This is a review of what is known about fluctuations and anomalous transport processes in tokamaks. It mostly considers experimental results obtained after, and not included in, the reviews of Liewer [Nucl. Fusion 25, 543 (1985)], Robinson [in Turbulence and Anomalous Transport in Magnetized Plasmas (Ecole Polytechnique, Palaiseau, France, 1986), p. 21], and Surko [in Turbulence and Anomalous Transport in Magnetized Plasmas (Ecole Polytechnique, Palaiseau, France, 1986), p. 93]. Therefore much of the pioneering work in the field is not covered. Emphasis is placed on results where comparisons between fluctuations and transport properties have been attempted, particularly from the tokamak TEXT [Nucl. Technol./Fusion 1, 479 (1981)]. A brief comparison of experimentally measured total fluxes with the predictions of neoclassical theory demonstrates that transport is often anomalous; fluctuations are thought to be the cause. The measurements necessary to determine any such fluctuation-driven fluxes are described. The diagnostics used to measure these quantities, together with some of the statistical techniques employed to analyze the data, are outlined. In the plasma edge detailed measurements of the quantities required to directly determine the fluctuation-driven fluxes are available. The total and fluctuation-driven fluxes are compared: the result emphasizes the importance of edge turbulence. No model adequately describes all the measured properties. In the confinement region experimental observations are presently restricted to measurements of density and potential fluctuations and their correlations. Various distinct turbulence features that have been observed are described, and their characteristics compared with the predictions of various models. Correlations observed between these fluctuations and plasma transport properties are summarized. A separate section on magnetic fluctuations shows there is very little information available inside the plasma, generally prohibiting quantified comparisons between fluctuation levels and transport. Both coherent and turbulent magnetic fluctuations are addressed, and the differences between low and high plasma pressure (low and high beta) are noted. The contributions of alternate confinement devices, such as stellarators and reversed field pinches, to understanding tokamak anomalous transport are discussed. Finally, future directions are proposed.

Direct evidence of zonal flow (ZF) predator-prey oscillations and the synergistic roles of ZF- and equilibrium E×B flow shear in triggering the low- to high-confinement (L- to H-mode) transition in the DIII-D tokamak is presented. Periodic turbulence suppression is first observed in a narrow layer at and just inside the separatrix when the shearing rate transiently exceeds the turbulence decorrelation rate. The final transition to H mode with sustained turbulence and transport reduction is controlled by equilibrium E×B shear due to the increasing ion pressure gradient.

The paradigm of shear suppression of turbulence as the mechanism for the low to high confinement mode (L to H) transition is examined by quantitative comparison of the predictions of the paradigm with experimental results from the DIII-D tokamak [Plasma Physics and Controlled Fusion Research (International Atomic Energy Agency, Vienna, 1986), p. 159]. The L to H transition trigger is V×B rotation, not the main ion pressure gradient. The radial electric field Er shear increases before the fluctuation suppression, consistent with increasing Er shear as the cause of the turbulence suppression. The spatial dependence of the turbulence reduction is consistent with shear suppression for negative Er shear. For positive Er shear, the turbulence suppression is consistent with the effect of Er curvature for modes for which an Er well is destabilizing. Finally, the transport barrier depends on the phase angle between the density and potential fluctuations inside the Er well, an effect not included in existing L to H transition models.

The L to H transition in the DIII-D tokamak [Plasma Physics and Controlled Nuclear Fusion Research, 1986 (IAEA, Vienna, 1987), Vol. I, p. 159] is associated with two clear signatures: edge density fluctuations are abruptly suppressed (in ≊100 μsec), while the edge poloidal rotation velocity vθ increases, implying that the radial electric field Er becomes more negative. Detailed new spectroscopic profile measurements show that the changes in vθ and Er generate a region of sheared electric field and poloidal flow of width ≊3–5 cm. This region develops simultaneously with, and has the same spatial extent as, the edge fluctuation suppression zone as measured using a reflectometer system. Furthermore, the radial extent of the shear and fluctuation suppression zones encompass the location of the H-mode edge transport barrier. These observations are consistent with recent theoretical models of the L–H transition, and a comparison with these theories is presented. Data are also presented on the evolution of edge parameters and density fluctuations after the transition: the shear and fluctuation suppression layers are maintained for the duration of the quiescent H-mode phase, while relative density fluctuation levels decrease and interior plasma confinement gradually improves. Precursors to several different types of edge localized mode (ELMs) are also discussed.

For the first time, profiles (0.3<ρ<0.9) of electron temperature and density fluctuations in a tokamak have been measured simultaneously and the results compared to nonlinear gyrokinetic simulations. Electron temperature and density fluctuations measured in neutral beam-heated, sawtooth-free low confinement mode (L-mode) plasmas in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] are found to be similar in frequency and normalized amplitude, with amplitude increasing with radius. The measured radial profile of two fluctuation fields allows for a new and rigorous comparison with gyrokinetic results. Nonlinear gyrokinetic flux-tube simulations predict that electron temperature and density fluctuations have similar normalized amplitudes in L-mode. At ρ=0.5, simulation results match experimental heat diffusivities and density fluctuation amplitude, but overestimate electron temperature fluctuation amplitude and particle diffusivity. In contrast, simulations at ρ=0.75 do not match either the experimentally derived transport properties or the measured fluctuation levels.

