Toroidal Alfvén Eigenmodes in High-Field Tokamaks: Comparison Between C-Mod Experiments and SPARC Simulations Using FAR3d

The SPARC tokamak, currently under construction in Devens, MA by Commonwealth Fusion Systems (CFS) is projected to achieve a fusion gain of Q > 5 [1]. At this gain, a burning plasma regime is realized where DT-fusion alpha particles dominate plasma heating. Understanding the stability of Alfvén Eigenmodes (AEs) is critical for tokamak operation as such instabilities can lead to confinement losses, reduced performance, and challenges for steady-state operation. To better understand this regime, this work investigates the behavior of Toroidal Alfvén Eigenmodes (TAEs) by combining experimental data from Alcator C-Mod with simulations for both C-Mod and the SPARC PRD using the FAR3d code [2,3,4]. FAR3d simulations for C-Mod were performed using EFIT, VMEC, and TRANSP derived equilibria from TAE-active discharges. Observed modes were identified using Mirnov coil arrays and verified through several methods [5]. Simulations accurately reproduced the observed TAEs, with toroidal mode numbers up to n=15, a range particularly relevant for high-field, compact tokamaks such as SPARC. Linear FAR3d simulations have found small TAE growth rates (𝛾/⍵ ≤ 0.4%) for all toroidal mode numbers on C-Mod and SPARC [4]. Both devices operate in sawtoothing regimes, and nonlinear FAR3d simulations capture the evolution of C-Mod TAEs through the crash cycle by dynamically updating plasma profiles. This enables an assessment of mode stability as the equilibrium evolves. Complete scans across toroidal mode numbers show strong agreement between simulation and experiment in C-Mod and provide a predictive spectrum for SPARC. These results offer an important direct comparison between experimentally validated TAEs in C-Mod and their SPARC analogs, predicting that TAEs will be moderately driven.

[1] Creely, A.J., et al. Journal of Plasma Physics 2020.

[2] Varela, J., et al. Nucl. Fusion 2017.

[3] Tinguely, R.A., et al. Nucl. Fusion, 2025.

[4] Nichols, L., et al. TMEP, 2025

[5] Zapata-Cornejo, E. d. D., et al. Plasma Phys. Control. Fusion 66 095016, 2024