Stellarator island divertor shape optimization for reduced peak heat fluxes

Abstract

An automated algorithm to construct island divertors for stellarators is presented and is used to find divertors that meet heat flux requirements determined by engineering and material limits. The algorithm uses just two initial conditions: two starting coordinates on the island separatrix. We leverage the simplicity of the algorithm to explore the divertor parameter space in a fixed magnetic equilibrium. Heat loads are approximated using the field line diffusion model implemented in the FLARE code. Optimal divertor solutions that satisfy engineering requirements are found using a parameter scan and a Bayesian optimization routine. The optimization achieves a 95% reduction in computational cost compared to the parameter scan. The resulting divertors are proven to be robust to varying plasma parameters through simulations with different cross-field heat diffusivities. This work represents a first step towards island divertor optimization for stellarators.

Figures (10)

• Figure 1: A cartoon of a V-shaped island divertor (green) in a stellarator island (blue cylinder, representative of a single stellarator island). Although in this cartoon the plates are shown to be planar, the ones created by the algorithm described in Fig. \ref{['fig:divertor_making_algorithm']} allow for curved geometries in order to target the proper strike angle at both points of contact with the island separatrix. The divertor extends from $\phi=\phi_{\text{start}}$ to $\phi=\phi_{\text{end}}$, where $\phi$ is the toroidal angle of the stellarator in standard cylindrical coordinates. A rounded junction where the plates meet avoids having a sharp discontinuity in the divertor and is described more in Sec. \ref{['subsec:div_making_algo']}.
• Figure 2: Algorithm that creates a divertor plate geometry from $\phi_{\text{init}}$ to $\phi_{\text{end}}$. The algorithm is run with $\pm\Delta\phi$ to create a V-shaped divertor.
• Figure 3: A visualization of how the coordinates of the divertor intersections with the control surface at different $\phi$ planes are chosen. The point $p_L^*$ is found near the point $p_{L.b}$ such that $\hat{b}_L\cdot \hat{d}_L=\cos(\alpha)$. The same is repeated for the right points, and the divertor section between $\phi_i$ and $\phi_{i+1}$ is a surface going through $p_{Li}, p_L^*, p_{Ri}, p_R^*$.
• Figure 4: Cost function landscape for 441 divertors chosen from starting angles between $0$ and $2\pi$. The axes are scaled to capture the region of parameter space where the divertor-making algorithm completed successfully. The white area represents $(\theta_L, \theta_R)$ initial conditions that did not produce a divertor because the divertor-making algorithm crashed.
• Figure 5: Cost function landscape as learned by a Bayesian optimization run. In black are the initial points used in the optimization, and in red the subsequent observations taken by the optimizer. The optimizer finds the large valley around $(\theta_L, \theta_R)=(4.5, 1.5)$.