Ideal magnetohydrodynamic theory and its application to magnetic fusion systems are reviewed. The review begins with a description and derivation of the model as well as a discussion of the region of validity. Next, the general properties are derived. These are valid for arbitrary geometry and demonstrate the inherently sound physical foundation of the model. The equilibrium behavior of the currently most promising toroidal magnetic fusion concepts are then discussed in detail. Finally, the stability of such equilibria is investigated. Included are discussions of the general stability properties of arbitrary magnetic geometries and of detailed applications to those concepts of current fusion interest.

Ideal magnetohydrodynamic theory of magnetic fusion systems

A review of experiments and theory of electron cyclotron resonance heating (ECRH) and current drive (ECCD) is presented. An outline of the basic linear theory of wave propagation and absorption in the electron cyclotron range of frequencies and their harmonics is given and compared with experimental results from many devices. The experimental data base on quasilinear and nonlinear physics as well as on parametric wave decay is reviewed and compared to theory. Experiments and theory on doppler shifted absorption either by bulk or tail electrons (which can be created by other means) are discussed. ECRH provides means for controlled plasma breakdown and current ramp up in tokamaks and plays a key role in net current-free stellarator research. Start-up was investigated in many tokamaks and stellarators and the results are discussed in the light of the present day theoretical understanding. The role of ECRH to improve the understanding of both particle and energy confinement is described and special heating correlated features, such as 'density pump out' during ECRH are discussed. The application of modulated ECRH for perturbative heat wave studies and the comparison with both sawtooth heat pulse propagation and the steady state power balance analysis is presented. Electron cyclotron current drive is a possible method for current profile and MHD control in tokamaks and provides means for bootstrap current compensation in stellarators. The basic theory of electron cyclotron current drive is presented and compared to experiments in both tokamaks and stellarators. Experiments on sawtooth stabilization and MHD control by ECRH or ECCD are discussed and compared to theory. An increasing number of fusion devices is equipped with ECRH for bulk heating and sophisticated plasma physics investigations. A remarkable extension of the accessible plasma parameter range became possible by the recent development of sources with high power (1 MW) and frequency (110-160 GHz). Particular emphasis is given to new experiments and the refinement of theory incorporating plasma phenomena and the mutual impact on the wave physics.

http://iopscience.iop.org/article/10.1088/0741-3335/36/12/001/pdf

Electron cyclotron resonance heating and current drive in toroidal fusion plasmas

Studies of transport in fusion plasmas using perturbations of an equilibrium state are reviewed. Essential differences between steady-state and perturbative transport studies are pointed out. Important transport issues that can be addressed with perturbative experiments are identified as: (i) Are the transport relations linear (or nearly so)? (ii) What are the dominant dependences on plasma parameters; can they be understood from theory? (iii) Are there significant off-diagonal terms in the transport matrix? If so, how important are these for global confinement? (iv) Do the data obtained with perturbative experiments indicate that tokamak performance can be optimized along lines different from those presently explored? The theoretical framework for perturbative transport experiments is given. It is shown that perturbative experiments yield transport coefficients that are essentially different from the steady-state transport coefficients. In particular, when transport can be described by a transport matrix with off-diagonal elements, a perturbative experiment yields (one or more of) the eigenvalues of the matrix. In contrast, the coefficients obtained by steady-state analysis are linear combinations of the matrix coefficients, with the actual values of the various gradients as multipliers. Hence, the outcome of a steady-state transport evaluation depends on the actual values of the gradients, whereas a perturbative experiment measures the underlying transport matrix. Experimental perturbation techniques and techniques for data analysis are reviewed. Perturbations include the sawtooth instability, oscillatory gas feed, modulated power input, pellet injection etc. Data analysis techniques range from the time-to-peak analysis employed in sawtooth pulse propagation through Fourier or Laplace transforms, to direct numerical modelling. A review of the most important sources of systematic error is given.

https://iopscience.iop.org/article/10.1088/0741-3335/37/8/001/pdf

Perturbative transport studies in fusion plasmas

In this paper we summarize the present status of experimental tokamak confinement studies. Under quiescent conditions, ion heat and impurity transport can be close to the neoclassical level. Generally, however, radial transport is enhanced by instabilities. There is evidence that anomalous ion heat and momentum transport may be caused by turbulence driven by the ion temperature gradient. The same level of understanding is not reached in electron heat and particle transport. Electron heat transport is characterized by a highly nonlinear relation between heat flux and temperature gradient. Particle transport is strongly governed by off-diagonal contributions. Where possible, the tokamak results are compared with those from stellarators, in particular with those from W7-AS. Such a comparison is meaningful because stellarators and tokamaks share many transport aspects. In both cases transport is generally anomalous, degrades with heating power and increases toward the edge. Bifurcations such as the tokamak H-mode transition are also observed in the W7-AS stellarator. Transport in stellarators, although anomalous, seems to be less confused by additional complexities such as large off-diagonal contributions, profile resilience, disparities between steady-state and perturbatively determined transport coefficients and an isotopic mass dependence in energy and particle transport. Differences in magnetic field and minor radius scaling seem to be introduced by operational restrictions: rotational transform iota is constant in stellarator field or size scans whereas qa generally varies with current, field, or size in tokamaks.

https://iopscience.iop.org/article/10.1088/0741-3335/35/10/002/pdf

Transport in toroidal devices-the experimentalist's view

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

Electron temperature perturbations produced by internal disruptions in the center of the Oak Ridge Tokamak (ORMAK) are followed with a multichord soft-x-ray detector array. The space-time evolution is found to be diffusive in character, but the conduction coefficient determined from a heat-pulse-propagation model is larger by a factor of 2.5-15 than that implied by the measured gross energy-containment time.

/pdf/experimental-measurement-of-electron-heat-diffusivity-in-a-1nq7vpdg9a.pdf

G. L. Jahns

Papers

Experimental Measurement of Electron Heat Diffusivity in a Tokamak