK code were used to further validate the magnetic island hypothesis. JOREK simulations were performed for both ELM-suppressed and ELMy plasmas, varying electron fluid velocity to investigate the effect on island formation. The island size was estimated from both experimental and simulation data. The axisymmetric position control system was taken into account, which was measured in otherwise identical discharges and then compensated. The equilibrium data was obtained from three distinct methods to evaluate the uncertainty.

The key finding of this study is the experimental observation of a magnetic island at the pedestal top in ELM-suppressed plasmas in the ASDEX-Upgrade tokamak. This observation was achieved through a detailed comparison of high-resolution measurements of perturbed magnetic surfaces with predictions from ideal magnetohydrodynamic (MHD) theory. In plasmas with ELMs, the measurements agreed well with ideal MHD predictions. However, in ELM-suppressed plasmas, significant deviations were observed, indicating the presence of a magnetic island. The analysis of electron temperature (Te) contours from ECE measurements revealed a distinct bump structure in the amplitude of the n = 2 magnetic surface perturbation and a corresponding phase jump near the q = 7/2 rational surface only in the ELM-suppressed case. These features were not reproduced by ideal MHD modelling and were consistent with the presence of a magnetic island. The size of the magnetic island at the ECE position was estimated to be approximately 9 mm (WECE), corresponding to an averaged island width of around 2 cm (Wist). This island size was found to be larger than the critical island width required to cause measurable Te perturbations. Further analysis isolating the island structure from the kink mode using equation (1) confirms the presence of a π phase jump close to the 7/2 surface during ELM suppression. Nonlinear resistive MHD simulations using the JOREK code qualitatively reproduced the key experimental observations, further confirming the role of magnetic islands in ELM suppression. Specifically, JOREK simulations with a 7/2 magnetic island of about 4 mm displayed a bump in the perturbation amplitude similar to the experimental results. Simulations without the island show no such bump. The study of another ELMy plasma with a similar structure around the 6/2 surface suggested the presence of a 6/2 magnetic island; however, this was not associated with ELM suppression in that case. The analysis of experiments without the compensation of the outer plasma boundary movements revealed the same displacement structures, consolidating the observations. The study revealed that the electron fluid velocity (ve) plays a crucial role in the formation of magnetic islands. A simulation with a zero-crossing of ve at the 7/2 rational surface led to the formation of a magnetic island, while a simulation with strongly negative ve did not.

The findings of this study provide strong experimental evidence supporting the magnetic island hypothesis for ELM suppression by RMPs. The observed deviations from ideal MHD predictions in ELM-suppressed plasmas, characterized by a bump structure in the perturbation amplitude and a phase jump near the rational surface, clearly indicate the presence of a magnetic island. The agreement between the experimental observations and the nonlinear resistive MHD simulations using JOREK further strengthens this conclusion. This study clarifies the mechanism behind RMP-induced ELM suppression, which is a key issue for the design and operation of future tokamak fusion reactors. The observed magnetic island formation suggests that RMPs can penetrate into the plasma edge and alter the magnetic topology despite the presence of strong screening currents in the pedestal region. This penetration occurs at the top of the pedestal where the pressure gradient is smaller, leading to a reduction in the electron fluid velocity which makes the penetration possible. The formation of the magnetic island then leads to enhanced transport and a reduction in the pressure gradient, thus preventing the ELM instability. The results have implications for predictive modelling of ELM suppression in future fusion devices, allowing for more accurate control strategies. The estimated island size is in the same order of magnitude as modelling results from similar-sized tokamaks. Future research should investigate whether the estimated island size is sufficient to explain the observed drop in temperature and density or if other mechanisms are involved.

This study presents the first experimental confirmation of magnetic island formation at the pedestal top during RMP-induced ELM suppression in a tokamak. High-resolution measurements and both ideal and resistive MHD modelling support the hypothesis that magnetic islands play a crucial role in this process. The findings are crucial for the development of physics-based models for ELM control in future fusion devices. Future work should investigate the interplay between magnetic islands and other mechanisms, such as turbulence and neoclassical transport, to further refine our understanding of ELM suppression.

The study acknowledges limitations inherent in the analysis, particularly the strong dependency of the phase analysis on the agreement between Te measurements and ideal MHD modelling. The JOREK simulations, while qualitatively reproducing key features, employ simplifying assumptions in the MHD description and kinetic effects. More advanced modelling incorporating kinetic effects is needed for a more complete understanding. The study also notes the need for a more thorough analysis of the electron fluid velocity profiles using 3D effects, which is beyond the scope of the current research. The limited range of RMP phases explored could potentially limit the complete mapping of the island structure.