Observation of magnetic islands in tokamak plasmas during the suppression of edge-localized modes

To achieve an economically viable tokamak fusion power plant, operation in high-confinement H-mode is required. The steep edge pressure gradient forms a pedestal that enhances core pressure but drives magnetohydrodynamic instabilities causing edge-localized modes (ELMs), which threaten plasma-facing components. Resonant magnetic perturbations (RMPs) from saddle coils can mitigate or suppress ELMs while maintaining confinement, but the underlying physics must be understood for predictive control. Rational magnetic surfaces, where field lines close after integer turns, are sensitive to aligned perturbations; with finite resistivity, reconnection can alter topology and form magnetic islands, potentially overlapping in the edge. Early ELM suppression explanations posited stochastic fields from RMP penetration leading to enhanced heat and particle transport, but experiments indicate primarily particle transport changes rather than the strong electron heat losses predicted by stochastic transport. Ideal MHD and generalized Ohm’s law predict helical screening currents at rational surfaces, especially in the H-mode pedestal with strong flows, impeding RMP penetration there; penetration is more likely where pressure gradients are small. Nevertheless, small 3D perturbations can excite marginally stable ideal kink responses that preserve topology but amplify boundary kinking, consistent with ideal MHD. A key hypothesis is that ideal kink responses extend into the gradient region and couple to a rational surface at the pedestal top, enabling magnetic island formation where flow is reduced, thereby limiting pedestal width (as in the EPED model) and suppressing ELMs. This hypothesis accounts for windows of suppression when scanning rational surface positions, the importance of kink–resonant surface coupling, and sudden magnetic probe changes at ELMy-to-suppressed transitions. However, definitive experimental identification of a pedestal-top island has been lacking, as observed Te flattening could arise from different mode numbers or turbulence. This study targets direct observation by comparing high-resolution measurements of internal magnetic topology against ideal MHD predictions in both ELM-suppressed and ELMy plasmas.

Prior work established that RMPs can suppress ELMs across multiple devices and that ideal kink responses to applied fields can amplify boundary distortions while preserving magnetic topology. Screening currents driven by electron fluid flow at rational surfaces inhibit RMP penetration in the pedestal. The EPED pedestal model predicts that limiting pedestal width via transport at a resonant surface can preclude ELMs. Experimental signatures supporting island-related suppression include phase-space control and windows of suppression when aligning resonant surfaces at the pedestal top, as well as abrupt changes in magnetic probe signals during transitions to suppression. Nonetheless, direct detection of a pedestal-top island has been challenging: stochastic transport predictions conflict with observed electron heat transport, and Te flattening could stem from other mode numbers or turbulence. Previous attempts relying on phase jumps during error-field compensation were inconclusive. This work builds on these findings, leveraging rotating RMP fields and Te-based topology measurements to isolate island signatures beyond ideal MHD response.

