Integrating Gyrokinetic Flux Predictions with Ideal MHD Stability Boundaries

Abstract: Accurate prediction of pedestal height and width in tokamaks remains a critical issue as it strongly influences the predicted plasma performance of all future reactors. We present an integrated pedestal-stability workflow that combines equilibrium scans with magnetohydrodynamic (MHD) stability analysis using ELITE and GATO and gyrokinetic transport predictions using CGYRO/QLGYRO. The workflow reproduces the characteristic KBM first- and second-stability structure previously identified in gyrokinetic pedestal studies. Applied to spherical tokamaks (STs), the workflow shows good agreement with past studies when low-n peeling stability is included, emphasizing the importance of resolving low-n physics in ST pedestals. Extending the analysis to SPARC-like, high toroidal field plasmas, kinetic ballooning mode (KBM) and microtearing mode (MTM) heat fluxes are found to increase strongly with toroidal field, suggesting that access to the KBM second-stability region may become significantly more difficult in high toroidal field devices. Comparison with global ELITE finite-n analysis at SPARC parameters suggests that the H-mode pedestal lies in an intermediate regime bounded by local KBM second stability on one side and global finite-n ballooning instability on the other, consistent with the EPED picture once global effects are included

• The paper integrates gyrokinetic flux predictions with ideal MHD stability limits to delineate operational H-mode pedestal regimes across various tokamak configurations.
• It employs a composite mapping using CGYRO, ELITE, and GATO simulations to assess KBM, MTM, and peeling–ballooning instabilities in both spherical and high-field devices.
• The study reveals that achieving high-performance H-mode operation requires navigating a narrow window defined by microturbulence thresholds and global MHD constraints, impacting reactor design.

Integrated Microturbulence-MHD Analysis of Tokamak Pedestal Stability

Overview

This work addresses a central challenge in predictive fusion science: determining the height and width of the H-mode pedestal in tokamak plasmas, which crucially impacts core confinement, transport, and the viability of future reactors. The study presents a comprehensive workflow integrating gyrokinetic transport predictions (CGYRO/QLGYRO) with ideal magnetohydrodynamic (MHD) stability boundaries (ELITE, GATO), allowing detailed exploration of the operational space constrained by both microinstabilities and macroscopic MHD limits. The approach is applied to a wide range of plasma configurations, including spherical tokamaks (STs) and conventional high-magnetic field devices, advancing beyond existing paradigms by resolving discrepancies observed in previous pedestal scaling and stability characterizations.

Methodology

The analysis constructs parameterized equilibrium scans over pedestal height ($B_{p,\mathrm{ped}}$) and width ($\Delta_{\mathrm{ped}}$) for representative high-performance discharges, employing the OMFIT modeling suite. For each equilibrium, linear gyrokinetic simulations are performed with CGYRO to assess KBM and MTM-driven transport channels, using the TGLF SAT1 rule for quasilinear flux estimation. These microturbulence predictions are then superimposed onto ideal MHD stability boundaries generated with ELITE (for higher-$n$ peeling–ballooning modes) and GATO (for low-$n$ peeling and global modes), establishing composite stability/transport maps for each scenario.

Notably, in the construction of these maps, the total plasma current is constrained self-consistently according to the bootstrap current scaling, enabling realistic edge current and safety factor profiles. The methodology enables the identification of operational regimes—including first-stable and second-stable KBM regions—as well as the delineation of parameter regimes dominated by peeling–ballooning or microtearing instabilities.

Key Numerical Results and Observations

Spherical Tokamaks

• For low aspect ratio (A ≈ 1.5–1.7) plasmas, as in NSTX, NSTX-U, and MAST-U, the computed maps exhibit a pronounced separation into four regimes: first KBM stability, KBM-unstable, KBM second stability, and MTM-unstable regions.
• The inclusion of low-$n$ peeling stability is shown to be essential for accurately delimiting the accessible pedestal space in STs. In particularly wide pedestals, the analysis reveals that lower-$n$ instabilities can become limiting well before high-$n$ ballooning modes destabilize.
• The integrated approach reproduces the characteristic KBM second stability region observed in recent gyrokinetic pedestal studies (e.g., GKPED), but also shows that experimentally observed H-mode pedestals often inhabit this region, leaving unresolved what ultimately constrains the pedestal width and gradient.

