Marshall N. Rosenbluth Outstanding Doctoral Thesis Award: Adjoint methods for stellarator shape optimization and sensitivity analysis

Modern stellarator design requires numerical optimization to navigate the high-dimensional spaces used to describe their geometry. Physical insight into the self-adjointness properties of the underlying equations enables advanced optimization methods through the efficient calculation of sensitivity information. 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 [1]. This adjoint method allows one to understand the sensitivity of neoclassical quantities, such as the radial collisional transport and bootstrap current, to perturbations of the magnetic field strength. The well-known self-adjointness property of the MHD 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. Adjoint methods have also been developed to reduce stellarator coil complexity [4], eliminate magnetic islands [5], and obtain quasisymmetric vacuum fields. Applications of these adjoint methods for sensitivity analysis and optimization are reviewed [6].

[1] E. J. Paul, I. G. Abel, M. Landreman, and W. Dorland, J. Plasma Phys. 85, 795850501 (2019).

[2] T. Antonsen, Jr., E. J. Paul, and M. Landreman, J. Plasma Phys. 85, 905850207 (2019). 

[3] E. J. Paul, T. Antonsen, Jr., M. Landreman, and W. A. Cooper, J. Plasma Phys. 86, 905860103 (2020). 

[4] E. J. Paul, M. Landreman, A. Bader, and W. Dorland, Nuclear Fusion 58, 076015 (2018). 

[5] A. Geraldini, M. Landreman, and E. J. Paul, J. Plasma Phys. 87, 905870302 (2021).

[6] E. J. Paul, M. Landreman, and T. M. Antonsen, J. Plasma Phys. 87, 905870214 (2021).