Device and plasma conditions: Experiments were conducted on the ASDEX-Upgrade tokamak (major radius 1.65 m, minor radius 0.5 m). ELM suppression scenario parameters: Bt = 1.835 T, plasma current Ip = 898 kA, upper triangularity 0.25. Auxiliary heating: 2.3 MW ECRH and 6 MW NBI. Two consecutive discharges were compared: ELM-suppressed (#40180, no additional gas after 2.6 s) and ELMy (#40181, deuterium puffing 2×10^21 s^-1 to raise density). The RMP field used n = 2 toroidal symmetry from 16 saddle coils in two rows, rotating rigidly at f_RMP = 0.75 Hz with fixed alignment; q95 ≈ 3.7. Eddy-current attenuation by nearby conductors was included via effective coil currents. Diagnostics and data processing: Electron cyclotron emission (ECE) radiometry (78–105 GHz) provided high-resolution Te profiles. The edge region (73–89 GHz) was covered by 36 channels (Δf = 300 MHz IF, 400–800 MHz channel spacing; Bt optimized to yield 400 MHz spacing ≈ 5 mm near the pedestal top). Sampling rate was 1 MHz. ECE data were analyzed from 3.3–7.2 s for #39993, #40180, #40181 and to 6.8 s for #40176. Optically thin or shine-through affected channels were excluded; only τ > 3 conditions were used, with forward modeling validating Trad ≈ Te in the region of interest. ELMs in ELMy phases were excised using wall tile shunt current Itile spikes. Small secular Te drifts during rotation were corrected by a linear scaling factor (0.9–1.1), with impact folded into uncertainties. Plasma boundary motion compensation: The axisymmetric position control system introduced periodic outer boundary motion R_axi; compensation was applied via feed-forward trajectories derived from otherwise identical discharges (#39993 ELMy and #40176 suppressed). Analyses were performed both with and without compensation to verify robustness. Measurement strategy: To probe potential islands phase-locked to RMPs and coexisting with ideal kinks of the same toroidal mode, the absolute RMP phase was continuously scanned by rotation, effectively sampling different toroidal phases at a fixed toroidal diagnostic location. ECE-derived iso-Te contours (ELM-suppressed: 0.6–1.1 keV; ELMy: 0.5–1.1 keV in 10 eV steps) near the outer midplane were tracked relative to R_axi. Each contour was fit with a sinusoid including higher harmonics along the ECE radial coordinate R to extract the fundamental n = 2 displacement amplitude |ξ| and phase φ across radius. Equilibrium reconstruction: Rational surface locations and boundary positions were constrained using three axisymmetric reconstructions: (1) CLISTE at a representative time with hand-fitted profiles and no SOL currents; (2) CLISTE at 1 ms resolution without kinetic constraints; (3) IDE at 1 ms with kinetic constraints and current diffusion, assuming axisymmetry. IDE provided rational surface bands in figures; (1) supplied inputs to 3D modeling. Uncertainties from reconstructions defined bands on measured displacements. Ideal MHD modeling: The 3D ideal MHD equilibrium code VMEC (PARVMEC) computed ideal kink responses using CLISTE equilibria constrained by kinetic profiles (Thomson scattering, ECE, Li-beam) near a phase of minimal distortion (~4.65 s). High radial resolution (up to 2001 flux surfaces; tests with 511, 1501, 2001 showed <0.1 mm differences around q = 7/2) and sufficient poloidal/toroidal mode content ensured accurate boundary and internal displacement predictions. Effective RMP coil currents accounted for eddy-current attenuation. VMEC boundary displacements were validated against helium beam boundary diagnostics. Island identification analysis: To isolate a potential magnetic island amid dominant ideal kinks, complex n = 2 components were formed from measurements and VMEC predictions: ξ_r,n=2 = |ξ| sin φ and ξ_i,n=2 = |ξ| cos φ. Subtracting ideal kink components (ξ_r,kink, ξ_i,kink) from measured ones yielded residuals attributed to island response. A phase diagnostic δφ_n=2 = arctan(ξ_i/ξ_r) − arctan(ξ_i,kink/ξ_r,kink) was used; a π jump in δφ_n=2 indicates an island. Amplitude bumps and local minima–maxima spacings were also used as island signatures and size proxies. Resistive MHD modeling: Nonlinear extended MHD simulations were carried out with JOREK coupled to STARWALL in realistic geometry using a reduced MHD model with bootstrap current evolution, two-fluid diamagnetic effects, neoclassical friction, realistic viscosity (~1 m^2 s^-1 in the pedestal), and anisotropic heat transport. Ion temperature was set equal to Te (reasonable within ~20% during suppression). Simulations used #40180 equilibria, experimental RMP currents, and kinetic profiles. A numerical experiment varied torque sources to scan electron fluid velocity ve profiles: one case with strongly negative ve (no or very small islands), and another with a ve zero-crossing at q = 7/2 enabling a single pedestal-top island. Synthetic Te contours and n = 2 amplitude/phase were compared to experiment and VMEC predictions.

- Ideal MHD vs measurements: In ELMy plasmas (#40181), measured n = 2 displacement amplitude |ξ| decreases from edge to core and matches VMEC predictions; phase φ shows no anomaly near q = 7/2 where amplitude is sufficient for accurate phase. In ELM-suppressed plasmas (#40180), |ξ| is globally reduced (lower pressure gradients) but exhibits a distinct bump and local minima–maxima structure inside the q = 7/2 surface, with an associated localized phase change—features not reproduced by ideal MHD across varied input profiles and high radial resolution. - Island detection: Subtracting the ideal kink response from measured complex components yields a residual consistent with a magnetic island at q = 7/2 during ELM suppression, including a clear δφ_n=2 ≈ π phase jump near q = 7/2. An ELMy reference shows no such jump. A separate ELMy discharge (#39993) exhibits a δφ_n=2 ≈ π jump at q = 6/2, indicating a 6/2 island located deeper inside the plasma; this did not lead to ELM suppression. - Robustness: The amplitude bump and phase features around q = 7/2 persist without R_axi compensation (#40176), with only a small φ offset (~1 mm equivalent), confirming the structures are not artifacts of boundary motion compensation. - Resistive MHD support: JOREK simulations without significant islands reproduce the ideal-MHD-like response (no amplitude bump), whereas simulations with a single q = 7/2 island (~4 mm size) reproduce the observed amplitude bump inside q = 7/2 and a localized phase change. Poincaré plots show an island with a clear o-point at the pedestal top only in the island-enabled case. - Island size: From Te measurements, the spacing between local amplitude minimum and maximum gives W_ECE ≈ 9 mm; an overall estimate yields W_ECE ≈ 1 cm at the ECE location corresponding to a surface-averaged island width W_ist ≈ 2 cm (~1% of major radius). This is about twice the critical island width W_crit ≈ 1 cm needed for parallel heat transport to dominate, consistent with observable Te perturbations without complete Te flattening at the o-point. - Contextual observations: ELM suppression correlates specifically with a pedestal-top island at q = 7/2; a single island deeper inside (q = 6/2) in an ELMy case is not sufficient for suppression. Ideal MHD adequately describes ELMy plasmas but is insufficient for ELM-suppressed plasmas where topology changes occur.

