Optimization of the Compact Stellarator with Simple Coils at finite-beta

TL;DR

The paper addresses finite-$\beta$ degradation of neoclassical confinement in the Compact Stellarator with Simple Coils (CSSC) and demonstrates that a single-stage optimization—varying only the currents and orientations of the inner coils relative to the fixed coil geometry—substantially mitigates the adverse effects. Using Fourier representations of the coils, VMEC for finite-$\beta$ equilibria, SFINCS for bootstrap current and NEO for $\epsilon_{eff}^{3/2}$ evaluation, the authors show that decreasing the inner-outer coil current ratio $\overline{I}$ (with $\delta \theta$ near zero) and, optionally, applying a vertical shift $\delta h$ can reduce the effective ripple to levels close to the vacuum CSSC. The optimized finite-$\beta$ configuration preserves or slightly improves magnetic well and global MHD stability, with a global stability limit around $3.2$–$3.5\%$ and onset of kink instabilities near $\sim4\%$. This work suggests that compact stellarators with simple coil sets can achieve robust confinement at finite beta, offering a practical pathway for experimental devices with reduced engineering complexity.

Abstract

An optimized stellarator at finite plasma beta is realized by single-stage optimization of simply modifying the coil currents of the Compact Stellarator with Simple Coils (CSSC)[Yu et al., J. Plasma Physics 88,905880306 (2022)]. The CSSC is an optimized stellarator obtained by direct optimization via coil shapes, with its coil topology similar to that of the Columbia Non-neutral Torus (CNT) [Pederson et al., Phys. Rev. Lett. 88, 205002 (2002)]. Due to its vacuum-based optimization, the CSSC exhibits detrimental finite beta effects on neoclassical confinement. The results of optimization show that the finite beta effects can be largely mitigated by reducing the coil currents of CSSC.

Figures (13)

• Figure 1: The CSSC coil set (gold) and the rotated IL coils of CSSC (silver).
• Figure 2: Comparison of effective ripple profiles of CSSC for two values of the volume-averaged plasma beta: $\beta=0$ and $\beta=1\%$.
• Figure 3: Comparison of bootstrapping current profiles from iteration process. Different colors correspond to different iteration steps.
• Figure 4: The profile of the effective helical ripple $\epsilon ˆ{3/2}$ before and after iteration.
• Figure 5: The profiles of effective helical ripple of different $\overline{I}$ and a fixed value of $\delta \theta=0$.