R. V. Bravenec

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.

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...

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.

Large-scale behavior of the tokamak density fluctuations

An analysis of tokamak density fluctuations data permits the determination of two characteristic exponents. The exponents correspond to the powers of a power-law dependence of the distributions of the long-lasting monotonic change (“flight”) of the density and the time length of these changes. Speculation based on these results leads to construction of the fractional kinetic equation for the distribution function of the flights. The asymptotic transport properties of the particle density distribution function are directly connected with the exponents obtained from the density fluctuations data.

COMPARISON OF THE DENSITY FLUCTUATION SPECTRUM AND AMPLITUDE IN TEXT WITH EXPECTATIONS FOR ELECTRON-DRIFT WAVES

Modifications to the spectrum and magnitude of turbulent density fluctuations in the Texas Experimental Tokamak (TEXT) [Plasma Phys. Controlled Fusion 27, 1335 (1985)], measured by far‐infrared scattering, are related to changes in plasma profiles (e.g., density and potential) induced by naturally occurring magnetic islands (i.e., m=2) of varying amplitude. The statistical dispersion relation of the microturbulence that propagates in the electron diamagnetic drift direction is observed to be consistent with expectations for electron drift‐wave turbulence when a spectral shift due to E×B plasma rotation is included. Observed spectral widths are several times larger than the linear mode frequency. The fluctuation amplitude is found to scale inversely with the electron density scale length.

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...

System for simulating fluctuation diagnostics for application to turbulence computations

Present-day nonlinear microstability codes are able to compute the saturated fluctuations of a turbulent fluid versus space and time, whether the fluid be liquid, gas, or plasma. They are therefore able to determine turbulence-induced fluid (or particle) and energy fluxes. These codes, however, must be tested against experimental data not only with respect to transport but also characteristics of the fluctuations. The latter is challenging because of limitations in the diagnostics (e.g., finite spatial resolution) and the fact that the diagnostics typically do not measure exactly the quantities that the codes compute. In this work, we present a system based on IDL® analysis and visualization software in which user-supplied “diagnostic filters” are applied to the code outputs to generate simulated diagnostic signals. The same analysis techniques as applied to the measurements, e.g., digital time-series analysis, may then be applied to the synthesized signals. Their statistical properties, such as rms fluct...

Effects of limited spatial resolution on fluctuation measurements (invited)

The finite sample volumes of fluctuation diagnostics distort the measurements not only by averaging the gross fluctuation parameters over the sample volumes, but more importantly (except for collective scattering), by attenuating the shorter wavelength components. In this work, the response of various sample volume sizes and orientations to a model fluctuation power spectrum S(k,ω) are examined. The model spectrum is fashioned after observations by far‐infrared scattering on TEXT. The sample‐volume extent in the direction of propagation of the turbulence is shown to be the most critical—not only does it reduce the measured fluctuation amplitude and increase the correlation length (as does an extent perpendicular to the propagation direction), but it also reduces the measured mean frequency and increases the apparent average phase velocity of the fluctuations. The differing sizes, shapes, and orientations of the sample volumes among fluctuation diagnostics, as well as deliberate variations within a single ...