The results directly address the long-standing hypothesis that ELM suppression by RMPs involves magnetic island formation at a rational surface near the pedestal top. Measurements of Te-based magnetic surface displacement reveal amplitude and phase structures around q = 7/2 that cannot be explained by ideal MHD kink responses, indicating a change in magnetic topology. By subtracting the ideal kink contribution, a π phase jump and residual displacement consistent with a q = 7/2 island are identified only during ELM suppression. This provides experimental confirmation that coupling of the ideal kink response to a resonant surface can drive a pedestal-top island, limiting pedestal width and preventing ELMs (consistent with EPED). The absence of such an island in the ELMy counterpart and the presence of a deeper-lying 6/2 island without suppression further corroborate the pedestal-top requirement. Nonlinear resistive MHD modeling (JOREK) reproduces the key experimental signatures only when a pedestal-top island is allowed, validating the physical interpretation and highlighting the role of electron fluid velocity profiles in allowing penetration and reconnection. These findings refine the physics basis for predicting ELM suppression windows and optimizing RMP configurations in future devices, where controlled island formation at the appropriate rational surface could be used to maintain high confinement without damaging ELMs.

This work provides experimental evidence that small 3D magnetic perturbations can change edge magnetic topology in H-mode plasmas, forming a pedestal-top magnetic island that is linked to the suppression of ELMs. High-resolution Te measurements during RMP rotation, combined with ideal MHD (VMEC) predictions and subtraction of the kink response, reveal island signatures at q = 7/2 only in ELM-suppressed plasmas. Ideal MHD suffices to describe ELMy plasmas but fails in suppressed regimes where topology changes occur. Nonlinear resistive MHD simulations (JOREK) qualitatively reproduce the observed amplitude bump and phase behavior only when a pedestal-top island is present, supporting the interpretation. The estimated island size (~1 cm at the ECE location, ~2 cm surface-averaged) exceeds the critical width for observable Te perturbations. These results strengthen the physics basis for ELM control strategies in ITER-class devices by clarifying the role of pedestal-top islands. Future work should refine measurements of 3D edge flows and electric fields to determine ve and vE with full 3D effects, quantify the transport contributions of islands versus turbulence and neoclassical mechanisms, include kinetic effects in response modeling, and assess nonlinear coupling among modes during suppression.

- The island identification relies on subtracting ideal MHD kink responses; residual mismatches between measurements and VMEC (e.g., due to profile uncertainties or non-ideal effects) can affect δφ_n=2 and residual structures. - Equilibrium reconstructions (CLISTE, IDE) and kinetic profile uncertainties introduce positional and amplitude errors for rational surfaces and predicted displacements, though bands and multiple methods were used to bound uncertainties. - JOREK simulations that reproduced islands used a ve zero-crossing at q = 7/2, which contrasts with some experimental indications; realistic 3D E×B and diamagnetic flow profiles at the pedestal may differ, and precise determination is beyond the present scope. - ECE interpretation assumes optical thickness; while validated in the region of interest, localized deviations or shine-through filtering may still influence specific channels. - The RMP rotation frequency (0.75 Hz) and diagnostic coverage limit temporal sampling; causality between island formation and ELM suppression is strongly suggested but not isolated via controlled parameter scans within a single discharge. - Estimated island size from Te-derived proxies carries uncertainty, and additional mechanisms (turbulence, polarization, neoclassical transport, nonlinear coupling) may contribute to observed pedestal modifications.