Table of contents

Please see the PDF file for the full text of this article.

The National Spherical Torus Experiment (NSTX) produces plasmas with toroidal aspect ratio as low as 1.25, which can be heated by up to 6 MW high-harmonic fast waves and up to 7 MW of deuterium neutral beam injection. Using new poloidal field coils, plasmas with cross-section elongation up to 2.7, triangularity 0.8, plasma currents I_p up to 1.5 MA and normalized currents I_p/aB_T up to 7.5 MA/m·T have been achieved. A significant extension of the plasma pulse length, to 1.5 s at a plasma current of 0.7 MA, has been achieved by exploiting the bootstrap and NBI-driven currents to reduce the dissipation of poloidal flux. Inductive plasma startup has been supplemented by coaxial helicity injection (CHI) and the production of persistent current on closed flux surfaces by CHI has now been demonstrated in NSTX. The plasma response to magnetic field perturbations with toroidal mode numbers n = 1 or 3 and the effects on the plasma rotation have been investigated using three pairs of coils outside the vacuum vessel. Recent studies of both MHD stability and of transport benefitted from improved diagnostics, including measurements of the internal poloidal field using the motional Stark effect (MSE). In plasmas with a region of reversed magnetic shear in the core, now confirmed by the MSE data, improved electron confinement has been observed.

Different methods of plasma formation have been studied in spherical tokamaks (ST). In inductive methods, breakdown and formation of ST plasma are achieved through the application of an electric field produced by a rapid change of currents in poloidal field coils, in the central solenoid or by using internal electrodes. In non-inductive methods, breakdown and formation of ST plasma are achieved by the application of radio frequency (RF) power, neutral beam injection or other ionization and current drive techniques. A combination of these methods is often used. Inductive methods utilizing flux from the central solenoid have limited performance as there is limited space for the central solenoid in STs, so methods not using the central solenoid flux are of special interest. In this paper we discuss different methods developed and used on the START and MAST STs at Culham; in particular, direct induction and electron cyclotron resonance preionization assisted formation are discussed in detail. These experiments have been performed at different RF frequencies and results of these studies are compared with the theory. Other methods, for example, the merging–compression and the double-null merging, are mentioned and prospects of different formation methods for future STs are discussed.

The results of the experimental campaign on Globus-M (R = 0.36 m, a = 24 m) devoted to investigating density limits and density control are reported. The experiments were performed at B_tor = 0.4 T, I_p = 0.18–0.25 MA, q₉₅ = 3.5–5 and plasma vertical elongation, κ ∼ 1.5–1.7. The density limits achieved with the gas puffing method of density control in the previous periods in ohmic heating (OH) regime are discussed. The progress made in OH scenario optimization helped the density to approach the Greenwald limit. Co-current neutral beam of deuterium with the power in the range of 0.45–0.6 MW at the beam energy of 28–29 keV was injected into deuterium target plasma at the early stage of the discharge, which allowed the density to overcome the Greenwald limit. Line averaged densities in excess of 1.5 × 10²⁰ m⁻³ were achieved, during the external gas puff. An ion temperature increase, measured by NPA was accompanied by a definite increase in the electron energy content, registered by Thomson scattering. Injection of a pure, highly ionized hydrogen plasma jet with a density up to 10²² m⁻³, total number of accelerated particles (1–5) × 10¹⁹ and a flow velocity of ∼110 km s⁻¹ was used as another instrument for density control. It increased plasma particle inventory in the Globus-M by ∼50% (from 0.65 × 10¹⁹ to 1 × 10¹⁹) in a single shot without target OH plasma parameter degradation. The injection resulted in a fast density increase with the time much shorter than with gas puff fuelling, which was confirmed by Thomson scattering measurements.

In spherical tokamaks the conventional ICR plasma heating has a number of specific features and therefore requires additional investigations. For this aim the modelling of wave propagation and absorption was performed by the 1-D code developed at the Ioffe institute. All possible mechanisms of RF absorption (cyclotron absorption at fundamental and second harmonics, TTMP, Landau) were taken into account. The calculations demonstrated the possibility of effective RF power absorption both by ions and electrons in a broad range of plasma parameters (including relative hydrogen concentration).

