In Chap. 3, we carefully showed that a magnetic bottle has to be doubly connected and not a sphere; hence tokamaks are toruses.1 How, then, can a tokamak be spheri­cal? No, spherical tokamak is not an oxymoron. A tokamak can be spherical as long as there is still a hole in the middle. This is shown in Fig. 10.11. These small, fat tokamaks have typical aspect ratios A between 1 and 2. There are many advantages to having small A, but the problem is how to fit all the necessary equipment into the small hole. Spherical tokamaks (STs) are so attractive that many clever ideas have been proposed for treating the small hole, and there are over two dozen STs all over the world testing these ideas.2 In fact, one can eliminate the hole in the vacuum chamber altogether as long as the magnetic field is still toroidal.

Aside from the small size and the consequent cost savings, STs have a large advantage in plasma stability. This is explained in Fig. 10.12, which shows the magnetic-field structure in an ST. The field lines behave very differently from those in a normal tokamak (Fig. 6.1). A particle following a field line spirals around the central column before returning to the outside of the plasma. Good and bad curva­tures are shown in Fig. 7.10. In good curvature, the bend is toward the plasma, and in bad curvature, it is away from the plasma. We see that there is a lot of good curvature around the central column, and a region of weaker bad curvature when the field line returns to the top. Since particles spend more time in good curvature than in bad, there are strong forces pushing the plasma inwards. Much smaller magnetic fields are needed in STs because of the good confinement.

In a 1986 paper [16], Martin Peng and D. J. Strickler noted that the vertical field needed in tokamaks (Fig. 6.19) had a natural tendency to elongate the plasma, and they laid out the basics for the design of STs. Elongation is the vertical length of the plasma compared with its minor diameter, and it has good consequences for STs. As the aspect ratio goes down from 2.5 to 1.2, the elongation increases from 1.1 to 2, and the magnetic field that gives the needed quality factor q for a given

^bar. qg aspect ratio
(conventTSnaL tokamak)

Small aspect
ratio (spherical
tokamak)

Aspect Ratio = Major radius / minor radius

A= R / a

Fig. 10.11 A spherical tokamak has an aspect ratio much smaller than a normal tokamak [15]

plasma current falls by a factor of 20! [15] The value of beta (ratio of plasma pressure to magnetic-field pressure) is therefore very high in STs.

The British machines START (Small Tight Aspect Ratio Tokamak) and its successor MAST (MegAmpere Spherical Tokamak) have given the most informa­tion on STs. A photograph of the spherical plasma in START is shown in Fig. 10.13. The graph of beta values obtained in START (Fig. 10.14) shows the great improve­ment over normal tokamaks. In that graph, BT is the toroidal beta (that calculated with the toroidal magnetic field), and BN is the normalized beta, as defined in Chap. 8 under Troyon Limit. The recent data (red dots) show that the density limit can be exceeded in a spherical torus.

In spite of their physical appearance, STs exhibit the same phenomena observed in large-A tokamaks; the H-mode and ELMs, for instance. MAST is suitable for studies of ELMs and was used for the design of ELM-suppression coils. The shape of the field lines also gives STs a natural divertor.

Now we tackle the question of how to minimize the width of the central column. The toroidal magnetic field in a tokamak is generated by coils that thread through the hole, as shown in Fig. 6.1. All the coil legs that go through the hole can be combined into a single copper bar carrying all the current, as shown in Fig. 10.13.

This is possible because the B-field is small in an ST, so the coil currents are reduced. To drive the toroidal plasma current, the brute force way is to put an iron core through the hole and drive the current by transformer action, as shown in Fig. 7.14. Most tokamaks use air-core transformers that have no iron. These consist of toroidal coils around the plasma, including some inside the hole. This is shown in Fig. 7.15. These methods are called inductive drive. The disadvantage is that the current has to be increasing to excite the current; and since it cannot increase for­ever, the tokamak has to be pulsed. Modern tokamaks use noninductive drive,

which consists of bootstrap current and wave-driven currents (Chap. 9). This would eliminate the need for toroidal coils inside the hole.

The problem is that you can’t launch a wave unless there’s a plasma, and you can’t confine a plasma unless there is already a rotational transform. So it seems that at least some small toroidal coils have to be crammed into the hole, but there may be a solution. Neutral-beam injection is the usual way to heat a large tokamak. Currently, there has been some success (in MAST [15]) in ramping up the NBI in such a way that it drives a current also. It is also possible to create plasmas in cor­ners of the chamber where poloidal coils can be inserted, and to have these plasmas drift and merge into the center. This is illustrated in Fig. 10.15.

While experimentation on STs is being conducted intensely worldwide, reactor studies have been made both in Europe and the USA. The ARIES-ST design of 1999 is shown in Fig. 10.16. The central column is made to be slid out and replaced easily. All blanket modules are on the outside. Note the natural divertors at the top and bottom.