Superconducting Coils

To confine plasma hotter than 100 million degrees, a fusion reactor needs a magnetic field hundreds of thousands of times stronger than Earth’s. If you tried to produce this field with ordinary copper-wire coils, most of the electrical power would be lost as heat. This is where superconducting coils, whose electrical resistance drops to zero, come in. On this page, we work step by step from the intuition behind superconductivity, to how the materials are chosen, the structure of large conductors, protection during accidents, and finally the cutting edge of high-temperature superconducting magnets.

Start with Intuition (High School)

Any wire that carries electricity has some electrical resistance. When there is resistance, the wire heats up every time current flows. An electric heater glows red and a light bulb filament shines because they exploit this heating. Sometimes that is useful, but when you want to make a magnetic field with a coil, this heating is pure loss.

The strength of a magnetic field is set mostly by how large a current flows through the coil. If you want a strong field, you need to run a lot of current. But heating grows in proportion to the square of the current, so increasing the current tenfold increases the heating a hundredfold. If you tried to produce the strong field a fusion reactor needs with copper coils, the heat generated would reach hundreds of MW (megawatts), comparable to the very power a power plant produces. Even after extracting energy through fusion, you would use it all up just running the coils.

Here the phenomenon of superconductivity comes to the rescue. Certain metals and compounds, when cooled to very low temperatures, lose their electrical resistance completely. With zero resistance, no matter how much current flows, there is no heating. Once you start a current flowing, it keeps flowing even if you cut off the power supply. In other words, you can run as large a current as you like without worrying about heating, and create a strong magnetic field.

Of course, this does not come for free. To bring the resistance to zero, the material must be cooled to near absolute zero (minus 273 degrees), to about 4 K (kelvin), that is, minus 269 degrees. This cooling uses liquid helium and a dedicated refrigerator that keeps it cold at all times. Cooling also takes electrical power, but far less than covering the heating of copper coils. Paying the cost of cooling in exchange for zero resistance is the basic idea behind superconducting coils.

Understand the Physics (Undergraduate)

First, let us confirm with a formula why copper coils are not enough. When a current $I$ flows through a conductor with resistance $R$, the Joule heat generated is given by the following equation.

$$P = I^2 R$$

$P$ is the heating power (W), $I$ is the current (A), and $R$ is the resistance (Ω). The key point is that heating is proportional to the square of the current. A fusion reactor’s toroidal field coil carries huge currents of tens of thousands of amperes, so even a tiny resistance makes $I^2 R$ enormous. In superconductors $R = 0$, so this term vanishes in principle.

There are two kinds of superconductors. A type-I superconductor can only exclude weak magnetic fields, and even a slightly stronger field destroys the superconductivity. Fusion uses type-II superconductors. These let the magnetic field partially penetrate the interior as thread-like fluxoids while maintaining superconductivity up to higher fields.

A type-II superconductor is characterized by the following three critical quantities. Once these are exceeded, superconductivity is lost and resistance returns.

The critical temperature $T_c$ is the upper temperature limit at which superconductivity is possible. Above it, the material will not become superconducting no matter how small the field or current. The upper critical field $B_{c2}$ is the upper limit of magnetic field the material can withstand. The critical current density $J_c$ is the upper limit of current that can flow per unit cross-sectional area.

These three are not independent of one another; together they form a single surface. Raising the temperature lowers the allowable field and current, and strengthening the field lowers the allowable current. In design, the operating temperature, operating field, and operating current must all fall inside this critical surface, and with a margin (operating margin) to spare.

There are two representative low-temperature superconducting materials used in fusion.

NbTi (niobium-titanium) is ductile, easy to process, and inexpensive. However, its critical field is relatively low, about 11.5 T (tesla) at 4.2 K, so it is used in regions where the field is not so strong. In ITER, it is used in the poloidal field coils that control the position and shape of the plasma.

Nb3Sn (niobium-tin) has a high critical field of around 25 T and withstands stronger fields. On the other hand, being a compound, it is brittle, and after being wound into a coil it must undergo high-temperature heat treatment to form the superconducting phase. It is sensitive to strain, which makes its manufacturing and support-structure design difficult. In ITER, it is used in the TF coils and the central solenoid, where the strongest fields are applied.

Deepen the Theory (Graduate)

In large superconducting coils, rather than winding the strands directly, a structure called a cable-in-conduit conductor (CICC) is widely used. Hundreds of superconducting strands, each a little under 1 mm in diameter, are twisted together in multiple stages into a cable, which is then housed inside a sturdy stainless-steel tube (the conduit). Supercritical helium flows through the gaps between the tube and the cable, cooling the cable directly to 4.5 K from the inside. The stainless-steel tube also serves as the structural material that withstands the enormous electromagnetic forces described below.

There are several reasons for making the structure this complex. The strands are split thin and twisted to suppress the AC loss that arises inside the strands when the magnetic field varies. In a single thick conductor, losses from eddy currents induced by a varying field are large. Twisting also breaks the electromagnetic coupling between strands, so that the current flows evenly through all of them. Helium is forced through the interior of the conductor so that cooling right next to the heat source keeps the temperature rise to a minimum.

The shape of the TF coils also reflects physics. ITER’s TF coils are D-shaped. This is the result of choosing a shape (a constant-tension shape) in which the Lorentz force produced by the current and the magnetic field applies no bending moment to any part of the coil and is balanced by tension alone. Since tension is structurally easier to handle than bending stress, the large electromagnetic forces can be supported safely. ITER has 18 TF coils, with a peak field of 11.8 T and a magnetic energy stored in the whole system reaching 41 GJ (gigajoules). The magnitude of this stored energy is the root of the difficulty of protection described next.

