Stellarator Optimization with Constraints

Abstract

In this work we consider the problem of optimizing a stellarator subject to hard constraints on the design variables and physics properties of the equilibrium. We survey current numerical methods for handling these constraints, and summarize a number of methods from the wider optimization community that have not been used extensively for stellarator optimization thus far. We demonstrate the utility of new methods of constrained optimization by optimizing a QA stellarator for favorable physics properties while preventing strong shaping of the plasma boundary which can be difficult to create with external current sources.

Figures (6)

• Figure 1: Sketch of optimization landscape (contours of $f$ in blue) with constraints (curve of $g(x)=0$ in black). Starting from $x_0$ and enforcing the constraints exactly at each step will follow the red path and end at $x_1$. If we allow ourselves to temporarily violate the constraints, we can follow the green path and arrive at the better solution $x_2$.
• Figure 2: Plasma boundary of NCSX at several cross sections, with the "bean" section at $\phi=0$.
• Figure 3: Plasma boundary of new optimized configuration with constraint on surface curvature.
• Figure 4: Lagrange multipliers for the curvature constraint plotted on the surface. The dark areas indicate places where the constraint is binding, and the optimizer wants to indent the boundary in those locations to improve the magnetic well.
• Figure 5: Plasma boundary of new optimized configuration with relaxed curvature constraint and stable magnetic well.