Optimization of core transport using adjoint sensitivities

With increasing focus on designing the core of a fusion pilot plant, the focus of simulations has moved from highly accurate verification and validation studies to the task of trying to design and optimize whole devices. Previous efforts [e.g. P. Kim et. al. J. Plas. Phys. 2024] that have focused on optimizing a parameter (e.g. the turbulent heat flux) at a single point produced some improvement. However, the interrelated and nonlinear nature of the system means that looking only at one point is unreliable for improving overall performance. This motivates efforts to instead optimize global figures-of-merit using a global transport model [see Abel et. al. 2013 Rep. Prog. Phys.].

Because the computation of fluxes for transport simulations often involves expensive simulations, we wish to use efficient gradient-based optimization schemes. Adjoint sensitivity analysis is well suited to this task, as it allows for calculation of the gradients with respect to many parameters for minimal additional cost [Plessix et. al. Geophys. J. Intl. 2006].

MaNTA [Abel et. al. in preparation], a code designed to solve an arbitrary system of 1D nonlinear reaction-diffusion equations, was modified to compute adjoint sensitivities. As a proof-of-concept example, we take classical transport in a cylindrical screw pinch and calculate derivatives of several important global functionals. Parallel work in neoclassical flux and equilibrium solvers with gradient information will enable global optimization of stellarator transport.