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In Spherical Tokamak (ST) devices, the restricted volume of the central solenoid within the compact center stack significantly limits the available inductive volt-seconds. This constraint poses a major challenge for reaching MA-scale plasma current ($I_p$) required for the burning regime in a reactor ST [1]. Consequently, non-inductive current drive (NICD) is essential not only for flux saving but also for assisting the current ramp-up. Electrostatic Helicity Injection (HI) is a possible candidate for these purposes. Indeed, Local Helicity Injection (LHI) using arc plasma guns has experimentally demonstrated its significant potential [2,3]. To evaluate its efficiency in reactor STs, predictive modelling is required to simulate current evolution alongside plasma parameters from the burn-through to the current ramp-up phase. In this work, we developed DYON-HI by self-consistently coupling an HI model [4] with the 0D plasma initiation code DYON [5]. By leveraging the separation of the ideal time-scales inherent in helicity transport [4] and the Taylor Principle [6] from the resistive time-scale of inductive flux consumption, the model derives an effective voltage form that incorporates essential experimental control parameters. This framework elucidates how HI-induced voltage modifies the standard circuit equation, formulated through the application of Poynting’s theorem [7]. The DYON-HI model was validated by replicating discharges from the Versatile Experiment Spherical Torus (VEST) [8]. We show that the model successfully reproduces the evolution of plasma parameters across various VEST scenarios, thereby demonstrating the reliable predictive capability of DYON-HI. By providing its direct link to experimental control, this work is envisaged to facilitate the evaluation of HI operation efficiency for the upcoming VEST upgrade, and ultimately reactor STs.
[1] H. Wilson et al. 2020 IOP Publishing, ISBN: 978-0-7503-2719-0, pp. 8–1 to 8–18.
[2] Park, J.Y. et al. 2025 Nature 644, 59–63.
[3] J.M. Perry et al. 2018 Nucl. Fusion 58 096002.
[4] T.H. Jensen, and M.S. Chu. 1984 Phys. Fluids 27 (12): 2881–2885.
[5] Hyun-Tae Kim et al. 2012 Nucl. Fusion 52 103016.
[6] J.B. Taylor. 1974 Phys. Rev. Lett. 33, 1139.
[7] S. Ejima et al. 1982 Nucl. Fusion 22 1313.
[8] Chung, K.J. et al. 2013 Plasma Sci. Technol. 15, 244.