This interesting device is not really a pinch; it has characteristics of spheromaks, pinches, inertial confinement, and even mirrors. A simple diagram is shown in Fig. 10.33. If you rotate the diagram 90°, it looks like a spheromak (Fig. 10.18), but it has one essential difference. There is no toroidal magnetic field. The toroidal direction is indicated by the ellipses for the current and an ion Larmor orbit. Toroidal coils on the outside create a magnetic field (B-field) going from right to left in the diagram. A toroidal current driven in the plasma creates a B-field oppo­site to the external field. The current is in the same direction as the electron diamag­netic current (Chap. 6), which adds to it. When the current is large enough to cancel the external field, there is a radius R at which the B-field is zero. This is the center of the tubular plasma. It is confined by a purely poloidal B-field. Inside of R, the B-field is opposite to that which was applied. Outside of R, the B-fields from the internal current and the external coils are squeezed up to the vacuum wall, which, being conducting, is a flux conserver. The field lines are divided into two types divided by a separatrix, shown by the dashed line, which represents a field line which leads to a B = 0 point on the axis. The field there has to be zero because it cannot point in two directions at the same time. Plasma inside the separatrix is confined in closed magnetic surfaces; those diffusing outside the separatrix are lost out the ends of the machine. There is therefore a natural divertor; and mirror coils, of which one is shown, can be designed to treat the escaping plasma the same way as in a mirror machine (Fig. 10.27), including the possibility of direct conversion.

Although the field lines on which the plasma lies are closed, this should be better than a mirror machine, but the FRC configuration is highly unstable. There are no helical field lines to link regions of good and bad curvatures, as there are in a spherical tokamak (Fig. 10.12). In fact, there is no good curvature anywhere. The curvature is especially bad at the ends of the machine, as shown in Fig. 10.33. How can an FRC plasma be stable against the main hydromagnetic instabilities? The FRC depends on finite-Larmor-radius effects (Chap. 6). The Larmor radius rLi of the ions at the bad — curvature regions is not negligible compared with the size of, say, the Rayleigh-Taylor instability (Chap. 5). That means that ions can travel across field lines far enough to short-circuit the voltages that the instability generates, keeping it from growing. Electrons, with much smaller Larmor radii, cannot do that; they are tied tightly to the field lines.

How large does rLi have to be? It has to be a sizable fraction of the plasma width, which can be measured by the distance between the center of the plasma and the last closed surface at r. This is R — r. The number of Larmor radii in that width is

s s

then s = (R — rs)/rLi. The parameter s has to be small to keep the plasma stable. In early FRC experiments, s was only 2 or less. However, plasma diffuses at a rate proportional to rLi via electron-ion collisions (Chap. 6), even if it is stable. So s has to be large to get long confinement times, and there is always this struggle to get stability at as large an s as possible.

If instabilities can be controlled, FRCs could have advantages as reactors [17]. They are small and do not require large B-fields. They naturally have high beta, since beta actually goes to infinity at the field null. Longer machines are predicted to be more stable, giving an easy way to get more plasma volume. FRCs have natu­ral divertors and the possibility of direct conversion. Once created, an FRC plasma can be moved into a compression chambers, where pulsed coils can pinch them to higher density and temperature. Research on FRCs has always been on the back burner, so they have not had the support of large computing efforts that tokamaks and laser fusion have had. Expensive equipment like neutral-beam heating has also

not been available. There is precious little information on how the early plasmas were created, but recent success in using rotating magnetic field (RMF) current drive has given the program new impetus. Invented more than 30 years ago by Ieuan Jones and Lance McCarthy at the University of Adelaide in Australia, this method applies a transverse magnetic field that rotates at radiofrequencies in the toroidal direction. Fig. 10.34 shows an end-on view of the RMF lines as they are affected by the plasma. Electrons are entrained by these field lines and rotate with them to the best of their ability, but they are slowed down by collisions with the ions. The rotating field has to have enough power to overcome this drag. There is also a radiofrequency skin depth so that the field does not penetrate all the way into the plasma. In the original Rotomak, the field lines were not closed, so confinement could not be good; but RMF works well in an FRC.

Experiments on the science of FRCs have been carried out in a series of machines in the Redmond Plasma Physics Laboratory of the University of Washington. The most troublesome instability has been the tilt mode, shown in Fig. 10.35. By 1995, stability had been obtained up to s=5 [17]. It was found that energy was lost mainly by radiation due to impurities coming off the walls. Conditions were greatly improved with a new vacuum system in the TCSU machine.

The reduced drag on RMF current drive allowed it to produce denser and hotter plas­mas. The total temperature (T+T) increased about a factor of 4 to »200 eV, the plasma

density about a factor of 3, and the plasma pressure about 50%. Diagnostics are still rudimentary. The plasma pressure can be expressed as a magnetic field Be which has the same pressure. Compared with the RMF amplitude Bw, Be is 4.9 times larger. RMF cur­rent drive in principle allows steady-state operation. These are encouraging results, but the plasma parameters are still very modest. It may be a long time before the conditions of an old reactor study [34] can be realized.

The high betas in FRCs make them suitable for advanced fuels, which require hotter and denser plasmas to ignite. This is being pursued in private industry with a FRC-type machine in which hydrogen ions are injected into a boron plasma for the p-B11 reaction. Tri-Alpha Energy in Irvine, California, was named for the three alpha particles which result from that reaction. The innovation involves adding rotation to the plasma in an FRC and is based on a theory by renowned plasma theo­rist Norman Rostoker [35].