A pinch is a plasma carrying a current so large that the surrounding magnetic field that it generates confines and compresses it. It is basically unstable to the kink instability (Fig. 6.2). A toroidal pinch has the current running around in a torus, so that it is also subject to the gravitational interchange instability (Fig. 5.7). A reversed-field pinch (RFP) adds a toroidal field imposed by external coils, as in a tokamak, and has special properties. The Zeta machine at Harwell, England, one of the first fusion experiments revealed to the world at the 1958 Geneva Atoms-for — Peace Conference, was an RFP (cf. Chap. 8). That machine suffered from a misin­terpretation of the neutrons it generated and was abandoned, but research on RFPs has continued since that time.

The Zeta experiment showed that, after an initial period, the plasma settled into a quiescent, stable state. This was explained by Bryan Taylor’s theory [9], which predicted that the plasma would self-organize into a minimum-force, maximum inductance state. In an RFP, this state has a current distribution that reverses the direction of the helical field lines, as shown in Fig. 10.30. This looks like the toka­mak field of Fig. 5.9, but notice that the outermost field lines are going backwards in the toroidal direction compared to those near the center. Hence the name reversed-field pinch.

In spite of the seeming quiescence of the Taylor state, the RFP suffers from magnetic fluctuations caused by the basic hydromagnetic instabilities, especially the tearing mode (Chap. 6). A conducting shell close to the plasma is needed to

control the resistive wall mode, and active feedback stabilization is needed also. If it can be made to work, the RFP has the great advantage of self-generated magnetic field, requiring the addition of only a small toroidal field from external coils. These coils need not be superconducting, since they consume little power. The relatively weak magnetic field means that very high beta values can be achieved. However, for a reactor, the conducting shell makes the design of the blanket and first wall problematical. The bootstrap current is small, so the large toroidal current has to be driven inductively with a transformer. That means that the plasma has to be pulsed. There is some evidence that a DC current can be created with a oscillating drive [30], but this is at a primitive stage.

In spite of doubts about its reactor relevance, considerable progress has been made in understanding the physics of RFPs. This research is also of interest to space scientists, since processes like reconnection also occur in space. New results come mainly from the RFX machine in Padua, Italy [31], and the MST in the University of Wisconsin [30]. At low power, the RFP does not self-organize suffi­ciently, and magnetic surfaces of many helicities are all tangled up. When the domi­nant mode exceeds 4% at a current of 1.5 MA, however, the plasma snaps into a single helix, whose cross section is shown in Fig. 10.31. The plasma moves off — center into a helical shape, the magnetic surfaces are no longer jumbled, and con­finement is much improved. The electron temperature is seen to increase a factor of 2 to about 850 eV.

In the MST, magnetic chaos is suppressed actively by shaping the current profile with pulsed poloidal current drive. Figure 10.32 is a computer simulation of the magnetic surfaces before and after the current drive is imposed. Plasma confine­ment time is increased ten times by this, up to 12 ms, which is comparable to that in small tokamaks. Electron temperature reaches 2 keV, and ion temperature

1.3 keV. Beta values of order 26% have been achieved. The plasma density sur­passes the Greenwald limit (Chap. 8) by 20% [30]. In spite of the weak magnetic

field, energetic ions have been found to be well contained. This was found by injecting 20 keV neutral beams, which turn into 20 keV deuterons. However, ions in RFPs are not heated by neutral beams because they are naturally heated by reconnection. This is a process in which magnetic-field lines merge, destroying some B-field and converting its magnetic energy into plasma energy. This phenom­enon also occurs in the earth’s magnetic field, so that RFP research, as well as spheromak research, has relevance to other fields of science.