The ICRH experiments were performed on the low aspect ratio tokamak Globus-M (R = 0.36 m, a = 0.24 m, B₀ = 0.3–0.4 T, I_p = 0.15–0.25 MA, vertical elongation 1.2–2, at RF power input level up to 200 kW at frequencies of 7.5–9.2 MHz. A 12-channel neutral particle analyser measured simultaneously hydrogen and deuterium fluxes and relative concentration of ion components. In the experiment the ion temperature increases twice, but the ion heating efficiency depends on the location of the second hydrogen cyclotron harmonic and on the concentration of the light ion component. It is shown that the position of the second hydrogen harmonic in front of the antenna decreases the efficiency of the ion heating. The increase in H-concentration in deuterium target plasma from 10% up to 70% does not influence ion heating efficiency essentially but seems to increase it moderately. The first results on 1.5-D transport ASTRA Modelling are described. They are in reasonable agreement with experimental data. The electron heating was not detected in the experiment due to comparatively low absorbed power with respect to OH one.

Several techniques for initiating the plasma current without the use of the central solenoid are being developed in TST-2. While TST-2 was temporarily located at Kyushu University, two types of start-up scenarios were demonstrated. (1) A plasma current of 4 kA was generated and sustained for 0.28 s by either electron cyclotron wave or electron Bernstein wave, without induction. (2) A plasma current of 10 kA was obtained transiently by induction using only outboard poloidal field coils. In the second scenario, it is important to supply sufficient power for ionization (100 kW of EC power was sufficient in this case), since the vertical field during start-up is not adequate to maintain plasma equilibrium. In addition, electron heating experiments using the X–B mode conversion scenario were performed, and a heating efficiency of 60% was observed at a 100 kW RF power level. TST-2 is now located at the Kashiwa Campus of the University of Tokyo. Significant upgrades were made in both magnetic coil power supplies and RF systems, and plasma experiments have restarted. RF power of up to 400 kW is available in the high-harmonic fast wave frequency range around 20 MHz. Four 200 MHz transmitters are now being prepared for plasma current start-up experiments using RF power in the lower-hybrid frequency range. Preparations are in progress for a new plasma merging experiment (UTST) aimed at the formation and sustainment of ultra-high β ST plasmas.

The Pegasus Toroidal Experiment was developed to explore the physics limits of plasma operation as the aspect ratio (A) approaches unity. Initial experiments on the device found that access to high normalized current and toroidal beta was limited by the presence of large-scale tearing modes. Major upgrades have been conducted of the facility to provide the control tools necessary to mitigate these resistive modes. The upgrades include new programmable power supplies, new poloidal field coils and increased, time-variable toroidal field. First ohmic operations with the upgraded system demonstrated position and current ramp-rate control, as well as improvement in ohmic flux consumption from 2.9 MA Wb⁻¹ to 4.2 MA Wb⁻¹. The upgraded experiment will be used to address three areas of physics interest. First, the kink and ballooning stability boundaries at low A and high normalized current will be investigated. Second, clean, high-current plasma sources will be studied as a helicity injection tool. Experiments with two such sources have produced toroidal currents three times greater than predicted by geometric field line following. Finally, the use of electron Bernstein waves to heat and drive current locally will be studied at the 1 MW level; initial modelling indicates that these experiments are feasible at a frequency of 2.45 GHz.

The design study of PROTO-SPHERA, a novel compact torus configuration, has been completed. It is composed of a spherical torus (ST) (with closed flux surfaces) and a force-free screw pinch (SP) (with open flux surfaces and fed by electrodes). PROTO-SPHERA is formed at spherical-tokamak-like densities (∼10¹⁹ m⁻³) with low voltage (∼200 V) between the electrodes. The idea of replacing the metal centrepost current (I_tf) of the spherical tokamaks with the SP plasma electrode current (I_e) is aimed mainly at getting rid of the rod at the centre of the plasma configuration, which is the most critical component of spherical tokamak design. As a consequence it should be possible to decrease the aspect ratio A = R/a (R = ST major radius, a = ST minor radius) in the course of experiment and to increase the ratio between the toroidal plasma current (I_ST) and the plasma electrode current, I_ST/I_e ≫ 1. Matching two plasma configurations, i.e. an open flux-surface SP and a closed flux-surface ST, brings to life several radically new issues. The purpose of this paper is to analyse the equilibrium, the ideal MHD stability and the formations and modelling issues of such a combined magnetic confinement system. The MULTI-PINCH experimental setup, which is being assembled inside the START vacuum vessel (now in Frascati), will represent the first phase of PROTO-SPHERA: its goal is to prove the feasibility of a stable disc-shaped SP around the electrodes.

