Including the vacuum energy in stellarator coil design

Being three-dimensional, stellarators have the advantage that plasma currents are not essential for creating rotational-transform; however, the external current-carrying coils in stellarators can have strong geometrical shaping, which can complicate the construction. Reducing the inter-coil electromagnetic forces acting on strongly shaped 3D coils and the stress on the support structure while preserving the favorable properties of the magnetic field is a design challenge. In this work, we recognize that the inter-coil forces are the gradient of the vacuum magnetic energy. We introduce an objective functional built on the usual quadratic flux on a prescribed target surface together with a weighed penalty on the vacuum energy. The Euler–Lagrange equation for stationary states is derived, and numerical illustrations are computed using a modern stellarator optimization framework. A study of the effect of the energy functional on the inter-coil forces is conducted and the energy is shown to be a promising quantity in producing coils with low forces.. Authors: Guinchard, S. [Ecole Polytechnique Federale Lausanne (EPFL) (Switzerland). Swiss Plasma Center] (ORCID:0009000466173956); Hudson, S. R. [Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)] (ORCID:0000000315302733); Paul, E. J. [Columbia Univ., New York, NY (United States)] (ORCID:0000000293555595). DOE Contract: AC02-09CH11466. Subjects: 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; coils; energy; optimization; stellarator