Geodesic acoustic modes (GAMs) and zonal flows are nonlinearly driven, axisymmetric (m=0andn=0) E×B flows, which are thought to play an important role in establishing the saturated level of turbulence in tokamaks. Results are presented showing the GAM’s observed spatial scales, temporal scales, and nonlinear interaction characteristics, which may have implications for the assumptions underpinning turbulence models towards the tokamak edge (r/a>rsim0.75). Measurements in the DIII-D tokamak [Luxon, Nucl. Fusion 42, 614 (2002)] have been made with multichannel Doppler backscattering systems at toroidal locations separated by 180∘; analysis reveals that the GAM is highly coherent between the toroidally separated systems (γ>0.8) and that measurements are consistent with the expected m=0andn=0 structure. Observations show that the GAM in L-mode plasmas with ~2.5-4.5 MW auxiliary heating occurs as a radially coherent eigenmode, rather than as a continuum of frequencies as occurs in lower temperature discharges; this is consistent with theoretical expectations when finite ion Larmor radius effects are included. The intermittency of the GAM has been quantified, revealing that its autocorrelation time is fairly short, ranging from about 4 to about 15 GAM periods in cases examined, a difference that is accompanied by a modification to the probability distribution function of the E×B velocity at the GAM frequency. Conditionally-averaged bispectral analysis shows the strength of the nonlinear interaction of the GAM with broadband turbulence can vary with the magnitude of the GAM. Data also indicate a wavenumber dependence to the GAM’s interaction with turbulence.

A wide variety of fast ion driven instabilities are excited during neutral beam injection ͑NBI͒ in the National Spherical Torus Experiment ͑NSTX͒ ͓Nucl. Fusion 40, 557 ͑2000͔͒ due to the large ratio of fast ion velocity to Alfvén velocity, V fast / V Alfvén , and high fast ion beta. The ratio V fast / V Alfvén in ITER ͓Nucl. Fusion 39, 2137 ͑1999͔͒ and NSTX is comparable. The modes can be divided into three categories: chirping energetic particle modes ͑EPM͒ in the frequency range 0 to 120 kHz, the toroidal Alfvén eigenmodes ͑TAE͒ with a frequency range of 50 kHz to 200 kHz, and the compressional and global Alfvén eigenmodes ͑CAE and GAE, respectively͒ between 300 kHz and the ion cyclotron frequency. Fast ion driven modes are of particular interest because of their potential to cause substantial fast ion losses. In all regimes of NBI heated operation we see transient neutron rate drops, correlated with bursts of TAE or fishbone-like EPMs. The fast ion loss events are predominantly correlated with the EPMs, although losses are also seen with bursts of multiple, large amplitude TAE. The latter is of particular significance for ITER; the transport of fast ions from the expected resonance overlap in phase space of a "sea" of large amplitude TAE is the kind of physics expected in ITER. The internal structure and amplitude of the TAE and EPMs has been measured with quadrature reflectometry and soft x-ray cameras. The TAE bursts have internal amplitudes of ñ / n = 1% and toroidal mode numbers 2 Ͻ n Ͻ 7. The EPMs are core localized, kink-like modes similar to the fishbones in conventional aspect ratio tokamaks. Unlike the fishbones, the EPMs can be present with q͑0͒ Ͼ 1 and can have a toroidal mode number n Ͼ 1. The range of the frequency chirp can be quite large and the resonance can be through a fishbone-like precessional drift resonance, or through a bounce resonance.

Robust validation of predictive turbulent transport models requires quantitative comparisons to experimental measurements at multiple levels, over a range of physically relevant conditions. Toward this end, a series of carefully designed validation experiments has been performed on the DIII-D tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] to obtain comprehensive multifield, multipoint, multiwavenumber fluctuation measurements and their scalings with key dimensionless parameters. The results of two representative validation studies are presented: an elongation scaling study performed in beam heated L-mode discharges and an electron heating power scan performed in quiescent H-mode (QH-mode) discharges. A 50% increase in the elongation j is observed to lead to a $50% increase in energy confinement time s e and accompanying decrease in fluctuation levels, qualitatively consistent with a priori theoretical predictions and nonlinear GYRO [J. Candy and R. E. Waltz, J. Comput. Phys. 186, 545 (2003)] simulations. However, these simulations exhibit clear quantitative differences from experiment in the predicted magnitudes and trends with radius of turbulent fluxes and fluctuation levels which cannot be fully accounted for by uncertainties due to transport stiffness. In the QH-mode study, local nonlinear GYRO simulations that neglect fast ion effects show a similar proportional response to the applied electron cyclotron heating as the experiment, but overpredict the magnitudes of transport and fluctuation levels by a factor of 10 or more. Possible sources of this overprediction, namely nonlocal effects and self-consistent fast beam ions, are identified and discussed. V