Adjoint approach to calculating shape gradients for threedimensional magnetic confinement equilibria
Abstract
The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradientbased optimization, sensitivity analysis and tolerance calculation. An efficient method for computing the shape gradient for toroidal threedimensional magnetohydrodynamic (MHD) equilibria is presented. The method is based on the selfadjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of O(N), where N is the number of parameters used to describe the outer flux surface or coil shapes.
 Publication:

Journal of Plasma Physics
 Pub Date:
 April 2019
 DOI:
 10.1017/S0022377819000254
 arXiv:
 arXiv:1812.06154
 Bibcode:
 2019JPlPh..85b9007A
 Keywords:

 fusion plasma;
 plasma simulation;
 Physics  Plasma Physics
 EPrint:
 doi:10.1017/S0022377819000254