W. A. Peebles

Fluctuations and anomalous transport in tokamaks

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...

Modifications in turbulence and edge electric fields at the L--H transition in the DIII-D tokamak

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 ...

Advanced plasma fluctuation analysis techniques and their impact on fusion research (invited)

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.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.

The spectrum, spatial distribution and scaling of microturbulence in the TEXT tokamak

Strong asymmetries in the spectrum and magnitude of low frequency (? ? ?ci) density fluctuations in the Texas Experimental Tokamak (TEXT) are described. Microturbulence is investigated under a variety of plasma parameters and a comparison with mixing length theory is made. Broadband fluctuations (??/? ? 1, ?k/k? ? 1.5, propagating in the electron diamagnetic drift direction) are observed throughout the plasma cross-section, but they peak at the limiter and possess a strong up-down asymmetry which inverts with reversal of plasma current direction. The spatial distribution of these fluctuations can be dramatically altered by the introduction of a point limiter. Inside the magnetic axis, a large-magnitude quasi-coherent fluctuation (??/? ? 0.2, ?k/k? ? 0.7, propagating in the electron diamagnetic drift direction) is seen to dominate the ubiquitous broadband microturbulence. This type of fluctuation peaks on the midplane. For high density discharges, a distinct ion mode (density fluctuations propagating in the ion diamagnetic drift direction) is observed in the microturbulence spectra. Onset of the ion feature occurs at plasma densities where a clear saturation is evident in the global energy confinement time.

Electron thermal confinement studies with applied resonant fields on TEXT

Externally applied magnetic fields are used on the Texas Experimental Tokamak (TEXT) to study the possibility of controlling the particle, impurity and heat fluxes at the plasma edge. Fields with toroidal mode number n = 2 or 3 and multiple poloidal mode numbers m (dominantly m = 7) are used, with a poloidally and toroidally averaged ratio of radial to toroidal field components 〈|br/Bo〉 ≅0. 1%. Calculations show that it is possible to produce mixed islands and stochastic regions at the plasma edge (r/a ≥ 0.8) without affecting the interior. The expected magnetic field structure is described and experimental evidence of the existence of this structure is presented. The edge electron temperature decreases with increasing 〈|br/Bo〉, while interior values are not significantly affected. The implied increase in edge electron thermal diffusivity is compared with theoretical expectations and is shown to agree with applicable theories to within a factor of three.

Characterization of tokamak edge turbulence by far-infrared laser scattering and Langmuir probes

The spectra, magnitude and spatial distribution of low-frequency (ω ωci) 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 (Γ ∝ n×B) and collective Thomson scattering permits an extension of these observations to the plasma interior. Results are presented for typical discharge conditions in a tokamak.

Instrumentation for magnetically confined fusion plasma diagnostics

Recent progress in magnetically confined plasma research has brought the goal of controlled thermonuclear fusion within reach. Simultaneously, the increased size, temperature, and density of these devices has resulted in rapid changes in diagnostic techniques. In this article, recent developments in instrumentation are reviewed together with trends for the future. The topics discussed include far‐infrared laser interferometry and polarimetry, ruby laser television Thomson scattering, excimer and Nd‐glass laser scattering, ion temperature determination via large‐α scattering with FIR and CO2 lasers, collective scattering, Schottky diode mixer technology, synchrotron radiation diagnostics and imaging, ion beam probes, x‐ray diagnostics and imaging, neutron diagnostics, resonance fluorescence scattering, ultraviolet diagnostics, and internal magnetic field measurement.

Measurements of core electron temperature and density fluctuations in DIII-D and comparison to nonlinear gyrokinetic simulations

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 de...

L-mode validation studies of gyrokinetic turbulence simulations via multiscale and multifield turbulence measurements on the DIII-D tokamak

A series of carefully designed experiments on DIII-D have taken advantage of a broad set of turbulence and profile diagnostics to rigorously test gyrokinetic turbulence simulations. In this paper the goals, tools and experiments performed in these validation studies are reviewed and specific examples presented. It is found that predictions of transport and fluctuation levels in the mid-core region (0.4 < ρ < 0.75) are in better agreement with experiment than those in the outer region (ρ ≥ 0.75) where edge coupling effects may become increasingly important and multiscale simulations may also be necessary. Validation studies such as these are crucial in developing confidence in a first-principles based predictive capability for ITER.

Electron heat transport in improved confinement discharges in DIII-D

In DIII-D tokamak plasmas with an internal transport barrier (ITB), the comparison of gyrokinetic linear stability (GKS) predictions with experiments in both low and strong negative magnetic shear plasmas provide improved understanding for ion and electron thermal transport within much of the plasma. As previously reported, the region for improved ion transport seems well characterized by the condition OE~B>Y-, where SERB is the ExB flow shear, calculated from measured quantities, and y,, is the maximum linear growth rate for ion temperature gradient (ITG) modes in the absence of flow shear. Within a limited region just inside the ITB, the electron temperature gradient (ETG) modes appear to control the electron temperature gradient and, consequently, the electron thermal transport. The increase in electron temperature gradient with more strongly negative magnetic shear is consistent with the increase in the ETG mode marginal gradient. Closer to the magnetic axis the Te profile flattens and the ETG modes are predicted to be stable. With additional core electron heating, FIR scattering measurements near the axis show the presence of high k fluctuations (12 cm-l), rotating in the electron diamagnetic drift direction. This turbulence could impact electron transport and possibly also ion transport. Thermal diffusivities for electrons, and to a lesser degree ions, increase. The ETG mode can exist at this wavenumber, but it is computed to be robustly stable near the axis.