The H-mode is a confinement mode of toroidal plasmas, which may make the goals of fusion possible—the development of a clean energy source at competitive electricity costs. The most challenging aspect of the H-mode physics is the sudden disappearance of the edge turbulence whereas its driving forces—the gradients—increase. As the physics behind the H-mode is subtle many features are not yet clarified. There is, however, substantial experimental and theoretical evidence that turbulent flows, which normally limit the confinement, are diminished by sheared poloidal flow residing at the plasma edge. There are many conceivable mechanisms giving rise to sheared flow. The most intriguing of these is that fluctuations themselves induce the flow, which acts back to its generating origin and annihilates the turbulence. This review concentrates mostly on the transition physics, describes one line of understanding the H-mode in more detail, recalls some of the older observations and summarizes the achievements in the H-mode for both tokamaks and stellarators. (Some figures in this article are in colour only in the electronic version)

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A quarter-century of H-mode studies

The present status of zonal flow experiments is reviewed with the historical process to attain the concept of zonal flows, which provides a new framework for understanding turbulence and transport in toroidal plasmas. The existence of zonal flows is experimentally confirmed to present a new paradigm of plasma turbulence. The paper presents contemporary experiments on zonal flows as major topics with a brief presentation of the zonal flow theories, the diagnostics and data processing techniques for turbulence and zonal flows and the peripheral issues of zonal flow physics. The accumulated experimental results introduced in this review include identification of zonal flows (both stationary zonal flows and geodesic acoustic modes), nonlinear interactions between zonal flows and turbulence, quantification of turbulent Reynolds stress, flow dynamics, energy transfer dynamics between turbulent wave components and the effects of zonal flows on plasma transport. These results have given rise to a new paradigm, namely, that the plasma turbulence is a system of zonal flows and drift waves, with an emphasis on the interaction between the disparate scale structures, e.g. zonal flows (mesoscale) and turbulence (micro-scale).

https://iopscience.iop.org/article/10.1088/0029-5515/49/1/013001/pdf

A review of zonal flow experiments

The theory of plasma confinement by non-axisymmetric magnetic fields is reviewed. Such fields are used to confine fusion plasmas in stellarators, where in contrast to tokamaks and reversed-field pinches the magnetic field generally does not possess any continuous symmetry. The discussion is focussed on magnetohydrodynamic equilibrium conditions, collisionless particle orbits, and the kinetic theory of equilbrium and transport. Each of these topics is fundamentally affected by the absence of symmetry in the magnetic field: the field lines need not trace out nested flux surfaces, the particle orbits may not be confined, and the cross-field transport can be very large. Nevertheless, by tailoring the magnetic field appropriately, well-behaved equilibria with good confinement can be constructed, potentially offering an attractive route to magnetic fusion. In this article, the mathematical apparatus to describe stellarator plasmas is developed from first principles and basic elements underlying confinement optimization are introduced.

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Theory of plasma confinement in non-axisymmetric magnetic fields

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)

Numerical results for the three mono-energetic transport coefficients required for a complete neoclassical description of stellarator plasmas have been benchmarked within an international collaboration. These transport coefficients are flux-surface-averaged moments of solutions to the linearized drift kinetic equation which have been determined using field-line-integration techniques, Monte Carlo simulations, a variational method employing Fourier–Legendre test functions and a finite-difference scheme. The benchmarking has been successfully carried out for past, present and future devices which represent different optimization strategies within the extensive configuration space available to stellarators. A qualitative comparison of the results with theoretical expectations for simple model fields is provided. The behaviour of the results for the mono-energetic radial and parallel transport coefficients can be largely understood from such theoretical considerations but the mono-energetic bootstrap current coefficient exhibits characteristics which have not been predicted.

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Benchmarking of the mono-energetic transport coefficients - Results from the International Collaboration on Neoclassical Transport in Stellarators (ICNTS)

In the last campaign, the TJ-II heliac has been operated under lithium-coated walls, representing the first stellarator ever working under these boundary conditions. Enhanced density control and discharge reproducibility, leading to the drastic enlargement of the operational window, have been obtained. A strong decrease in recycling together with changes in the shot by shot fuelling characteristics and in the wall particle inventory have been recorded. These changes, associated with the new wall scenario, had led to a long-lasting good density control. The new conditions were also mirrored in the plasma profiles under NBI heating scenarios with increased peaking of the electron density profiles. Fuelling rates corresponding just to the nominal beam current were obtained for the first time, and transitions from bell to dome-type plasma profiles, with different collapsing limits, were observed and tentatively ascribed to changes in the local edge power balance. ELM-type activity was observed in concomitance to reduced fluctuation levels and confinement improvement. Record values of plasma energy content were measured at central densities up to 8 × 1019 m−3 under Li-coated walls.

