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. The diagnostics used to measure these quantities, together with some of the statistical techniques employed to analyze the data, are outlined. In the plasma edge detailed measurements of the quantities required to directly determine the fluctuation‐driven fluxes are available. The total and fluctuation‐driven fluxes are compared: the result emphasizes the importance of edge turbulence. No model adequately describes all the measured properties. In the confinement region experimental observations are presently restricted to measurements of density and potential fluctuations and their correlations. Various distinct turbulence features that have been observed are described, and their characteristics compared with the predictions of various models. Correlations observed between these fluctuations and plasma transport properties are summarized. A separate section on magnetic fluctuations shows there is very little information available inside the plasma, generally prohibiting quantified comparisons between fluctuation levels and transport. Both coherent and turbulent magnetic fluctuations are addressed, and the differences between low and high plasma pressure (low and high beta) are noted. The contributions of alternate confinement devices, such as stellarators and reversed field pinches, to understanding tokamak anomalous transport are discussed. Finally, future directions are proposed.

Fluctuations and anomalous transport in tokamaks

The three-dimensional transition of the flow behind a bluff body is studied, with an emphasis placed on the evolution of large-scale structures in the wake. It has previously been found that there are two fundamental modes of three-dimensional vortex shedding in the wake of a circular cylinder (each mode being dependent on the range of Reynolds number), with a spanwise lengthscale of the same order as the primary streamwise wavelength of the vortex street. However. it is shown in the present study that the wake transition also involves the appearance of large-scale spot-like ‘vortex dislocations’, that grow downstream to a size of the order of 10–20 primary wavelengths. Vortex dislocations are generated between spanwise vortex-shedding cells of different frequency. The presence of these dislocations explains the large intermittent velocity irregularities that were originally found by Roshko (1954) and later by Bloor (1964) to characterize transition. The presence of these vortex dislocations in wake transition is largely responsible for the break-up to turbulence of the wake as it travels downstream.In order to study their evolution in detail, dislocations have been (passively) forced to occur at a local spanwise position with the use of a small ring disturbance. It is found that ‘two-sided’ dislocations are stable in a symmetric in-phase configuration, and that they induce quasi-periodic velocity spectra and (beat) dislocation-frequency oscillations in the near wake. Intrinsic to these dislocations is a mechanism by which they spread rapidly in the spanwise direction, involving helical twisting of the vortices and axial core flows. This is felt to be a fundamental mechanism by which vortices develop large-scale distortions in natural transition. As the wake travels downstream, the energy at the low dislocation frequency decays slowly (in contrast to the rapid decay of other frequencies), leaving the downstream wake dominated by the large dislocation structures. Distinct similarities are found between the periodic forced dislocations and the intermittent dislocations that occur in natural transition. Further similarities of dislocations in different types of flow suggest that vortex or phase dislocations could conceivably be a generic feature of transition in all shear flows.

The natural and forced formation of spot-like vortex dislocations in the transition of a wake

Experimental and theoretical studies of runaway electrons in toroidal devices are reviewed here, with particular reference to tokamaks. The complex phenomenology of runaway effects, which have been the subject of research for the past twenty years, is organized within the framework of a number of physical models. The mechanisms and rates for runaway production are discussed first, followed by sections on runaway-driven kinetic relaxation processes and runaway orbit confinement. Next, the equilibrium and stability of runaway-dominated discharges are reviewed. Models for runaway production at early times in the discharge and the scaling of runaway phenomena to larger devices are also discussed. Finally, detection techniques and possible applications of runaways are mentioned.

https://iopscience.iop.org/article/10.1088/0029-5515/19/6/008/pdf

Runaway electrons in toroidal discharges

This is a general review of anomalous resistivity with emphasis on its applicability in space and more specifically on ionospheric plasmas. It is addressed to the general ionospheric community rather than the specialist. Therefore a substantial amount of rigor has been sacrificed in favor of simplified physical pictures. However, several prescriptions are presented, on the basis of which one can compute the anomalous resistivity resulting from each specific mechanism. Following a conceptual discussion of resistivity a general formalism is presented for its computation on the basis of the spectrum of electric field fluctuations. On the basis of this it is shown that stable nonthermal plasmas can at most enhance resistivity by a few percent. The same is true for collisionally driven instabilities. From the current-driven instabilities, only the ion acoustic instability can produce a steady state anomalous resistivity. The rest result in transient resistivity and the appearance of hot electron or ion spots. A more satisfying picture emerges when the low-frequency turbulence that produces resistivity is excited parametrically by a high-frequency instability. The case where such a driver arises from the interaction of precipitating electrons is discussed in detail. Finally, the relevance of the various resistivity mechanisms and their importance in ionospheric electron acceleration is discussed. Although a large number of physical notions are well understood, the efforts toward their incorporation into a gross modeling picture remain embarrassingly small.

/pdf/a-review-of-anomalous-resistivity-for-the-ionosphere-131n90aaqk.pdf

A review of anomalous resistivity for the ionosphere

Fundamental Statistical Descriptions of Plasma Turbulence in Magnetic Fields

Renormalized turbulence theory for the ion acoustic problem

The structure of drift modes in tokamaks is investigated taking into account modes that are weakly ballooning on the magnetic surfaces. The toroidal mode theory of Conner, Hastie, and Taylor is used to find the surface eigenfunctions and shear damping as a function of the system parameters.

Weakly localized two‐dimensional drift modes

Infinite-order perturbation theories of Vlasov turbulence are developed to obtain a renormalized formulation of the mode coupling and quasilinear equations for current-driven ion-acoustic turbulence. The renormalized theory eliminates divergence problems from nonlinear electron interactions and predicts an ion acceleration mechanism producing substantial ion tails at t..omega../subp//subi/ approx. 50 from initially cold-ion distributions. Time-dependent numerical solutions of the turbulence equations are presented, and comparisons are drawn from experiments and computer simulation. (AIP)

Ion-acoustic heating from renormalized turbulence theory

Calculations for the stochastic diffusion of electrons in Tokamaks due to a spectrum of electro-magnetic drift fluctuations are presented. The parametric dependence of the diffusion coefficient on the amplitude and phase velocity of the spectrum, and the bounce frequency for the electrons is studied. The wavenumber spectrum is taken to be a low order (5*5) randomly-phased, isotropic, monotonic spectrum extending from kperpendicular to min approximately= omega ci/cs to kperpendicular to max approximately=3 omega pe/c with different power laws of decrease phi k approximately= phi 1/km, 1<or=m<or=3. A nonlinear Ohm's law is derived for the self-consistent relation between the electrostatic and parallel vector potentials. The parallel structure of the fluctuations is taken to be such that k/sub ///nl nu e< omega k due to the nonlinear perpendicular motion of the electrons described in the nonlinear Ohm's law. The diffusion coefficient scales approximately as the neo-Alcator and Merezhkin-Mukhovatov empirical formulas for plasma densities below a critical density.

https://iopscience.iop.org/article/10.1088/0741-3335/29/7/008/pdf

Electron diffusion in tokamaks due to electromagnetic fluctuations

The influence of a spectrum of drift wave fluctuations on the trapped ion mode is investigated and shown to inhibit the onset of these modes. The stochastic damping of the trapped ion mode becomes comparable to the linear growth rate when the drift wave spectrum is described by previous theoretical models.

Duk In Choi

Papers

Renormalized turbulence theory for the ion acoustic problem

Weakly localized two‐dimensional drift modes

Ion-acoustic heating from renormalized turbulence theory

Electron diffusion in tokamaks due to electromagnetic fluctuations

Inhibition of the trapped ion mode by drift wave fluctuations