Complete and Robust Magnetic Field Confinement by Superconductors in Fusion Magnets

Abstract

The fusion created by magnetically confined plasma is a promising clean and essentially unlimited future energy source. However, net energy generation has not been yet demonstrated in fusion experiments. Some of the main problems hindering controlled fusion are the imperfect magnetic confinement and the associated plasma instabilities. Here, we theoretically demonstrate how to create a fully confined magnetic field with the precise three-dimensional shape required by fusion theory, using a bulk superconducting toroid with a toroidal cavity. The combination of the properties of superconductors with the toroidal topology makes the vacuum field in the cavity volume consisting of nested flux surfaces, a condition for optimum plasma confinement. The coils creating the field, embedded in the superconducting bulk, can be chosen with very simple shapes, in contrast with the cumbersome arrangements in current experiments, and can be spared from the large magnetic forces between them. Because the field shape in the cavity is given by the boundary conditions in the superconductor surface, the system will always tend to maintain the optimum field distribution in response to instabilities or turbulence in the plasma. This field shape is preserved even when holes are drilled in the superconductor to access the plasma region from the exterior. We demonstrate how a fully-confined magnetic field with the three-dimensional spatial distribution required in two of the most advanced stellarators, Large Helical Device and Wendelstein 7-X, can be exactly generated, using simple round coils as magnetic sources. We argue that state-of-the-art high-temperature superconductors already have the necessary properties to be employed to construct the bulk superconducting toroid. The present strategy can lead to optimized robust magnetic confinement and largely simplified configurations in future fusion experiments.

Figures (12)

• Figure 1: (a) and (b) Finite-element simulations of the 3D and 2D magnetic-field strength B field maps, respectively, for an embedded toroidal current loop in a bulk superconductor toroid with a cavity, for which B leaks outside the superconducting toroid. (c) and (d) 3D and 2D maps, respectively, for an embedded poloidal current loop; in this case, all the field is confined inside the toroidal cavity.
• Figure 2: (a), (b), and (c) Finite-element simulations of the magnetic-field strength distribution for 18 current loops similar to the ones used at ITER shinomura. (d), (e), and (f) Field distribution of the same loops when embedded inside a bulk superconducting toroid. (g), (h), and (i) Field distribution when 5 out of the 18 loops are removed. The total current circulating in the previous 18 loops is now distributed in the remaining 13 loops; the obtained field is exactly the same as in (d), (e), and (f).
• Figure 3: (a) Finite-element simulations of the 3D colour map of the magnetic-field strength created by a superconducting toroid with a toroidal cavity and 10 circular loops immersed in the superconductor, corresponding to the scheme of the LHD experiment. (b) Created magnetic flux surface at the superconducting-air boundary in the cavity. (c) Field profiles at two cross-sectional cuts of the cavity at different elliptical rotations. (d) and (e) Two views of the same configuration as in (a)-(c) (with 5 currents loops instead of 10), when five symmetric holes are drilled in the superconductor, in order to have ways of access to the plasma region from the exterior. The magnetic flux leakage to the holes is practically zero, thus preserving the flux shape in the cavity (see Supplemental Material for further data and discussion).
• Figure 4: (a) Finite-element simulations of the 3D colour map of the magnetic-field strength created by a superconducting toroid with a toroidal cavity and 5 circular loops immersed in the superconductor, corresponding to the scheme in the W7-X experiment. (b) Created magnetic flux surface at the superconducting-air boundary in the cavity.
• Figure S1: Horizontal cross-section of a torus with a toroidal cavity and an interlaced embedded perpendicular current wire (left of the torus). A red curve $C$ is drawn centered at the center of the torus to perform Ampère's calculation.