Optimization of stellarator configurations combining omnigenity and piecewise omnigenity

Abstract

We present a method for optimizing stellarator configurations that combine omnigenity and piecewise omnigenity (pwO). Within the \texttt{OOPS} optimization framework [Liu \textit{et al.}, arXiv:2502.09350 (2025)], we introduce a mapping technique that can ``squeeze'' general omnigenous fields to approximate pwO in the high-field side. Using this approach, we obtain a range of optimized configurations that combine poloidal omnigenity (PO) and pwO, spanning different field periods and aspect ratios. We further show that these configurations are compatible with a magnetic well. The resulting configurations exhibit favorable neoclassical transport and bootstrap current properties while partially relaxing the strict constraints of omnigenity. These results suggest that such configurations are promising candidates for future stellarator reactors.

Figures (10)

• Figure 1: The field strength $B$ of a poloidal-omnigenous magnetic field in Boozer coordinates; the black dashed line shows a straight-field-line trajectory.
• Figure 2: Effect of varying D on the "squeeze" process with all other mapping parameters held fixed. The region enclosed by the outermost contour is manually fitted using a zero-bootstrap-current pwO mapping ($w_2=\pi$) in calvo_piecewise_2025. (a) Changing the parameter $c$ deforms $D(x)$, thereby altering the degree of compression of the bounce-angle span. (b) For $c=-0.5$, the PO-mapping coordinate is compressed by $\Delta\eta=1.65$; a plausible pwO region within the unmapped interval is characterized by $(t_1,t_2)=(-0.15,\,8.5)$. (c) For $c=-1$, the compression is $\Delta\eta=2.34$; a candidate pwO region is $(t_1,t_2)=(-0.2,\,6.5)$. (d) For $c=-2$, the compression is $\Delta\eta=2.74$; a candidate pwO region is ($t_1,t_2)=(-0.25,\,6)$.
• Figure 3: Effect of varying $S$ on the "squeeze" process. For all examples, $a=0.3$ is fixed. The region enclosed by the outermost contour is manually fitted using a zero-bootstrap-current pwO mapping ($w_2=\pi$). (a) Dependence of the apparent straightness on $b$. The colored dashed line shows the tangent at the point of interest; the degree of overlap serves as a visual proxy for local linearity. (b) For $c=-0.5, b=0.6$, the PO-mapping coordinate is compressed by $\Delta\eta=1.65$; a plausible pwO region within the unmapped interval is characterized by $(t_1,t_2)=(-0.08,\,5.4)$. (c) For $c=-2, b=0.4$, the PO-mapping coordinate is compressed by $\Delta\eta=2.76$; a plausible pwO region within the unmapped interval is characterized by $(t_1,t_2)=(-0.17,\,3.6)$. (d) For $c=-2, b=0.6$, the PO-mapping coordinate is compressed by $\Delta\eta=2.76$; a plausible pwO region within the unmapped interval is characterized by $(t_1,t_2)=(-0.135,\,3.1)$.
• Figure 4: A gallery of PO–pwO configurations. Magnetic-field-strength distributions in Boozer coordinates on the LCFS for optimized configurations with different field periods and aspect ratios.
• Figure 5: A gallery of PO–pwO configurations. Geometries of the LCFS for optimized configurations with different field periods and aspect ratios; colors indicate the $|\mathbf{B}|$ on the surface.