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

The area of energetic particle (EP) physics in fusion research has been actively and extensively researched in recent decades. The progress achieved in advancing and understanding EP physics has been substantial since the last comprehensive review on this topic by Heidbrink and Sadler (1994 Nucl. Fusion 34 535). That review coincided with the start of deuterium?tritium (DT) experiments on the Tokamak Fusion Test Reactor (TFTR) and full scale fusion alphas physics studies.Fusion research in recent years has been influenced by EP physics in many ways including the limitations imposed by the ?sea? of Alfv?n eigenmodes (AEs), in particular by the toroidicity-induced AE (TAE) modes and reversed shear AEs (RSAEs). In the present paper we attempt a broad review of the progress that has been made in EP physics in tokamaks and spherical tori since the first DT experiments on TFTR and JET (Joint European Torus), including stellarator/helical devices. Introductory discussions on the basic ingredients of EP physics, i.e., particle orbits in STs, fundamental diagnostic techniques of EPs and instabilities, wave particle resonances and others, are given to help understanding of the advanced topics of EP physics. At the end we cover important and interesting physics issues related to the burning plasma experiments such as ITER (International Thermonuclear Experimental Reactor).

Energetic particle physics in fusion research in preparation for burning plasma experiments

Basic principles of heterodyne techniques are introduced and the various components of a heterodyne system are summarized. Special applications in ECE, interferometry and reflectometry are discussed after introducing the diagnostic principles. Realized systems as described in the literature are briefly outlined. Ordering principles are radiometer types in the case of ECE, mixing scheme and generation and stabilization of local oscillator and intermediate frequency signals in the case of interferometry and reflectometry. Special techniques and their impact on the performance of the diagnostic instruments are discussed.

https://iopscience.iop.org/article/10.1088/0741-3335/39/11/001/pdf

Heterodyne methods in millimetre wave plasma diagnostics with applications to ECE, interferometry and reflectometry

Wendelstein 7-AS was the first modular stellarator device to test some basic elements of stellarator optimization: a reduced Shafranov shift and improved stability properties resulted in β-values up to 3.4% (at 0.9 T). This operational limit was determined by power balance and impurity radiation without noticeable degradation of stability or a violent collapse. The partial reduction of neoclassical transport could be verified in agreement with calculations indicating the feasibility of the concept of drift optimization. A full neoclassical optimization, in particular a minimization of the bootstrap current was beyond the scope of this project. A variety of non-ohmic heating and current drive scenarios by ICRH, NBI and in particular, ECRH were tested and compared successfully with their theoretical predictions. Besides, new heating schemes of overdense plasmas were developed such as RF mode conversion heating—Ordinary mode, Extraordinary mode, Bernstein-wave (OXB) heating—or 2nd harmonic O-mode (O2) heating. The energy confinement was about a factor of 2 above ISS95 without degradation near operational boundaries. A number of improved confinement regimes such as core electron-root confinement with central Te ≤ 7 keV and regimes with strongly sheared radial electric field at the plasma edge resulting in Ti ≤ 1.7 keV were obtained. As the first non-tokamak device, W7-AS achieved the H-mode and moreover developed a high density H-mode regime (HDH) with strongly reduced impurity confinement that allowed quasi-steady-state operation (τ ≈ 65 · τE) at densities (at 2.5 T). The first island divertor was tested successfully and operated with stable partial detachment in agreement with numerical simulations. With these results W7-AS laid the physics background for operation of an optimized low-shear steady-state stellarator.

Major results from the stellarator Wendelstein 7-AS (Review Article)

The use of high resolution x-ray crystal spectrometers to diagnose fusion plasmas has been limited by the poor spatial localization associated with chord integrated measurements. Taking advantage of a new x-ray imaging spectrometer concept [M. Bitter et al., Rev. Sci. Instrum. 75, 3660 (2004)], and improvements in x-ray detector technology [Ch. Broennimann et al., J. Synchrotron Radiat. 13, 120 (2006)], a spatially resolving high resolution x-ray spectrometer has been built and installed on the Alcator C-Mod tokamak. This instrument utilizes a spherically bent quartz crystal and a set of two dimensional x-ray detectors arranged in the Johann configuration [H. H. Johann, Z. Phys. 69, 185 (1931)] to image the entire plasma cross section with a spatial resolution of about 1 cm. The spectrometer was designed to measure line emission from H-like and He-like argon in the wavelength range 3.7 and 4.0 A with a resolving power of approximately 10,000 at frame rates up to 200 Hz. Using spectral tomographic techniques [I. Condrea, Phys. Plasmas 11, 2427 (2004)] the line integrated spectra can be inverted to infer profiles of impurity emissivity, velocity, and temperature. From these quantities it is then possible to calculate impurity density and electron temperature profiles. An overview of the instrument, analysis techniques, and example profiles are presented.

Spatially resolved high resolution x-ray spectroscopy for magnetically confined fusion plasmas (invited)

In order to support the operation of ITER and the planned experimental programme an extensive set of plasma and first wall measurements will be required. The number and type of required measurements will be similar to those made on the present-day large tokamaks while the specification of the measurements—time and spatial resolutions, etc—will in some cases be more stringent. Many of the measurements will be used in the real time control of the plasma driving a requirement for very high reliability in the systems (diagnostics) that provide the measurements. The implementation of diagnostic systems on ITER is a substantial challenge. Because of the harsh environment (high levels of neutron and gamma fluxes, neutron heating, particle bombardment) diagnostic system selection and design has to cope with a range of phenomena not previously encountered in diagnostic design. Extensive design and R&D is needed to prepare the systems. In some cases the environmental difficulties are so severe that new diagnostic techniques are required. a Author to whom any correspondence should be addressed.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S07/pdf

Chapter 7: Diagnostics

An upper bound for the local electron heat coefficient ?(r) in electron cyclotron heated (ECH) discharges is determined experimentally. The method applied uses power modulation of the ECH and measures the time delay of the electron temperature response as a function of radius by means of a multi-channel radiometer for second-harmonic electron cyclotron emission (ECE). The evaluation is restricted to plasma radii between 3 and 6.5 cm, where the pre-conditions of the method are best verified experimentally. The theoretical transport model considers only processes related to the electron temperature gradient and neglects the dependence of ? on Te.

https://iopscience.iop.org/article/10.1088/0029-5515/26/5/014/pdf

Evaluation of the local heat conductivity coefficient by power-modulated electron cyclotron heating in the Wendelstein VII-A Stellarator

Enhanced density fluctuations associated with the rational q = 2 (l = 0.5) surface have been observed by microwave reflectometry in currentless discharges heated by neutral beam injection, with pellet injection at an edge value of the rotational transform l of 0.52. A radial scan of the MHD activity located the coherent density fluctuations at r/a = 0.7. The frequency and amplitude of these fluctuations have been estimated. The correlation between the level of the local density fluctuation and the l value during l modulation at 300 Hz leads to the conclusion that the broadband density fluctuation is enhanced at the points where the rational l values are crossed. A phase jump in the turbulence modulation occurs for r/a = 0.7, indicating the location of the resonant l = 0.5 surface. This effect can become the basis of a new method to analyse the evolution of the l profile inside the plasma, with interesting applications to current control experiments, especially in low shear configurations.

H. J. Hartfuss

Papers

Chapter 7: Diagnostics

Evaluation of the local heat conductivity coefficient by power-modulated electron cyclotron heating in the Wendelstein VII-A Stellarator

Observation of density fluctuations associated with the resonant q = 2 surface in the Wendelstein VII-AS stellarator