An adjoint method for neoclassical stellarator optimization

The design of modern stellarators often employs gradient-based optimization to navigate the high-dimensional space describing the magnetic field geometry. However, computing the gradient of a target function is typically quite expensive, necessitating the use of simplified physics models. The adjoint method provides a means to efficiently compute analytic gradients of a target function with respect to many input parameters. We implement the adjoint method in the SFINCS drift kinetic solver to compute gradients of moments of the distribution function, such as the bootstrap current and radial particle fluxes, with respect to input parameters, such as the Boozer spectrum. We perform adjoint-based optimization with the STELLOPT framework using a quasi-Newton method, targeting the neoclassical quantities computed with SFINCS. To demonstrate, we present a W7X-like configuration optimized for minimal bootstrap current. In addition, we use the gradients to compute the sensitivity of moments of the distribution function to local perturbations of the magnetic field strength on a surface. This local sensitivity information provides greater insight into the optimization and engineering tolerances than parameter derivatives.