Journal of Computational Physics 278 (2014) 117–132 Contents lists available at ScienceDirect Journal of Computational Physics www.elsevier.com/locate/jcp Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method W. Dekeyser a,∗ , D. Reiter b , M. Baelmans a a KU Leuven, Department of Mechanical Engineering, Celestijnenlaan 300A, 3001, Leuven, Belgium b Institute of Energy and Climate Research IEK-4, Forschungszentrum Juelich GmbH, EURATOM Association, Trilateral Euregio Cluster, D-52425 Juelich, Germany a r t i c l e i n f o a b s t r a c t Article history: Received 27 January 2014 Received in revised form 14 August 2014 Accepted 15 August 2014 Available online 22 August 2014 Keywords: Divertor design Edge plasma modeling Shape optimization Shape sensitivity analysis Continuous adjoint method One-shot method As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation of the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry. © 2014 Elsevier Inc. All rights reserved. 1. Introduction Power and particle exhaust are key performance issues for next-step fusion reactors. Divertors have to be designed such that they could safely handle the large power loads. Specifically, their design needs to prevent from exceeding limits imposed by the divertor materials and the plasma facing component cooling in order to avoid excessive material erosion, surface melting and failure of the component as a whole due to beyond-design power fluxes. At the same time, sufficient particle throughput, in particular Helium pumping capacity, has to be ensured. In the divertor design process, numerical simulations of the plasma edge are heavily used to assess divertor perfor- mance. Typically, plasma edge codes such as B2-Eirene [1] are used as analysis tools, for example in the design of the ITER divertor [2]. Unfortunately, due to the complex nature of the edge plasma flows and the large number of design variables, extended parametric studies with these edge codes are computationally very demanding, precluding investigating a wide range of divertor geometries and operational points. In this paper, we elaborate in detail a novel, optimization-based approach to computational divertor design. By recast- ing the design problem as a mathematical optimization problem, a range of computational tools developed over the past * Corresponding author. E-mail address: Wouter.Dekeyser@kuleuven.be (W. Dekeyser). http://dx.doi.org/10.1016/j.jcp.2014.08.023 0021-9991/© 2014 Elsevier Inc. All rights reserved.