P. M. Schoch

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.

Experimental progress on zonal flow physics in toroidal plasmas

The present status of experiments on zonal flows in magnetic confinement experiments is examined. The innovative use of traditional and modern diagnostics has revealed unambiguously the existence of zonal flows, their spatio-temporal characteristics, their relationship to turbulence and their effects on confinement. In particular, a number of observations have been accumulated on the oscillatory branch of zonal flows, named geodesic acoustic modes, suggesting the necessity for theories to give their proper description. In addition to these basic properties of zonal flows, several new methods have elucidated the processes of zonal flow generation from turbulence. Further investigation of the relationship between zonal flows and confinement is strongly encouraged as cross-device activity including low temperature, toroidal and linear devices.

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.

TEXT heavy ion beam probe system

A good signal‐to‐noise ratio has been obtained during initial operation of the 500‐keV TEXT heavy ion beam probe. A number of problems were identified during the start up phase and they have been or are being corrected. Present sensitivity for detecting changes in the space potential is 50 V, but it is expected that this can be reduced to 5 V when additional calibration and alignment procedures are completed.

Heavy‐ion beam probe diagnostic systems (invited)

Heavy‐ion beam probing generally consists of passing a beam of 1+ ions through a plasma imbedded in a magnetic field. Secondary ions with higher ionization levels are produced by ionizing collisions with the plasma electrons. Detection of the secondary ions with a small‐aperture electrostatic energy analyzer allows continuous fluctuation measurements of the plasma density and space potential with both spatial and temporal resolution. Spatial resolution is the order of 0.1 cm3 and temporal resolution is presently electronics limited to ∼1 μs. The energy of the probing beam is determined primarily by the requirement that the secondary ion must escape from the plasma. Typical beam energies extend from 10 to 500 keV. The range of plasma densities that have been investigated is 1012 cm−3<ne<1014 cm−3. At the higher densities, beam attenuation becomes a serious problem. Higher beam energies provide better penetration of the magnetic field, and reduced beam attenuation. Heavy‐ion beam probes were first used to m...

Quasi-linear transport inferred from density fluctuation spectra

Expressions for the quasi-linear electrostatic electron particle and heat fluxes are derived in the wave frequency and electron collisionality regimes appropriate to the interior of the TEXT tokamak. These are expressed in terms of moments of the density fluctuation spectrum accounting for poloidal plasma rotation. Minimal assumptions are made as to the origin of the turbulence. The fluxes are then evaluated for an appropriate discharge condition on TEXT, using the density fluctuation frequency spectrum and equilibrium plasma potential measured by a heavy ion beam probe (HIBP). These are compared with the experimental fluxes for two measurements of the normalized rms poloidal wave number k-theta,rms-rho-s. For k-theta,rms-rho-s almost-equal-to 0.1, which is an upper bound of the HIBP two-point phase shift measurements, the electrostatic fluxes are negligible and the rms frequency of the fluctuations is much larger than the Doppler shifted electron diamagnetic drift frequency. However, for k-theta,rms-rho-s almost-equal-to 0.3, as supported by far-infrared (FIR) scattering and as expected for drift waves, the electrostatic fluxes are sufficient to account for the observed fluxes in the region of low collisionality. In addition, the rms frequency (consistent with FIR scattering) agrees with the Doppler shifted electron diamagnetic drift frequency. However, the computed fluxes fall increasingly short of the observed fluxes with increasing radius.

Fluctuations and anomalous transport (in tokamaks, particularly TEXT)

Links between turbulent fluctuations and transport processes in tokamaks, particularly in TEXT, are discussed. In the plasma edge probes allow detailed measurements of the quantities required to directly determine the fluctuation driven fluxes. The total flux of particles is well explained by the measured electrostatic fluctuation driven flux. However, a satisfactory model to explain the origin of the fluctuations has not been identified. The processes responsible for determining the edge electron heat flux are less clear. In the confinement region experimental observations are restricted to measurements of density and potential fluctuations and their correlations. Three distinct features have been identified: (1) the ubiquitous broadband turbulence and (2) a quasi-coherent feature, both of which propagate in the electron diamagnetic drift direction, and (3) an ion feature which by definition propagates in the ion drift direction. The characteristics of the measured fluctuations are discussed and compared with the predictions of various models. Comparisons between measured particle, electron heat and ion heat fluxes, and those fluxes predicted to result from the measured fluctuations, are made.

Core turbulence and transport studies on the Texas Experimental Tokamak

Recent experiments on the Texas Experimental Tokamak (TEXT) [Plasma Phys. Controlled Fusion 27, 1335 (1985)] have focused on identifying the drives and transport significance of the turbulence in the interior of discharges in the neo‐Alcator confinement regime. Far‐infrared (FIR) scattering consistently observes density fluctuations indicative of electron drift waves, i.e., ωk∼ωe*+kθvE, where vE≡−Er/B (the electron diamagnetic frequency Doppler‐shifted by the E×B poloidal plasma rotation) and an amplitude that scales inversely with the density scale length Ln. Although consistent with scattering on the power‐weighted frequency ω, heavy‐ion beam probe (HIBP) data typically indicate kθρs<0.1 such that ω≫ωe*+kθvE and n/ne≪1/kθLn. Experiments with a modulated gas feed and/or electron‐cyclotron resonance heating (ECRH) seem to rule out ∇Te as the turbulent drive, although little evidence for ∇ne is apparent either. In fact, the interior fluctuations seen by the HIBP seem to depend more on edge condition...