The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S02/pdf

Chapter 2: Plasma confinement and transport

Electron transport in tokamaks has many different features which are briefly reviewed. The paper is focused on electron heat transport in conventional tokamak plasmas. An inter-machine comparison indicates that the non-dimensional gradient length of the electron temperature profiles R/L-Te, is almost independent of the devices and varies little with plasma parameters. This strongly suggests that electron heat transport is governed by turbulence with a threshold in R/L-Te.. This is confirmed by modulation experiments using electron cyclotron heating. Simulations with empirical and physics-based transport models confirm this assumption.

/pdf/experimental-studies-of-electron-transport-2bt4vyarbm.pdf

Experimental studies of electron transport

Electron transport in tokamaks has many different features which are briefly reviewed. The paper is focused on electron heat transport in conventional tokamak plasmas. An inter-machine comparison indicates that the non-dimensional gradient length of the electron temperature profiles R/L Te is almost independent of the devices and varies little with plasma parameters. This strongly suggests that electron heat transport is governed by turbulence with a threshold in R/L Te . This is confirmed by modulation experiments using electron cyclotron heating. Simulations with empirical and physics-based transport models confirm this assumption.

This paper deals with the formulation of microinstability-based thermal transport coefficients (chi/sub j/) for the purpose of modelling anomalous energy confinement properties in tokamak plasmas. Attention is primarily focused on ohmically heated discharges and the associated anomalous electron thermal transport. An appropriate expression for chi/sub e/ is developed which is consistent with reasonable global constraints on the current and electron temperature profiles as well as with the key properties of the kinetic instabilities most likely to be present. Comparisons of confinement scaling trends predicted by this model with the empirical ohmic data base indicate quite favorable agreement. The subject of anomalous ion thermal transport and its implications for high density ohmic discharges and for auxiliary-heated plasmas is also addressed.

/pdf/microinstability-based-model-for-anomalous-thermal-1e4xotk523.pdf

Microinstability-based model for anomalous thermal confinement in tokamaks

Experimental results on transport in stellarators and tokamaks are reviewed in a comparative sense. The objective is to learn about the importance of plasma current and magnetic shear for anomalous transport in high-temperature plasmas. On the basis of scaling expressions, the absolute values and parameter dependences of the confinement time are similar if the plasma current is expressed in terms of magnetic field parameters. The degradation of confinement with heating power is of the same order in both devices and it is difficult to explain it in terms of a diffusivity which depends on temperature or temperature gradient. The density dependence of confinement observed in stellarators has similar features as in ohmically heated tokamak discharges. A linear and a saturated regime can be distinguished. The critical density, at which saturation sets in, has a similar value and it seems to decrease with increasing machine size. Power degradation, transient transport, profile consistency and non-local transport are treated as related problems, which are connected to the question of the temperature dependence of the thermal diffusivity. Results from the various experiments cannot yet be described with a consistent physical picture. However, the importance of non-local effects is established in stellarators and tokamaks, although observed in different types of perturbation experiments. In stellarators and tokamaks, fluctuation measurements in the scrape-off layer are consistent with drift-wave-like turbulence being responsible for anomalous transport. In the core, density fluctuation amplitudes increase together with the diffusivity when the density is increased but the two parameters show opposite trends with increasing heating power. It turns out that transport in the two classes of devices is more alike than it has previously appeared. This indicates that the strong toroidal plasma current, major rational values of the rotational transform inside the plasma or strong magnetic shear are not the central elements of a theoretical model for anomalous transport in fusion plasmas.

