Before leaving this basic description of a tokamak, there is one more essential part that needs to be described: the vertical field. A ring of hot plasma will try to expand. Its internal pressure will push outwards so as to make the cross section fatter, and we have countered this force with a strong toroidal magnetic field. However, the plasma pressure will also tend to make the entire ring expand in radius, as shown in Fig. 6.19. The toroidal field is not good at restraining this motion because it is weaker on the outside of the ring than on the inside. Furthermore, the toroidal current in a tokamak creates a hoop force that also pushes on the ring to expand its major radius. This force arises from the magnetic field that the plasma current generates. This field is also stronger inside the hole of the torus than outside, so that its magnetic pressure is outward. Fortunately, these hoop forces are easily balanced by applying a small magnetic field in the vertical direction. Remember that in a tokamak there is always a current in the toroidal direction to give the field lines a twist. This current is mostly carried by the electrons. The Lorentz force on a moving charge, described in Chap. 4, is perpendicular to both the velocity of the particle and the magnetic field. By superposing a magnetic field in the vertical direction, either up or down, depending on the direction of the current, the tokamak current creates a Lorentz force that pushes the plasma ring inwards, toward the center of the torus.

Note that this effect is different from all the plasma drifts that we discussed previously. Those concerned individual particle motions; it did not matter how many particles there were. Here, we are considering the immense pressure of a hot gas.

VERTICAL-FIELD COIL

*- INWARD FORCE

EXPANSION

CURRENT

VERTICAL B-FIELD

Thus, there are three main types of fields in a tokamak: the toroidal field generated by poloidal coils; the poloidal field generated by a plasma current; and a vertical field generated by large toroidal coils above and below the torus. These vertical- field coils can be combined with the coils that drive the plasma current, as will be described in the next chapter, so they do not always appear as a separate set.