AbstractThe Madison Symmetric Torus (MST) is the newest and largest reversed-field pinch (RFP) currently in operation. It incorporates a number of design features that set it apart from other pinches, including the use of the conducting shell as both a vacuum vessel and single-turn toroidal field coil. Specially insulated voltage gaps are exposed to the plasma. Magnetic field errors at these gaps as well as at the various diagnostic and pumping ports are minimized through a variety of techniques. The physics goals of MST include study of the effect of large plasma size on confinement and the detailed investigation of RFP turbulence, dynamo, and transport. Details of the design and initial operation of the device are presented.

Madison Symmetric Torus

After a general discussion of the experimental characteristics of the L-H transition and consideration of basic theoretical principles underlying models for it, this paper reviews the various theories of the L-H transition available in the literature, providing some background information on each theory and expressing the transition criteria in forms suitable for comparison with experiment. Some conclusions on the relevance of these models for explaining the experimental data on the transition are drawn.

https://iopscience.iop.org/article/10.1088/0741-3335/42/1/201/pdf

A review of theories of the L-H transition

Transport is the outstanding physics issue in the quest for fusion by magnetic confinement. In spite of the intrinsic difficulty, a great deal of progress has been made in the past 25 years. Experiments have gone from being dominated by high anomalous losses, of the order of Bohm diffusion losses, to operation with no anomalous transport. This success is due to a combination of improved experimental infrastructure and the high degree of knowledge on how to control plasma discharges, Both have made it possible to access enhanced confinement regimes and to unravel new effects in confinement physics. Although there is not yet a complete understanding of the dynamical mechanisms underlying the anomalous transport process, there is some understanding of important components such as the ion transport loss mechanism at the plasma core and of the main mechanism for turbulence suppression in the enhanced confinement regimes.

Progress in anomalous transport research in toroidal magnetic confinement devices

Experimental drift turbulence and zonal flow studies in magnetically confined plasma experiments are reviewed. The origins of drift waves, transition to drift turbulence and drift turbulence?zonal flow interactions in open field line and toroidal closed flux surface experiments are discussed and the free energy sources, dissipation mechanisms and nonlinear dynamics of drift turbulence in the core, edge and scrape-off layer plasma regions are examined. Evidence that turbulence across these regions is linked and that turbulence-driven zonal flows exist is presented, and evidence that these flows help regulate the turbulent scale lengths, amplitude and fluxes is summarized. Seemingly contradictory reports exist regarding the scale of turbulent transport events; gyro-Bohm behavior of turbulence correlation lengths as well as evidence for long-range transport phenomena both exist. Changes in turbulence during and after transport barrier formation are summarized and compared. The inferred turbulent particle and heat fluxes due to turbulent transport are usually consistent with global confinement, and edge plasma momentum transport appears to be linked to plasma flows at the last-closed flux surface and in the open field line region. However, inconsistencies between observed transport and turbulence have sometimes been reported and are pointed out here. Special attention is given to open issues, and suggestions for future experimental studies are given.

https://iopscience.iop.org/article/10.1088/0741-3335/51/11/113001/pdf

A review of experimental drift turbulence studies

Azimuthal flow is driven in the edge of the Large Plasma Device (LAPD) [W Gekelman, {\itshape et al}, Rev Sci Instr {\bfseries 62}, 2875 (1991)] through biasing a section of the vacuum vessel relative to the plasma source cathode As the applied bias exceeds a threshold, a transition in radial particle confinement is observed, evidenced by a dramatic steepening in the density profile, similar to the L- to H-mode transition in toroidal confinement devices The threshold behavior and dynamic behavior of radial transport is related to flow penetration and the degree of spatial overlap between the flow shear and density gradient profiles An investigation of the changes in turbulence and turbulent particle transport associated with the confinement transition is presented Two-dimensional cross-correlation measurements show that the spatial coherence of edge turbulence in LAPD changes significantly with biasing The azimuthal correlation in the turbulence increases dramatically, while the radial correlation length is little altered Turbulent amplitude is reduced at the transition, particularly in electric field fluctuations, but the dominant change observed is in the cross-phase between density and electric field fluctuations The changes in cross-phase lead to a suppression and then apparent reversal of turbulent particle flux as the threshold is exceeded

