Title: Adjoint methods for stellarator shape optimization
Abstract: Stellarators, which confine plasma with non-axisymmetric magnetic fields, provide a promising route toward steady-state fusion. Modern stellarator design requires numerical optimization to navigate the high-dimensional spaces used to describe their complicated geometry. Physical insight into the self- adjointness properties of the underlying equations enables advanced optimization methods through the efficient calculation of sensitivity information. In this way, stellarator design presents a unique opportunity for fruitful interaction between applied mathematics and physics.
The first applications of the adjoint method to stellarator design are reviewed. An adjoint drift-kinetic equation is derived based on the self-adjointness property of the Fokker-Planck collision operator . This adjoint method provides the sensitivity of physical quantities, such as the collisional transport of heat and collision-driven current, to perturbations of the magnetic field. The well-known self-adjointness property of the magneto-hydrodynamic force operator is generalized to include perturbations of the rotational transform and the currents outside the confinement region [2-3]. This adjoint method enables evaluation of the sensitivity of equilibrium properties to perturbations of coil shapes or the plasma boundary. Applications for optimized configurations are reviewed .
 E. J. Paul, I. G. Abel, M. Landreman, and W. Dorland, "An adjoint method for neoclassical stellarator optimization," Journal of Plasma Physics 85, 795850501 (2019).
 T. Antonsen, Jr., E. J. Paul, and M. Landreman, "Adjoint approach to calculating shape gradients for 3D magnetic connement equilibria," Journal of Plasma Physics 85, 905850207 (2019).
 E. J. Paul, T. Antonsen, Jr., M. Landreman, and W. A. Cooper, "Adjoint approach to calculating shape gradients for 3D magnetic connement equilibria," Journal of Plasma Physics 86, 905860103 (2020).
 E. J. Paul, M. Landreman, and T. M. Antonsen, "Gradient-based optimization of 3D MHD equi- libria," Journal of Plasma Physics 87, 905870214 (2021).
Biography: Elizabeth Paul is a Presidential Postdoctoral research fellow at Princeton University. She received her undergraduate degree in astrophysical sciences from Princeton University in 2015 and her Ph.D. in physics from the University of Maryland in 2020. Her dissertation research was on advancing tools for the optimization of stellarator magnetic fields and coils using adjoint methods. At PPPL, she is developing adjoint-based tools for the optimization of MHD equilibria under the supervision of Prof. Amitava Bhattacharjee. Her interests include neoclassical transport, coil design, MHD equilibrium properties of stellarators, and problems at the intersection of plasma physics and applied math.