The major instabilities encountered in early toroidal confinement research have been controlled. The remaining microinstabilities are of the drift-wave type, which we described in some detail in Chap. 6. They differ only in the energy source that

feeds them and in the collisional process that allows guiding centers to be unglued from magnetic lines. The effect of these instabilities on how long a plasma can remain trapped depends on the type of turbulence that the waves grow into — their nonlinear behavior, as physicists would say. In fluids like water or air, turbulence can the form of swirling eddies. For instance, in the picture of the surface of Jupiter shown in Fig. 7.21a, turbulence driven by winds is visible in the cloud patterns, including the largest eddy, the famous Great Red Spot. In water or air, flows are driven by pressure differences. In a magnetized plasma, flows across the magnetic field are driven instead by electric fields (the aforementioned E x B drift), but can also give rise to turbulent eddies. However, in a tokamak, Mother Nature reveals another of her helpful tricks: these eddies are self-limiting in their sizes! This means that large eddies like the Great Red Spot cannot occur — eddies that could otherwise bring plasma toward the wall rapidly across their diameters.

Referring back to Fig. 6.17, we see that drift waves create poloidal electric fields by the bunching of alternately positive and negative charges. These E-fields cause inward or outward flow of plasma in the radial direction, and the net loss of plasma comes about because the E-fields are phased so that the drift is always outward where the density is high and inward where the density is low. A better picture of these eddies is shown in Fig. 7.22. The distribution of “+”and “-” charges is, as shown in Fig. 6.17, generating the alternating electric field shown by the short red arrows. Together with the toroidal magnetic field, this E-field causes an E x B drift of the plasma in the closed loops or eddies, also called convective cells. The density pattern of the drift wave is displaced with respect to these eddies in such a way that the density is higher (blue) where the drift is outward and lower (red) where the drift is inward. Thus, the net motion of the plasma is outward. The danger is that these convective cells could be long “streamers” in the radial direction, as drawn here, so that the plasma can move a long way toward the wall in each cycle of the wave.

Fortunately, this does not happen because the turbulence takes on a different form as it grows. Alternating drifts in each radial layer automatically arise,

as shown in Fig. 7.23. These are the zonal flows. The flows are E x B drifts driven by “+”and charges on the boundaries of each zone. They break up the large convective cells into small ones, only about a centimeter wide, the size of an ion Larmor radius, so that the rapid convection in each cell can move the plasma only a short distance. The flows themselves cannot remove plasma, since they are parallel to the wall. In the picture of Jupiter taken by the Hubble Space Telescope shown in Fig. 7.21b, one can see zonal flows clearly in the upper half of the picture. In those stripes, the wind blows in alternating directions. The shear in the wind speed at the

zone boundaries causes the turbulence seen more clearly in the bottom half of the picture. The zonal flows in a toroidal plasma, however, are fundamentally different. In the plasma, the zonal flows do not create the turbulence. It is the turbulence that creates the zonal flows! In other words, a zonal flow is an instability that is driven by another instability! Since a zonal flow is the same all around the torus in both the toroidal and the poloidal directions, it takes little energy to set it into motion. There is no need to add angular momentum to spin the flows around the poloidal direction, since the flows are in opposite directions in adjacent layers, so that the net angular momentum is zero. Microinstabilities in a torus develop into a turbulent state that incorporates zonal flows, a type of turbulence that is self-limiting in its eddy sizes. In principle, this should cause anomalous diffusion to be slower than theoretically expected, though this has not yet been shown experimentally.

Zonal flows were seen in many computer simulations of the nonlinear state of microinstabilities and have received extensive treatment by theorists [7]. The tool of computer simulation has greatly advanced progress in fusion in the past decade; this subject will be described shortly. Theories have been proposed on many details of zonal flows, including how a drift-wave instability can drive zonal flows through what is called a modulational instability. Such details have not been verified by experiment, but the existence of plasma flows that do not vary in either the poloidal or toroidal direction has been established experimentally [8]. In two Japanese labo­ratories, one with a tokamak and the other with a compact helical system (a type of stellarator), a sophisticated diagnostic called a heavy ion beam probe was used for this purpose. A beam of ions, usually cesium (Cs+), is accelerated to such high energy that it has a Larmor radius larger than the plasma radius, and so it can be aimed at any part of the plasma. When it gets ionized to a doubly charged state (Cs2+), its Larmor radius gets smaller and its orbit changes. By catching the Cs2+ ions at a particular part of the periphery, it is possible to tell the exact spot inside the plasma where this re-ionization occurred. Then the number and energy of the Cs2+ ions can tell the electron density and electric field at that spot, even if these are fluctuating at a high frequency. With this tool, fluctuations matching the charac­teristics of zonal flows have been detected. However, the predicted connection between the existence of zonal flows and an improvement in confinement time has yet to be quantified in the laboratory.