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MAGNETIC CONFINEMENT FUSION 75 particular, the experiments imply that the size of the turbulent eddies is not always controlled by the electron or ion gyroradius size, but presumably is set by macroscopic scale lengths. New diagnostic techniques used in recent measurements of the turbulent fluctuations within tokamak plasmas have found that the spectrum and implied transport are dominated by moderately long- wavelength modes. Measured changes in the plasma transport are well correlated with changes in the fluctuation amplitude, implicating them as the cause of the transport. In contrast, the measured transport parallel to the magnetic field is in good agreement with the predictions of "neoclassical" theory. One of the major scientific achievements of tokamak transport and turbulence studies has been the development of a model explaining the formation of the transport barrier in H-mode. This model is based on stabilization of turbulence by sheared E Ã B flow (here E is the radial electric field observed in the vicinity of the tokamak edge, and B is the toroidal magnetic field). The measured levels of E Ã B flow shear are well above those theoretically required for such stabilization. Furthermore, the increased E Ã B flow shear is correlated with the reduction of density fluctuations, cross-field energy, and particle transport both spatially and temporally. These results provide some of the best evidence to date of the close connection between fluctuations and transport. Similar E Ã B shear stabilization effects may also take place in the core of tokamak plasmas (e.g., the confinement improvement from H-mode to VH-mode). The concept of electric field flow shear stabilization of turbulence may be one of the most fundamental contributions of tokamak physics to general fluid dynamics. Although flow shear stabilization can take place in ordinary fluids, a sheared velocity field is usually a source of free energy; hence it usually drives instabilities rather than stabilizing them. Only in a plasma can magnetic shear prevent instabilities driven by velocity shear (e.g., Kelvin-Helmholtz instabilities) so that flow shear can then affect the other instabilities. Another recent result is the importance of the plasma current density profile in controlling confinement. Experiments modifying the current profile transiently, by inductively driving a skin current, changing the plasma shape, or using external current drive, have shown that, with peaked current profiles, the cross-field transport can be substantially reduced. Although this effect is not understood theoretically, measurements of the local ion thermal transport indicate that it may be reduced by increasing magnetic shear. Future Prospects The eventual goal of the magnetic fusion program is the realization of a commercial reactor to generate electricity. Present limitations on confinement and total pressure in the plasma force reactor designers in the direction of multigigawatt units. Understanding and reducing turbulent transport in tokamaks
MAGNETIC CONFINEMENT FUSION 76 FIGURE 4.1 The loss of thermal energy from magnetically confined plasmas is dominated by turbulent transport. The high-confinement regime (H-mode) in tokamaks is characterized by reduced turbulence at the plasma edge, which inhibits this outward transport of energy. The existence of this regime is believed to be caused by a shear in the drift velocity, associated with a radial electric field. Recently, an even higher confinement regime (the VH-mode) has been discovered, in which the region of high shear and low turbulence extends deeper into the plasma. Shown in this figure are, from top to bottom, the electric field, the velocity shear, and the thermal diffusivity as functions of the normalized minor radius, , for the H- and VH-modes. The inset at the top of the figure shows the time evolution of the normalized density fluctuations, as measured by microwave scattering. (Reprinted, by permission, from K.H. Burrell, T.H. Osborne, R.J. Groebner, and C.L. Rettig, Proceedings of the 20th European Physical Society Conference on ControlledFusion and Plasma Physics, European Physical Society, Geneva, 1993, vol. 17C, part 1, pp. 1â6. Copyright Â© 1993 by the European Physical Society.)