Toroidal and Poloidal Coils

3D model of the TJ-II heliac, showing the helical plasma configuration produced by its complex magnetic coil system.

When discussing magnetic confinement in thermonuclear fusion, two directions are commonly distinguished: toroidal and poloidal. To visualise them, imagine a doughnut, technically called a torus. The toroidal direction runs around the large circular axis of the torus, while the poloidal direction runs around its smaller cross-section, from the inner side through the top and outer side and back again. Toroidal field coils are arranged around the torus in the poloidal direction.

The poloidal direction runs around the small cross-section of the torus. Poloidal field coils, when used, encircle the device in the toroidal direction and help shape and adjust the magnetic configuration. Together with other coil systems, they can influence plasma position, shape and equilibrium.

Helical and Modular Coils

A stellarator also requires coils that generate the helical twist of the magnetic field. Depending on the design, these may take the form of continuous helical windings around the torus or separate modular coils of complex non-planar shape. They may be combined with toroidal or poloidal field coils, or both, depending on the stellarator configuration.

Helical coils are relatively regular and therefore somewhat easier to calculate and manufacture, but because they wind continuously around the vacuum vessel they can severely restrict access to it. Modular coils provide greater flexibility in arranging access between individual coils. Their non-planar shapes are carefully optimised to generate the required three-dimensional magnetic field and achieve good plasma confinement.

Large stellarators may contain several dozen coils, but designers try to limit the number of different coil types by using repeated modules. This reduces manufacturing complexity and cost. For example, Wendelstein 7-X has five-fold symmetry and uses 50 non-planar coils of only five different shapes.

Shape Calculation

Non-planar magnetic coil of the Wendelstein 7-AS stellarator.

The shape of stellarator coils is determined by advanced numerical optimisation. First, an appropriate three-dimensional magnetic configuration is calculated to provide good plasma equilibrium and confinement, minimise particle losses, reduce unwanted magnetic islands and control instabilities. Coil geometries are then optimised so that the magnetic field they produce reproduces this desired configuration as closely as possible. Engineering constraints such as the number of coils, minimum spacing, allowable curvature, mechanical loads, manufacturability and access requirements must also be included in the optimisation.

Manufacturing

Manufacturing tolerances are extremely demanding, because deviations of only a few millimetres can significantly distort the magnetic field. The coils must therefore be positioned with millimetre-scale accuracy and held by a strong support structure capable of withstanding large electromagnetic forces. In devices with independently powered coil sets, varying the coil currents allows several different magnetic configurations to be produced.

Superconducting Materials

To reduce resistive power losses, large modern stellarators use superconducting coils. Below their operating temperature, superconductors can carry very high currents with essentially no electrical resistance. This allows strong magnetic fields to be maintained with much lower resistive power consumption than in conventional copper magnets, although cryogenic cooling is required.

Many superconducting stellarators, including Wendelstein 7-X, use niobium–titanium (NbTi), which is comparatively ductile and suitable for manufacturing complex coil shapes. Its performance is limited at very high magnetic fields, however. Present large stellarators typically operate with magnetic fields of a few tesla; Wendelstein 7-X, for example, operates at about 2.5 T.

Future stellarator power plants may benefit from higher magnetic fields, for which high-temperature superconductors such as REBCO (Rare-Earth Barium Bopper Oxide) are promising candidates. REBCO can retain high current density in very strong magnetic fields and can operate at significantly higher temperatures than conventional low-temperature superconductors. These properties make it attractive for future stellarators and other magnetic-confinement fusion devices. Stellarators may also use additional coils for plasma shaping, position control, magnetic-field adjustment and diagnostic measurements.

Stronger Magnetic Field

In present experimental stellarators, the magnetic coils can be placed relatively close to the vacuum vessel. A deuterium–tritium fusion power plant, however, would expose the magnets to an intense flux of high-energy neutrons, so substantial shielding would be required. A lithium-containing breeding blanket would also be placed between the plasma and the magnets to produce tritium and absorb much of the neutron energy. The breeding blanket and neutron shielding would increase the distance between the plasma and the magnetic coils. Maintaining the required magnetic field at the plasma would therefore demand stronger magnets, a larger device, or a combination of both.