Conventional High-Field Tokamaks

• When applied to SPARC-like parameters with high toroidal field up to 12 T and aspect ratio $A = 3.2$, the gyrokinetic-predicted KBM and MTM-driven heat fluxes increase sharply with $B_t$. For example, moving from 2 T to 12 T, the required KBM-driven heat flux to cross from first to second stability rises from $\sim$9 W/cm² to $\Delta_{\mathrm{ped}}$0500 W/cm².
• The power required to access the KBM second-stability regime (interpreted as an H-mode access threshold) scales steeply with magnetic field, diverging from empirical ITPA $\Delta_{\mathrm{ped}}$1 scalings at high $\Delta_{\mathrm{ped}}$2. This is attributed predominantly to changes in the gyroBohm normalization, with collisionality and magnetic geometry providing secondary but significant contributions.
• Finite-$\Delta_{\mathrm{ped}}$3 global ELITE analysis at high field finds that the H-mode pedestal resides in an intermediate regime bounded below by local KBM second stability and above by global (finite-$\Delta_{\mathrm{ped}}$4) ballooning instabilities, consistent with and extending the EPED paradigm once global effects are accounted for.

Model Implications

• The composite mapping uncovers a narrow, geometry-dependent operating window for the H-mode pedestal set jointly by local microinstability thresholds and global MHD limits; the interplay of these mechanisms supersedes any single-mode interpretation.
• KBM second stability is confirmed as a broad feature in both spherical and conventional configurations, but the flux required to traverse into the high-performance regime becomes increasingly stringent at low collisionality and high magnetic field, potentially complicating access in devices like SPARC.

Theoretical and Practical Implications

The unified stability-transport framework provides an enhanced tool for interpreting pedestal phenomena, designing future devices, and planning pedestal optimization experiments:

• For experiment: The mapping can inform real-time adjustments of pedestal operational points to avoid regions of excessive microturbulence or low-$\Delta_{\mathrm{ped}}$5 MHD activity.
• For theory and reduced modeling: It underlines the necessity of incorporating both local and global effects in predictive pedestal models, challenging simple width–height scaling assumptions inherent to standard EPED models, especially for STs and high-$\Delta_{\mathrm{ped}}$6 scenarios.
• For reactor design: The findings indicate that, for high-magnetic-field reactors, pedestal accessibility may become a bottleneck due to the much higher power required to enter the KBM second-stability region, emphasizing the need to accommodate augmented heating and current drive in design envelopes.

Future Directions

Several key avenues are highlighted for further investigation:

• Inclusion of kinetic electron temperature gradient (ETG) modes and non-ideal MHD effects may be necessary to fully explain the empirical pedestal gradient constraints in regimes where KBM second stability is accessed.
• Improved absolute calibration of gyrokinetic fluxes for KBM/MTM turbulence saturation and nonlinear global effects is required to strengthen quantitative predictions.
• Quantification of the interplay between bootstrap current modification, collisionality, and pedestal structure at the limits of achievable aspect ratio and shaping.
• Extension to dynamic, time-dependent pedestal evolution (e.g., incorporating ELM cycles or transient events) to inform control strategies in ITER-class plasmas.

Conclusion

The integration of gyrokinetic transport predictions with ideal MHD stability boundaries yields a coherent and comprehensive map of tokamak pedestal operating space, capturing the coupled constraints of microinstabilities and macroscopic modes. The study demonstrates that neither transport nor ideal MHD analysis alone suffices to demarcate the achievable pedestal in present or future devices. Instead, the nuanced interplay of local and global stability phenomena defines a narrow and sometimes challenging window for sustained H-mode operation, particularly in high-field machines. The framework advanced herein will inform subsequent theoretical, computational, and experimental efforts targeting robust, predictive control of the H-mode pedestal in fusion reactors.