http://iopscience.iop.org/article/10.1088/0741-3335/50/12/124051/pdf

Plasma performance and confinement in the TJ-II stellarator with lithium-coated walls

Electron cyclotron resonance heating (ECRH) has become an attractive technique in today's fusion experiments not only as a heating mechanism but also as a diagnostic tool and a way to induce controllable currents through electron cyclotron current drive (ECCD). In this paper we show, using ray tracing simulations, how one can address all these issues with the ECRH system designed for the TJ-II stellarator. This ECRH set up consists of two 500 kW gyrotrons at f = 53.2 Ghz coupled to the plasma through two quasi-optical transmission lines, placed at two stellarator symmetric positions, and equipped with an internal steerable mirror. Using the three-dimensional (3D) Hamiltonian ray tracing code, TRECE, almost full single-pass absorption with localized power deposition is found for both on- and off-axis heating for any magnetic configuration. The simulations also show that it is possible to induce an appreciable ECCD despite the small oblique incidence angles attainable with the movable mirrors because of the rapid variation of the magnetic field direction and strength with the toroidal angle in TJ-II.

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Electron cyclotron heating and current drive in the TJ-II stellarator

Neoclassical transport theory describes local diffusive transport. For those magnetic configurations where this approach is valid it has the benefit of being independent of the plasma profiles. In contrast for configurations where many particle orbits have large deviations from their birth surface, non-local contributions to the particle flux have to be considered. In this work a newly developed Monte Carlo code has been used to compute global ion fluxes for the same plasma parameters for two devices with very different magnetic configurations, namely the Wendelstein 7-X helias, which is under construction at Greifswald (Germany), and the TJ-II heliac, in operation at Madrid (Spain). Whereas the results indicate that the local diffusive approach is valid for W7-X under the considered plasma conditions, a non-local treatment is mandatory for TJ-II. These global flux simulations show the appearance of fluxes in regions where there are no gradients; larger fluxes than those expected from local estimations in the gradient regions; and fluxes which are increasing towards the edge.

Neoclassical global flux simulations in stellarators

Transitions to improved core electron heat confinement are triggered by low order rational magnetic surfaces in TJ-II electron cyclotron heated (ECH) plasmas. Experiments are performed changing the magnetic shear around the rational surface n = 3/m = 2 to study its influence on the transition; ECH power modulation is used to look at transport properties. The improvement in the electron heat confinement shows no obvious dependence on the magnetic shear. Transitions triggered by the rational surface n = 4/m = 2 show, in addition, an increase in the ion temperature synchronized with the increase in the electron temperature. Ion temperature changes had not been previously observed either in TJ-II or in any other helical device. SXR measurements demonstrate that, under certain circumstances, the rational surface positioned inside the plasma core region precedes and provides a trigger for the transition.

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Transitions to improved core electron heat confinement triggered by low order rational magnetic surfaces in the stellarator TJ-II

The neutral beam power transmitted into the helical axis stellarator TJ-II is calculated for the final duct design of TJ-II. The transmitted beam is intercepted by the first toroidalfield coil before reaching the plasma. The nontrappedfraction of the beam hits various vacuum vessel components. The adopted design of the graphite thermal shields used as vacuum vessel protection at TJ-II is presented. The design achieves a compromise between maximum power into the torus and minimum loads on sensitive parts. A three-dimensional version of the beam geometric code DENSB is set up to calculate the power loads due to shine-through neutrals on the shields under these circumstances. Power load maps are the input to the finite element code ANSYS for the calculation of temperature distributions. For the usual duty cycle at TJ-II (300-ms pulses every 300 s), the peak surface saturation temperatures at all surfaces remain under 650 °C, well below the tolerable limits for graphite.

J. Guasp

Papers

Plasma performance and confinement in the TJ-II stellarator with lithium-coated walls

Electron cyclotron heating and current drive in the TJ-II stellarator

Neoclassical global flux simulations in stellarators

Transitions to improved core electron heat confinement triggered by low order rational magnetic surfaces in the stellarator TJ-II

Thermal load calculations at TJ-II vacuum vessel under neutral beam injection