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.

A reversal has been observed in the mean phase velocity of the turbulent fluctuations in the edge plasma of the TEXT tokamak. The observations can be described by a model in which the wave velocity in the lab frame is dominated by a nonuniform Er×B velocity and a gradient driven drift. The measurements also exhibit a localized instability which occurs in the region of maximum velocity shear.

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Particle transport in an ohmically heated tokamak plasma was investigated in the Texas Experimental Tokamak (TEXT). Spectroscopic measurements of the electron source were used with electron density measurements to derive particle confinement times from the continuity equation. Scalings were developed for particle confinement time with electron density, plasma current, toroidal field, and plasma positioning. Simultaneous measurement of electrostatic fluctuations with Langmuir probes may suggest a correlation between edge particle transport in TEXT and electrostatic turbulence. In addition, two major features of transport were isolated. First, transport is poloidally asymmetric at least in the plasma edge. Secondly, in some cases, the particle confinement scalings are closely associated with the scalings for recycling at particular surfaces. Similarities of the TEXT global particle confinement time scalings to those observed in other tokamaks may allow the conclusions of this work to be extended to other devices.

The nonlinear coupling coefficient and the energy transfer associated with three-wave interactions are computed from measured data of the turbulent edge plasma of the Texas Experimental Tokamak(TEXT) [Nucl. Technol. Fusion 1, 479 (1981)]. The results show the presence of three-wave interactions. The interactions cause energy to cascade away from the dominant waves of the spectrum primarily toward lower, but also toward higher frequencies. The results are obtained with a new digital spectral analysis technique based on the estimation of higher-order cumulants. The method is discussed and tested on a simulation experiment. The same technique is useful for neutral fluids as well.

This article reviews digital spectral analysis techniques that yield experimental insight into plasma turbulence. Methods to quantify the statistical properties of the fluctuations and to measure the particle and heat flux caused by electrostatic fluctuations are presented. Furthermore, analysis techniques to study the nonlinear coupling process of turbulence and the redistribution of energy among the different modes are discussed. The impact of the analysis techniques on fusion research is demonstrated with experimental results collected with Langmuir probes, heavy-ion beam probes, and laser scattering in the tokamak TEXT. Special emphasis is given to the characterization of the wavenumber distribution and the correlation lengths in all toroidal directions, including a first measurement of k∥ in a tokamak.

A quantitative comparison of the fluctuation-induced energy flux with the total energy flux has been made in the edge region of the TEXT tokamak using fluctuation measurements from Langmuir, heavyion-beam, and magnetic probes. At all but the lowest densities the convected energy flux due to electrostatic fluctuations dominates the energy losses caused by plasma transport. Energy loss through magnetic fluctuations is insignificant in the edge region. PACS numbers: 52.55.Fa, 52.25.Gj It is well known that the energy lost from tokamaks through transport processes is much larger than predicted by neoclassical theory (Refs. 1 and 2, and references therein). Plasma turbulence is generally invoked to account for the anomalous losses. Unlike neoclassical transport which depends on the mean plasma parameters and collisions, turbulent transport results from Auctuations in plasma parameters (electric and magnetic fields, density, temperature, etc.). Fluctuation-induced particle and energy Auxes have been measured in the edge region of several tokamaks.It has been established in the Texas Experimental Tokamak (TEXT) that the total particle flux in the edge plasma is primarily due to electrostatic fluctuations.In this work we investigate the role Auctuations play in the total edge energy transport.Specifically, we compare radial profiles of the energy Aux due to Auctuations with profiles of the total plasma energy flux in the edge of TEXT. The importance of the edge region is demonstrated by the improved global energy confinement in 0-mode discharges, TFTR supershots, and recent Ohmic discharges, in ASDEX. ' TEXT is a medium size tokamak with a major radius R of 1 m and a minor radius a of 0.26 m defined by a full poloidal limiter. The data presented here were taken in steady-state, Ohmically heated discharges with sawteeth and low Mirnov activity. The radial profiles were collected over a number of similar shots, with at least three shots for each radial position. The density, potential, and temperature fluctuation data were collected with Langmuir probes (LP) in the far edge region of the discharge and in the scrape-oA' layer (SOL) outside of the outermost closed flux surface (r/a-= 1). With a heavy-ion-beam probe'' (HIBP) the density and potential fluctuation data can be measured in the plasma interior. We use data in to r/a=0. 8. Magnetic fluctuation data were collected with magnetic probes (MP) located in the SOL. The Auctuation measurements of both the LP and the HIBP were taken approximately 180 away in the toroidal direction from the poloidal limiter; the MP was positioned about halfway between these diagnostics and the limiter. The fluctuation data were digi-0.8 CA 0.6 CD O 0 4 O V CD ) 0 2 C5 CD n n Te Te 0.0 0.8 0.9 r/a t 1.2FICs. I. Relative fluxuation levels of density n/n, plasma potential ep~~/ke T"electron temperature T,/T"and magnetic field 8,/8&, as functions of radius. Filled symbols represent data from Langmuir probes, and open symbols from the HIBP. tized with a 10-bit digitizer at a I-ps sampling in...

The spectra, magnitude and spatial distribution of low-frequency (w <3 w ci ) density fluctuation have been measured by two independent experimental methods in the edge plasma of the TEXT tokamak. Good agreement between far-infrared laser scattering and Langmuir probe measurements has been achieved and the strengths of each technique are evaluated. Langmuir probes are used to directly determine the particle flux induced by edge fluctuations (F oc (ni>£ xB )) and collective Thomson scattering permits an extension of these observations to the plasma interior. Results are presented for typical discharge conditions in a tokamak.