Including the vacuum energy in stellarator coil design

TL;DR

This paper introduces a novel approach to stellarator coil design by incorporating vacuum magnetic energy into the optimization process, aiming to reduce inter-coil forces and improve coil construction feasibility.

Contribution

It presents a new objective functional that combines quadratic flux with vacuum energy penalties, deriving the Euler-Lagrange equations and demonstrating the method through numerical examples.

Findings

Vacuum energy influences inter-coil force reduction.

The energy functional effectively produces coils with lower forces.

Numerical results validate the approach's potential benefits.

Abstract

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.