An on-line plasma shape reconstruction algorithm is necessary to design the plasma position and shape control system in modern tokamaks. An algorithm aimed at solving this problem is proposed. A description of the mathematical procedure is provided and experimental data incorporation is discussed. An example of an application of this algorithm is demonstrated using experimental data from Globus-M discharge #10292.

The simulation of eddy currents induced in the vacuum vessel and central column of spherical tokamaks is discussed, improving upon previously published methods. The present model allows us to describe the vacuum vessel either as a thin shell or as a large collection of rings, formally reducing the problem to a set of coupled circuit equations. Results are compared with measurements of the electromotive force and current distribution on the vacuum vessel of the ETE spherical tokamak. The mathematical model is described in detail, enabling application to other machines.

A self-consistent simulation, including a model for improved core energy confinement, demonstrates that externally applied, inductive current perturbations can be used to control both the location and strength of internal transport barriers (ITBs) in a fully non-inductive tokamak discharge. We find that ITB structures formed with broad non-inductive current sources such as LHCD are more readily controlled than those formed by localized sources such as ECCD. Through this external control of the magnetic shear profile, we can maintain the ITB strength which is otherwise prone to deteriorate when the bootstrap current increases. The inductive current perturbation, which can be implemented by a weak Ohmic power, offers steady-state, advanced tokamak reactors an external means of efficient ITB control for regulating the fusion-burn net output and spatial profile.

The paper presents the application of modern computational methods for tokamak plasma control system analysis. Several different approaches for feedback controller synthesis are described. General positions of the modern robust analysis theory are briefly formulated. The technique of robust features comparative analysis for feedback controllers is presented. The application of these computational methods is illustrated by the example of the MAST tokamak plasma vertical feedback control system.

Edge turbulence called 'filaments' is one of the most interesting things to study in the field of plasma science. In this paper, it is demonstrated that a plasma model based on filaments could be made using a single-fluid MHD approach including ions and electrons. According to this model, non-uniform heating with, for example, neutral beam injection or cooling with local recycling makes a 'blob', and the blob extent is mainly along the magnetic field. Due to large thermal conduction parallel to the magnetic field the blob should have a shape called a 'filament'. During the extension process by which a blob becomes a filament it moves and/or rotates across the magnetic field due to an unbalanced jxB force. Using this model, the energy confinement time will be proportional to the total plasma current, if the filament generation rate is independent of the magnetic field.

The dynamic ergodic divertor (DED) on the TEXTOR tokamak allows for the creation of static and rotating helical magnetic perturbation fields. In the 3/1 configuration the strong m/n = 2/1 sideband excites a locked 2/1 tearing mode above a critical perturbation field strength. The mode onset threshold depends strongly on the plasma fluid rotation with respect to the mode. Rotation in plasma current direction destabilizes the mode in a certain range of rotation frequencies, whereas counter-rotation has a stabilizing influence. The threshold shows a minimum when the frequency of the external perturbation equals the MHD frequency of the mode.

The toroidal rotation driven by negative neutral beam injection (NNBI) into the International Thermonuclear Experimental Reactor is predicted using the GLF23 transport model. It is found that a significant gain in the fusion power output is achieved with reasonable levels of NNBI power. The increase in fusion power with co-injected NNBI is steeper than with balanced NNBI or pure electron heating. This is due to the toroidal rotation increasing the threshold gradient for the ion temperature gradient modes in the GLF23 model. The increase in fusion power is found to be weakly dependent on the NNBI voltage over a range of values from 250 keV to 1 MeV.

It is shown that the error field in a tokamak can be shielded by a flowing liquid metal wall. In particular, a flowing liquid metal wall can prevent resonance amplification of the error field by the plasma near its no-wall stability limit.

A general expression for the growth rate of Alfvén instabilities driven by circulating and semi-trapped energetic ions in stellarators is derived, which generalizes that obtained in a recent work (Kolesnichenko Ya.I. et al 2004 Phys. Plasmas11 158) by taking into account the finite orbit width of the energetic ions. It is found that the finite orbits typically reduce the growth rate, but in some cases they enhance instabilities, leading to additional resonances. The developed theory is applied to a particular shot (shot #34723) in Wendelstein 7-AS, where Alfvénic activity had a bursting character, being strongest at the end of each burst. Although the presented analysis of this shot is not complete, it is sufficient to conclude that the finite orbit width triggers a weak instability at the initial stage of each instability burst, but it weakens a strong instability at the burst end. The latter effect makes the perturbative approach used in the paper applicable. An analysis of destabilized Alfvén eigenmodes in W7-AS precedes the stability analysis. In addition, an invariant of the particle motion in the stellarator field is derived, and the mode structure in weak-shear systems is determined.