Modifications of turbulence and turbulent transport associated with a bias-induced confinement transition in LAPD

As a model example of the effect of shear flow on the cross phase between electrostatic potential and pressure fluctuations, a nonlinear theory of resistive pressure gradient driven turbulence (RPGDT) in a shear flow is presented. This work builds on numerical studies of RPGDT, which have shown that both flow shear and curvature can affect the cross phase as well as the fluctuation levels. In this work, we show that the effect of shear flow on transport can be expressed through the temporal response of pressure to potential. It is shown heuristically that even in the case where the fluctuation levels are not modified, the flow shear still acts to reduce the phase angle between potential and pressure fluctuations, thereby suppressing transport. The scaling of the cross phase with flow shear and flow curvature is presented.

http://iopscience.iop.org/article/10.1088/0741-3335/38/8/034/pdf

Transport reduction via shear flow modification of the cross phase

The total magnetic fluctuation‐induced electron thermal flux has been determined in the Madison Symmetric Torus (MST) reversed‐field pinch [Fusion Technol. 19, 131 (1991)] from the measured correlation of the heat flux along perturbed fields with the radial component of the perturbed field. In the edge region the total flux is convective and intrinsically ambipolar constrained, as evidenced by the magnitude of the thermal diffusivity, which is well approximated by the product of ion thermal velocity and the magnetic diffusivity. A self‐consistent theory is formulated and shown to reproduce the experimental results, provided nonlinear charge aggregation in streaming electrons is accounted for in the theory. For general toroidal configurations, it is shown that ambipolar constrained transport applies when remote magnetic fluctuations (i.e., global modes resonant at distant rational surfaces) dominate the flux. Near locations where the dominant modes are resonant, the transport is nonambipolar. This agrees with the radial variation of diffusivity in MST. Expectations for the tokamak are also discussed.

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Ambipolar magnetic fluctuation‐induced heat transport in toroidal devices

The role of rapid timescale Alfvenic and slow timescale fluid-straining interactions on spectral transfer in hydromagnetic turbulence is delineated, with electron density evolution incorporated as an integral part of the turbulent response. At issue is the spectral index of electron density fluctuations in the diffuse interstellar medium. The popular interpretation of this index as the rational number 5/3 is at odds with hydromagnetic turbulence in which the fluctuation energies are equipartitioned and fluctuations are on the order of mean values. From analytical and numerical analyses of the turbulent response and its role in spectrum balance relations, it is found that transfer of internal energy is mediated by the slow-scale, local (in wavenumber space) fluid-straining decorrelation over the range of observed scales. The transfer of magnetic energy is always mediated by the fast-scale, nonlocal Alfvenic decorrelation. Kinetic energy transfer is mediated by Alfvenic decorrelation over most of the spectrum, with a one to two decade range extending to larger scales from the inner scale in which transfer is mediated by the fluid-straining decorrelation. The result is a spectrum in which magnetic and kinetic energies have spectral indices of 3/2 over all but the smallest scales, and internal energy has an index of 7/4. This result, which is consistent with the dynamics of one-fluid MHD and a passively advected electron density, is in good agreement with the observed spectrum. At the smallest scales, electron compressibility effects, complicated cross-field energy transfer involving density, and the dominance of the fluid-straining decorrelation in kinetic energy transfer must be considered to determine spectral indices correctly.

A. S. Ware

Papers

Transport reduction via shear flow modification of the cross phase

Ambipolar magnetic fluctuation‐induced heat transport in toroidal devices

A Drift-Alfvén Model for Interstellar Turbulence