A. J. Wootton

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...

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.

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.

An experimental counter‐example to the local transport paradigm

The response of a tokamak discharge to a sharp drop in edge temperature differs significantly from that expected from typical local transport models in several important respects. Laser ablation of carbon induces large (ΔT/T≤70%), rapid (<200 μs) electron temperature drops in the outermost region of the plasma, r/a≥0.9. This cold pulse proceeds through the outer plasma (r/a≥0.75), rapidly compared with power balance or sawtooth predictions. However, the pulse shrinks markedly thereafter, disappearing near r/a∼0.5. Within r/a∼0.3, the temperature rises promptly. The results are inconsistent with conventional local transport models; a nonlocal phenomenology, in which transport coefficients increase in the edge and decrease in the core, is suggested. The turbulence levels measured with a heavy ion beam probe increase near the edge but are unchanged in the core.

Global particle confinement in the Texas Experimental Tokamak

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.

Core temperature fluctuations and related heat transport in the Texas Experimental Tokamak‐Upgrade

The mechanism(s) responsible for anomalous heat transport in the tokamak plasma core has remained elusive to experimental verification. In this paper the hypothesis that high‐frequency electrostatic turbulence can account for the measured electron heat transport in Ohmically heated tokamak discharges of the Texas Experimental Tokamak‐Upgrade (TEXT‐U) [Proceedings of the 15th Symposium on Fusion Technology, Utrecht (Elsevier, Amsterdam, 1989), Vol. 1, p. 342] is tested. To accomplish this, core temperature fluctuations have been determined from the measured correlation between two electron cyclotron radiation signals detected by a multichannel high‐frequency‐resolution heterodyne radiometer. It is found that long wavelength modes (poloidal wave number ≲1 cm−1) are present, with an electron temperature fluctuation amplitude comparable to the density fluctuation amplitude. However, these modes cannot account for observed transport. An extrapolation of the observed turbulent temperature spectrum to the shorte...

Analytical tokamak equilibrium for shaped plasmas

A general analytical solution of the Grad–Shafranov equation is presented. Specific functional forms of pressure and plasma current are used; the solution allows arbitrary plasma size, aspect ratio, elongation, triangularity, current, and poloidal beta, without imposing undue constraints amongst those variables.

A new scheme for Langmuir probe measurement of transport and electron temperature fluctuations

A new scheme to extend the triple Langmuir probe technique for the measurement of electron temperature fluctuations and the fluctuation‐driven transport has been developed. The extension is aimed at reducing the phase delay error introduced by finite probe tip separations in standard triple‐probe method. The modified triple‐probe scheme provides a more reliable measurement of the temperature fluctuations for a proper interpretation of the density and potential fluctuations and the transport measurement from Langmuir probe data. New results on fluctuations have been obtained from Phaedrus‐T and TEXT‐U tokamaks.

The space potential in the tokamak text

A heavy ion beam probe has been used to measure the plasma space potential profiles in the tokamak TEXT [Nucl. Fusion Technol. 1, 479 (1981)]. The Ohmic discharges studied were perturbed by externally produced resonant magnetic fields (an ergodic magnetic limiter or EML). Without these perturbations the plasma central potential is generally consistent with the value calculated from radial ion momentum balance, using experimental values of density and ion temperature and assuming a neoclassical poloidal rotation velocity. Exceptions to the agreement are found when operating with reduced plasma parameters. Possible reasons for this discrepancy are explored, in particular, the effects of intrinsic magnetic field fluctuations, and modifications to the self‐consistent radial electric sheath. With the application of the EML fields the edge electric field and potential increase during periods of magnetic island overlap. A test particle calculation of electron transport shows increases in diffusivity also occur d...

Particle transport studies with applied resonant fields on TEXT

Externally applied resonant magnetic fields have been used on TEXT to modify the particle flux and the radial electric field near the plasma edge. Magnetic fields with primary mode numbers m/n = 7/3 and 7/2, and an average radial field amplitude |br|/B ? 0.1% have been employed. This perturbation produces mixed islands and stochastic regions at the plasma edge (r/a ? 0.8) without affecting the interior. Working particle transport is shown to be increased by typically 30% only in the presence of (computed) magnetic islands. The effect is diminished at high perturbing field strength when the islands become stochastic. A novel transport mechanism due to ? convection is proposed to explain this. Outward impurity transport is increased as well.