Tokamak or stellarator?

Twisting the field lines

Coils around a ring make a toroidal magnetic field, which runs the long way round the ring. On its own it cannot hold a plasma. The coils are closer together on the inside of the ring, so the field is stronger there, and the field lines are curved. As you saw in the chapter Charged particles and magnetic confinement, this makes ions and electrons drift apart, an electric field builds up, and the whole plasma drifts outward.

The cure is a poloidal field, which runs the short way round the plasma's cross-section. Together the two make helical field lines that wind around the ring like the stripes on a candy cane. A particle on such a line visits the inside and the outside, the top and the bottom, so the separated charges can flow back along the lines and the outward drift does not build up.

The toroidal field

Ampère's law gives the field of $N$ turns carrying a current $I$, at a distance $R$ from the central axis of the ring:

$$B = \frac{\mu_0 N I}{2 \pi R}$$

The tokamak: a current in the plasma

The tokamak was proposed by Igor Tamm and Andrei Sakharov in the Soviet Union in the early 1950s. A large plasma current $I_\text{p}$ flows round the ring in the plasma itself, and its magnetic field is the poloidal field. In ITER it will be $15\ \text{MA}$.

The current is driven like the current in a transformer: the central solenoid in the middle of the ring is the primary coil, and the plasma is a one-turn secondary coil. A changing current in the solenoid induces the plasma current, which also heats the plasma. The coils are flat and fairly simple, and tokamaks have reached the best plasma conditions so far. The risk is a disruption: the plasma suddenly loses its confinement, and its large current dies within milliseconds, putting large forces and heat loads on the vessel.

The stellarator: twisted coils

The stellarator was invented by Lyman Spitzer at Princeton in 1951. Its coils, bent into complicated three-dimensional shapes, make the whole twist. No large plasma current is needed, so there are no disruptions of the tokamak kind.

Early stellarators confined plasma worse than tokamaks. Modern ones are optimised: computers search for coil shapes that hold the plasma well. Wendelstein 7-X in Greifswald, Germany, has 50 non-planar and 20 planar superconducting coils. It made its first plasma in December 2015 and held a plasma for about eight minutes in February 2023. The price is the coils: they are very hard to design, build and place accurately.

Pulsed or steady?

A transformer works only while the current in its primary coil keeps changing, and that cannot go on for ever. So inductive current drive alone gives pulses: ITER's solenoid can drive $15\ \text{MA}$ for about $300$ to $500\ \text{s}$.

But a tokamak current can also be driven without induction:

• neutral beams: fast neutral atoms enter the plasma, become fast ions and carry current round the ring;
• radio-frequency waves, such as lower hybrid waves, push electrons along the field;
• the bootstrap current: the plasma's own pressure gradient drives part of the current.

On 12 February 2025 the French tokamak WEST held a plasma for $1337\ \text{s}$, about 22 minutes, with its current driven by lower hybrid waves. A stellarator needs no driven current, so it can run steadily by design.

Key idea

Both designs hold the plasma in twisted field lines. The tokamak twists them with a plasma current: simpler coils and the best results so far, but disruptions, and steady operation needs non-inductive current drive. The stellarator twists them with three-dimensional coils: steady operation without disruptions, but coils that are very hard to make.

Worked example

Common misconception

"Every tokamak can only run in short pulses, because its current comes from a transformer." Inductive drive alone is limited in time, but neutral beams, radio-frequency waves and the bootstrap current can drive the current without induction. WEST held a plasma for over 22 minutes in this way. A second mistake: "A stellarator has no magnetic field inside the plasma made by currents." It has no large plasma current, but its twisted coils carry very large currents.

Summary

• A purely toroidal field cannot hold a plasma: in the curved field that is stronger on the inside, ions and electrons drift apart and the plasma drifts outward. The field lines must be twisted (toroidal + poloidal = helical).
• The toroidal field is $B = \mu_0 N I / (2\pi R)$, so it falls as $1/R$ across the plasma.
• Tokamak: the poloidal field comes from a large plasma current, driven inductively by the central solenoid (pulses) or non-inductively by beams, waves and the bootstrap current (long pulses, perhaps steady). Risk: disruptions.
• Stellarator: the twist comes from three-dimensional coils. Steady by design and without disruptions, but the coils are difficult. In 2025 Wendelstein 7-X set a record triple product for long plasmas.