In addition to the operational limits imposed by MHD stability on plasma current and pressure, an independent limit on plasma density is observed in confined toroidal plasmas. This review attempts to summarize recent work on the phenomenology and physics of the density limit. Perhaps the most surprising result is that all of the toroidal confinement devices considered operate in similar ranges of (suitably normalized) densities. The empirical scalings derived independently for tokamaks and reversed-field pinches are essentially identical, while stellarators appear to operate at somewhat higher densities with a different scaling. Dedicated density limit experiments have not been carried out for spheromaks and field-reversed configurations, however, `optimized' discharges in these devices are also well characterized by the same empirical law. In tokamaks, where the most extensive studies have been conducted, there is strong evidence linking the limit to physics near the plasma boundary: thus, it is possible to extend the operational range for line-averaged density by operating with peaked density profiles. Additional particles in the plasma core apparently have no effect on density limit physics. While there is no widely accepted, first principles model for the density limit, research in this area has focussed on mechanisms which lead to strong edge cooling. Theoretical work has concentrated on the consequences of increased impurity radiation which may dominate power balance at high densities and low temperatures. These theories are not entirely satisfactory as they require assumptions about edge transport and make predictions for power and impurity scaling that may not be consistent with experimental results. A separate thread of research looks for the cause in collisionality enhanced turbulent transport. While there is experimental and theoretical support for this approach, understanding of the underlying mechanisms is only at a rudimentary stage and no predictive capability is yet available.

https://iopscience.iop.org/article/10.1088/0741-3335/44/8/201/pdf

Density limits in toroidal 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

The 2014-2016 JET results are reviewed in the light of their significance for optimising the ITER research plan for the active and non-active operation. More than 60 h of plasma operation with ITER first wall materials successfully took place since its installation in 2011. New multi-machine scaling of the type I-ELM divertor energy flux density to ITER is supported by first principle modelling. ITER relevant disruption experiments and first principle modelling are reported with a set of three disruption mitigation valves mimicking the ITER setup. Insights of the L-H power threshold in Deuterium and Hydrogen are given, stressing the importance of the magnetic configurations and the recent measurements of fine-scale structures in the edge radial electric. Dimensionless scans of the core and pedestal confinement provide new information to elucidate the importance of the first wall material on the fusion performance. H-mode plasmas at ITER triangularity (H = 1 at β N ∼ 1.8 and n/n GW ∼ 0.6) have been sustained at 2 MA during 5 s. The ITER neutronics codes have been validated on high performance experiments. Prospects for the coming D-T campaign and 14 MeV neutron calibration strategy are reviewed.

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Overview of the JET results in support to ITER

The SPARC tokamak is a critical next step towards commercial fusion energy. SPARC is designed as a high-field () relevant to fusion power plants. SPARC's place in the path to commercial fusion energy, its parameters and the current status of SPARC design work are presented. This work also describes the basis for global performance projections and summarizes some of the physics analysis that is presented in greater detail in the companion articles of this collection.

/pdf/overview-of-the-sparc-tokamak-1uymrcesxa.pdf

Overview of the SPARC tokamak

The behaviour of tungsten in the core of hybrid scenario plasmas in JET with the ITER-like wall is analysed and modelled with a combination of neoclassical and gyrokinetic codes In these discharges, good confinement conditions can be maintained only for the first 2?3?s of the high power phase Later W accumulation is regularly observed, often accompanied by the onset of magneto-hydrodynamical activity, in particular neoclassical tearing modes (NTMs), both of which have detrimental effects on the global energy confinement The dynamics of the accumulation process is examined, taking into consideration the concurrent evolution of the background plasma profiles, and the possible onset of NTMs Two time slices of a representative discharge, before and during the accumulation process, are analysed with two independent methods, in order to reconstruct the W density distribution over the poloidal cross-section The same time slices are modelled, computing both neoclassical and turbulent transport components and consistently including the impact of centrifugal effects, which can be significant in these plasmas, and strongly enhance W neoclassical transport The modelling closely reproduces the observations and identifies inward neoclassical convection due to the density peaking of the bulk plasma in the central region as the main cause of the accumulation The change in W neoclassical convection is directly produced by the transient behaviour of the main plasma density profile, which is hollow in the central region in the initial part of the high power phase of the discharge, but which develops a significant density peaking very close to the magnetic axis in the later phase The analysis of a large set of discharges provides clear indications that this effect is generic in this scenario The unfavourable impact of the onset of NTMs on the W behaviour, observed in several discharges, is suggested to be a consequence of a detrimental combination of the effects of neoclassical transport and of the appearance of an island

https://iopscience.iop.org/article/10.1088/0029-5515/54/8/083028/pdf

Tungsten transport in JET H-mode plasmas in hybrid scenario, experimental observations and modelling

A zone of reduced anomalous diffusivity for impurities in the central region of the discharge has been reported from several Tokamaks. In this paper the authors point out that this condition is not an occasional occurrence, but a very general feature. Indeed all JET cases analyzed, where the experimental conditions allow adequate sensitivity and space resolution for the measurement of the impurities diffusion coefficient, show unambiguously that this quantity is close to neoclassical levels within r=0.4a. Furthermore, from the analysis of the electron density profile in sawtooth-free phases of JET discharges with moderate electron temperature, the authors deduce that the electron particle diffusivity Dp is also close to neoclassical in the same region. The values obtained for Dp in that region during the early pre-sawtooth phases are the same as in Ohmic post-pellet phases.

Comparison of impurity and electron particle transport in JET discharges

First results of gyrokinetic analysis of JET ELMy H mode plasmas are presented. ELMy H mode plasmas form the basis of conservative performance predictions for tokamak reactors of the size of ITER. Relatively high performance for long durations has been achieved and the scaling appears to be favourable. It will be necessary to sustain low Zeff and high density for high fusion yield. The article studies the degradation in confinement and the increase in the anomalous heat transport observed in two JET plasmas: one with an intense gas puff and the other with a spontaneous transition from type I to III ELMs at the heating power threshold. Linear gyrokinetic analysis gives the growth rate γlin of the fastest growing modes. The flow shearing rate γE×B and γlin are large near the top of the pedestal. Their ratio decreases approximately at the time when the confinement degrades and the transport increases. This suggests that tokamak reactors may require intense toroidal or poloidal torque input to maintain sufficiently high γE×B/γlin near the top of the pedestal for high confinement.

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N. C. Hawkes

Papers

Tungsten transport in JET H-mode plasmas in hybrid scenario, experimental observations and modelling

Comparison of impurity and electron particle transport in JET discharges

Local physics basis of confinement degradation in JET ELMy H mode plasmas and implications for tokamak reactors