The coil system is broadly divided into three roles. The TF coils create the toroidal field that surrounds the plasma and form the backbone of confinement. The central solenoid acts as the primary winding of a transformer, and by varying its current over time it induces a current in the plasma itself. ITER’s central solenoid is made of Nb3Sn with a peak field of about 13 T, which enables pulsed operation lasting hundreds of seconds. The poloidal field coils control the vertical position and cross-sectional shape of the plasma.

The power required for cooling is also not negligible. Because of the Carnot efficiency constraint, pumping out 1 W of heat at 4.5 K requires about 300 W of power on the room-temperature side. ITER’s cryogenic facility has a refrigeration capacity on the order of tens of kW referred to 4.5 K, and its power consumption reaches tens of MW. The heat loads are designed by dividing them into static heat loads that enter steadily through radiation and conduction, and dynamic heat loads such as AC loss during field variations and nuclear heating from fusion neutrons.

Research Frontier (PhD)

The most serious accident in a superconducting coil is a quench. If part of the conductor loses its superconductivity and reverts to the normal state for some reason, resistance appears there and generates heat, and that heat warms the neighboring region, spreading the normal zone further, in a chain reaction. If the enormous magnetic energy stored in the coil were released concentrated in a small local volume, the conductor would melt.

This is why detection and protection are key. To detect a quench, the differential voltage method, which compares the voltages across various parts of the coil, is often used. A non-inductive voltage appears at the place where resistance has arisen, and this is what is identified. Once detected, the stored energy is either quickly diverted to an external dump resistor, or the whole coil is intentionally quenched using heaters embedded throughout it, dispersing the energy over the entire coil. The goal is to hold the maximum temperature reached by the conductor below roughly 150 to 200 K. A keyword that appears often in research here is the hot-spot temperature.

The recent frontier is high-temperature superconductors (HTS). Among them, REBCO (rare-earth barium copper oxide) has a critical temperature of about 92 K, above the temperature of liquid nitrogen, and an irreversibility field exceeding even 100 T. Thanks to this high critical field, magnets in the 20 T class, previously out of reach, have come into view. REBCO is processed into thin tapes, so coils are built up as stacks of tape.

Being able to strengthen the field matters greatly. Fusion power density is roughly proportional to the fourth power of the magnetic field, so doubling the field increases the power density by a factor of 16. The idea that you can make a device much smaller for the same fusion power is the compact-tokamak approach. In 2021, MIT and Commonwealth Fusion Systems (CFS) demonstrated a 20 T field with a prototype large TF coil using REBCO, giving this approach real credibility. This technology is used in the company’s SPARC, which aims for a fusion gain of $Q > 1$ in a device far smaller than ITER.

HTS also has its own difficulties. REBCO’s quench propagation velocity is only about 1 to 10 mm per second, orders of magnitude slower than in low-temperature superconductors, so a local region overheats before the normal zone can spread, making quench detection difficult. This is why large operating margins and dense monitoring are being studied. In addition, in no-insulation windings, where insulation is deliberately omitted between turns, the current can bypass a spot of locally increased resistance between turns, so they are expected to behave in a self-protecting manner and are being studied intensively. Beyond these, reducing the mass-production cost of REBCO tape, jointing technology, and demonstrating radiation hardness against neutron irradiation are the major challenges toward practical reactors.

Check Your Understanding

Q1. What is the biggest reason for using superconducting coils instead of copper coils in a fusion reactor?

A Superconducting coils are lighter than copper, allowing the whole device to be miniaturized B In copper coils, the Joule heating from electrical resistance would reach hundreds of MW, exceeding the energy gained from fusion C Superconducting coils need no cooling at all, so the operating cost becomes zero D Copper melts under strong magnetic fields and cannot be used at all

Q2. Which combination correctly gives the three critical quantities that characterize a type-II superconductor?

A Critical temperature, critical field, and critical current density, representing the upper limits of temperature, field, and current density at which superconductivity can be maintained B Critical temperature, critical pressure, and critical volume C Critical voltage, critical field, and critical frequency D Critical temperature, critical density, and critical time

Q3. Which is the correct explanation of how NbTi and Nb3Sn are used differently?

A NbTi has a high critical field and is used for strong fields, while Nb3Sn is easy to process and used for weak fields B Both have the same critical field and are chosen based on price alone C NbTi is easy to process and inexpensive but has a low critical field, so it is used for the weak-field PF coils, while Nb3Sn has a high critical field but is brittle and needs heat treatment, so it is used for the TF coils and central solenoid D NbTi is a high-temperature superconductor and Nb3Sn a low-temperature one, chosen by operating temperature

Q4. Why are the superconducting strands in a CICC split thin and twisted together?

A Because it is cheaper to manufacture than a single thick strand B To suppress the AC loss and eddy-current loss caused by field variations, break the electromagnetic coupling between strands, and make the current flow evenly C Because twisting raises the critical temperature itself D Because making the strands thin lowers the temperature at which they become superconducting, making cooling easier

Q5. When high-temperature superconducting REBCO enables 20 T-class fields, why can the device be made smaller?

A Because a stronger field removes the need to cool the superconductor, so the refrigerator can be omitted B Because strengthening the field lets you lower the plasma temperature, making the device thinner C Because fusion power density is roughly proportional to the fourth power of the field, so doubling the field increases the power density about 16-fold, obtaining the same output in a smaller device D Because REBCO is tape-shaped and light, so the volume of the coil itself becomes small

Related Topics

• Tokamak Approach - The magnetic-field configuration created by superconducting coils and the components of a tokamak
• ITER Project - The world’s largest tokamak, equipped with 11.8 T-class TF coils using Nb3Sn
• SPARC - A compact tokamak aiming for 20 T-class fields with REBCO high-temperature superconductors