P. W. Terry

Influence of sheared poloidal rotation on edge turbulence

The impact of radially sheared poloidal flows on ambient edge turbulence in tokamaks is investigated analytically. In the regime where poloidal shearing exceeds turbulent radial scattering, a hybrid time scale weighted toward the former is found to govern the decorrelation process. The coupling between radial and poloidal decorrelation results in a suppression of the turbulence below its ambient value. The turbulence quench mechanism is found to be insensitive to the sign of either the radial electric field or its shear.

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...

Theory of dissipative density‐gradient‐driven turbulence in the tokamak edge

We appreciate the interest of Krommes in our recent paper and welcome the opportunity to discuss his comments and other related issues. In our opinion, most of the objections hea has raised follow from a misunderstanding of the physics treated by clump and hole theory. In particular, throughout his critique Krommes attempts to extrapolate results and intuition of homogeneous Navier-Stokes turbulence (HN-ST) to the more complicated case of dissipative drift-wave turbulence (DD-WT). Since these two cases are so dissimilar with regard to their fundamental constituents, drive, characteristic scales and interaction mechanisms, extrapolations from one case to the other are unwarranted and misleading. Moreover, the hypotheses and results of clump and hole theories have fared well in several tests using laboratory and simulation data which is relevant to the theoretical models analyzed. 7 refs.

Stochasticity and the random phase approximation for three electron drift waves

The interaction of three nonlinearly coupled drift waves is investigated for the occurrence of stochastization of the phases and the applicability of the random phase approximation. The drift wave nonlinearities include the E×B and polarization drift couplings for waves that are linearly unstable for appropriate values of the perpendicular wavenumber. The conservation properties and sample numerical solutions for the exact three wave interaction are given along with the conservation properties and solutions of the corresponding random phase approximation equations.

Drift wave turbulence in a low‐order k space

In the low‐order isotropic k space introduced by Kells and Orszag for the two‐dimensional Euler equation, the evolution of the fluctuations arising from the electron drift wave instability is studied. The two‐dimensional drift wave model contains the E×B and polarization drift nonlinearities in the hydrodynamic ions and linear, dissipative electrons. The strength of the electron dissipation is shown to determine the spectral width and the level of the fluctuations.

Validation in fusion research : Towards guidelines and best practices

Because experiment/model comparisons in magnetic confinement fusion have not yet satisfied the requirements for validation as understood broadly, approaches to validating mathematical models and numerical algorithms are recommended as good practices. Previously identified procedures, such as, verification, qualification, and analysis of errors from uncertainties and deficiencies, remain important. However, particular challenges intrinsic to fusion plasmas and physical measurement therein lead to identification of new or less familiar concepts that are also critical in validation. These include the primacy hierarchy, which tracks the integration of measurable quantities, and sensitivity analysis, which assesses how model output is apportioned to different sources of variation. The use of validation metrics for individual measurements is extended to multiple measurements, with provisions for the primacy hierarchy and sensitivity. This composite validation metric is essential for quantitatively evaluating comparisons with experiments. To mount successful and credible validation in magnetic fusion, a new culture of validation is envisaged.

Theory of shear flow effects on long-wavelength drift wave turbulence

A simple, paradigmatic model of long‐wavelength drift wave turbulence in the presence of a sheared poloidal flow is analyzed in detail. Linear theory predicts that velocity shear induces a strong stabilizing effect by shifting the eigenmode away from the k⋅B=0 resonant surface, thereby enhancing ion damping. However, multiple‐helicity numerical calculations indicate that velocity shear has little or no effect on saturated fluctuation levels. Analysis suggests that this result is related to the incidence of a spiky, radially intermittent profile of the turbulent fluctuation levels, induced by low‐q mode rational surfaces, and occurs when the turbulent diffusivity exceeds the product of diamagnetic frequency and gyroradius squared. An analytical theory that explains the observed suppression of velocity and magnetic shear damping is presented.

Self-organization in sheared drift-wave turbulence

Turbulent drift‐wave dynamics in a sheared magnetic field are studied using direct numerical simulations. Self‐consistent nonadiabatic electron and parallel ion dynamics are both retained in a 2‐D sheared‐slab model. Magnetic shear causes division of the system into two physically distinct regions with differing cascade dynamics. In a hydrodynamic layer centered upon the mode resonant surface, linear coupling between the density and potential is weak, and the density gradient acts to force spontaneous nonlinear alignment of density fluctuations with the turbulent flows. Further away, shear‐induced collisional dissipation constrains the density fluctuations to respond adiabatically, so that the density cannot vary on flow streamlines. The dynamics of the interregion spatial energy flow leads to strong phase coherence between modes at scales larger than the hydrodynamic layer width. Concurrently, the alignment between flows and density fluctuations at scales comparable to the layer width becomes even strong...

Effects of a radial electric field on tokamak edge turbulence

Turbulence associated with sheared radial electric fields such as those arising in tokamak edge plasmas is investigated analytically. Two driving mechanisms are considered: in the region of maximum vorticity (maximum electric field shear), the electric field is the dominant driving mechanism. Away from the maximum, turbulence is driven by the density gradient. In the latter case, previous work is extended to include the effects of the electric field on the spatial scales of density correlation in the frequency‐Doppler‐shifted, density‐gradient‐driven turbulence. For radial‐electric‐field‐driven turbulence, the effects of magnetic shear on linear instability and on fully developed turbulence are examined. In the case of weak magnetic shear, saturation occurs through an enstrophy cascade process which couples regions of driving and dissipation in wavenumber space. For stronger magnetic shear, such that the width of the dissipation region resulting from parallel resistivity is comparable to the radial electr...

Suppression of Transport Cross Phase by Strongly Sheared Flow

flow with a linearly varying mean shows thatthe cross phase factor in the transport flux is strongly reduced in the strong shear regime (shearingrate . eddy turnover rate), leading to significant transport suppression. The cross phase scales muchmore strongly with shear strength than do fluctuation amplitudes, allowing significant transport reductioneven if fluctuations increase, or decrease only slightly. Cross-phase suppression thus can be the dominanttransport-reduction mechanism in transport barriers.