https://iopscience.iop.org/article/10.1088/0741-3335/40/1/002/pdf

A comparative study of transport in stellarators and tokamaks

Electron heat transport on TFTR and other tokamaks is several orders of magnitude larger than neoclassical calculations predict. Despite considerable effort, there is still no clear theoretical understanding of this anomalous transport. The electron temperature profile, Te(r), has shown a marked consistency on many machines for a wide range of plasma parameters and heating profiles. This could be an important clue as to the process responsible for this enhanced thermal transport. In the first section of the paper the result is presented that TFTR electron temperature profile shapes are even more constrained than previous models of profile consistency suggested. The profile shapes, Te(r)/Te(a/2), are found to be invariant (for r > 0.4 a) for a wide range of parameters, including q(a). In the second section, an experiment is discussed which uses a fast current ramp to transiently decouple the current density profile, J(r), and the Te(r) profiles. From this experiment, it has been determined that the J(r) profile can be strongly modified with no measurable effect on the electron temperature profile shape. Thus, while the electron temperature profile is apparently constrained, the current profile is not.

Profile consistency on TFTR

Blackbody electron cyclotron emission was used to ascertain and study the evolution and behaviour of the electron temperature profile in ohmically heated plasmas in the Tokamak Fusion Test Reactor (TFTR). The emission was measured with absolutely calibrated millimetre wavelength radiometers. The electron temperature profile normalized to the central temperature and the minor radius was observed to broaden substantially with decreasing limiter safety factor qa and to be insensitive to the plasma minor radius. Sawtooth activity was seen in the core of most TFTR discharges and appeared to be associated with a flattening of the electron temperature profile within the plasma core where q 1. Two types of sawtooth behaviour were identified in large TFTR plasmas (minor radius a 0.8 m): a 'normal' sawtooth with typically 35–40 ms period and a 'compound' sawtooth with 70–80 ms period. The compound sawtooth was characterized by what appeared to be a partial reconnection, which occurs away from the plasma core, in addition to a full reconnection. A multiple linear regression analysis of the central electron temperature Te(0), with toroidal field BT, major radius R, minor radius a, plasma current Ip and effective ion charge Zeff, results in a scaling of the form , for which the major radial dependence was obtained by comparison with earlier PLT data.

/pdf/evolution-of-the-electron-temperature-profile-of-ohmically-2fjaldjywo.pdf

Evolution of the electron temperature profile of ohmically heated plasmas in TFTR

The electron temperature profiles on the Tokamak Fusion Test Reactor (TFTR) are determined by several diagnostics, including multi-point Thomson scattering and electron cyclotron emission measured with heterodyne radiometers and a Michelson interferometer The electron temperature profiles are characterized by very high central temperatures (>8 keV) and large Shafranov shifts (>35 cm) The large Shafranov shifts suggest the necessity of mapping to magnetic flux surfaces when investigating the profile behaviour During 1986 ,TFTR was operated with up to 20 MW of deuterium neutral beam injection (NBI) and a deuterium pellet injector The electron temperature profile measurements were made on plasmas with 27 < BT < 51 T, βpdia up to 22, 1 × 1019<e<15 × 1020 m−3 and 25 < qcyl < 10 In many of the NBI plasmas the core was broadened by either sawteeth or convection In multiple pellet fuelled discharges, where pellets penetrate to the plasma core, the radiation profile became significantly peaked on axis, resulting in hollow temperature profiles In the light of work on 'profile consistency', various methods of mapping Te(R) to flux surfaces are investigated as well as the extent to which the electron temperature profile away from the core remains invariant to these perturbations

https://iopscience.iop.org/article/10.1088/0029-5515/29/1/001/pdf

Electron temperature profile behaviour in TFTR during neutral beam injection and multiple pellet fuelling

Absolute calibration of electron cyclotron emission (ECE) diagnostics allows for the determination of temporal electron temperature measurements independent of other diagnostics. Calibration of MM and SMMW diagnostics with a blackbody of known temperature using synchronous detection and co-adding techniques is described.

F. J. Stauffer

Papers

Profile consistency on TFTR

Evolution of the electron temperature profile of ohmically heated plasmas in TFTR

Electron temperature profile behaviour in TFTR during neutral beam injection and multiple pellet fuelling

Calibration techniques for broadband MM & SMMW diagnostic instruments