Description
Spherical Tokamaks (STs) leverage high-β operation for compact reactor pathways, yet 3D field control remains a critical challenge due to the complex physics induced by the low aspect ratio geometry [1, 2]. This research utilizes the Generalized Perturbed Equilibrium Code (GPEC) to analyze 3D plasma response and quantify figures of merit for the MAST-U device [3]. Based on a perturbed equilibrium approach, this modeling methodology calculates the linear response in the form of a multi-modal toroidal harmonic matrix by utilizing plasma equilibrium data and current information from 3D coils, including RMP coils, error field (EF) correction coils, and intrinsic EF induced by PF coils. Modeling of 3D field scenarios identifies resonant response characteristics and field penetration proxies, such as the Chirikov parameter, to determine the operational windows required for edge-localized mode (ELM) suppression without core mode-locking [4, 5]. While these physical parameters can be evaluated using an ideal plasma response, self-consistent kinetic effects are further incorporated by solving the generalized plasma response torque equations, accounting for kinetic profiles such as temperature, density, and toroidal rotation [6]. The analysis highlights ST-specific phenomena, including significant kinetic dissipation and reduced plasma response due to self-shielding effects, which result in a remarkably narrow operational window for ELM suppression that avoids triggering mode-locking. Furthermore, a comparative study of magnetic configurations reveals that double-null (DN) shapes exhibit a lower high-field side (HFS) ideal kink response, thereby fundamentally hindering the resonant field penetration required for effective pedestal control [7]. These findings provide a robust physics-based foundation for optimizing multi-modal 3D coil scenarios and defining operational boundaries, ultimately supporting the design of 3D control systems for future ST-based fusion reactors.
Acknowledgments
This research was supported by the National R&D Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (2021M3F7A1084418). It was also conducted under the UKAEA-SNU Collaboration Agreement (COL046-2024).
References
[1] A. Kirk et al., Nucl. Fusion 53, 043007 (2013).
[2] D. A. Ryan et al., Plasma Phys. Control. Fusion 66, 105003 (2024).
[3] J.-K. Park et al., Phys. Plasmas 14, 052110 (2007).
[4] J.-K. Park et al., Nat. Phys. 14, 1223 (2018).
[5] N. C. Logan et al., Nucl. Fusion 65, 076029 (2025).
[6] J.-K. Park and N. C. Logan, Phys. Plasmas 24, 032505 (2017).
[7] P. Lunia et al., Nucl. Fusion 65, 086041 (2025).