A novel pellet acceleration concept using millimetre microwaves from MW gyrotron sources is presented that could pave the way for high-speed >3 km s⁻¹ inner-wall pellet injection on ITER-class tokamaks. In the proposed concept, the high gas pressure is created by vapourization of a composite 'pusher' medium attached behind the deuterium–tritium (DT) fuel pellet. The pusher medium consists of small micron-sized conducting particles, e.g. Li embedded homogeneously in a D₂ ice slug, thus facilitating microwave energy absorption by dissipation of eddy currents flowing within the conducting particles only. Gyrotron power P_gyr can be absorbed continuously in the pusher gas, and therefore the high gas pressure can be sustained behind the pellet while it is being accelerated down the waveguide/launch tube. A scaling law is derived which predicts that a pellet of mass M_p accelerated over a distance L reaches a velocity v_p ≅ (P_gyrL/M_p)^1/3, with a hydrodynamic efficiency of 45%.

The degradation of energy confinement with increased toroidal beta β_T was shown by non-dimensional analysis in JT-60U. The dependence of the energy confinement on β_T was examined by both the JT-60U ELMy H-mode confinement database and the dedicated experiment on a single β_T scan while and ν^* were kept fixed as well as the other magnetic geometrical parameters. In both cases, the degradation of energy confinement with increasing β_T was observed, satisfying the relation of . This dependence is a little weaker than that predicted by the IPB98(y, 2) scaling. The fusion power production rate was estimated to increase in proportion to .

Modelling of the pellet ablation cloud evolution including the ∇B induced drift motion is performed. The model includes cloud heating, expansion and ionization, acceleration in the low-field side (LFS) direction, Alfven conductivity of the background plasma, compensation of ∇B currents in different parts of the cloud during its propagation along the magnetic field, cooling of the background plasma and simulation of the pellet ablation rate in a self-consistent manner. The time evolution of cloud density and temperature profiles and the mass deposition after the pellet injection are calculated. The LFS and high-field side injection scenarios with plasma and pellet parameters typical for the ASDEX-Upgrade tokamak are compared. An effect of pre-cooling on the pellet penetration depth is studied. The calculated size of the neutral part of the cloud, the characteristic values of cloud density and temperature far from the pellet and the fuelling efficiency (for LFS pellets) are in reasonable agreement with those observed in experiments on the ASDEX-Upgrade.

This paper describes what we can learn on the regimes of spontaneous electron temperature oscillations discovered in Tore Supra from the analysis of MHD activity. Since the first observations of this oscillating behaviour of plasma equilibrium, and its interpretation as a predator–prey system involving lower hybrid waves power deposition and electron confinement, analysis of MHD modes has confirmed the reality of safety factor profile oscillations. This points towards the importance of rational values of the safety factor in the transition to transport barriers in reversed magnetic shear plasmas.

Based on theoretical analysis, numerical simulations and experimental results, the paper outlines a self-consistent physics picture of the island divertor transport in W7-AS, as it emerges from the present understanding, documented over the past several years of theoretical and experimental research on the subject. Key function elements of a divertor, such as particle flux enhancement, neutral screening, impurity retention, thermal power removal via impurity line radiation and detachment, are examined for the island divertor and assessed with respect to tokamak divertors. The paper focuses on describing the global scrape-off layer (SOL) transport behaviour associated with the specific island topology and aims at illustrating the elementary differences and similarities in divertor physics between a tokamak and a typical helical device. Shown and analysed are also the correlation between the SOL and core plasma and the role of the island divertor for improving the global plasma performance. Discussion is mainly based on simple models and estimations, while three-dimensional modelling calculations serve only for control of self-consistency and for determining basic functional dependences not accessible otherwise. The island divertor physics is presented within a theoretical frame with most key issues, however, being related to experimental results.

A physical design of a device that can be a base for a direct-conversion nuclear electric power station is considered. The project considers the aneutronic reaction P–¹¹B in the asymmetric centrifugal trap. Kinetic energy of nuclear particles (alpha particles) is converted into electrical energy inside this device; no thermal cycle is used. Heating and recuperation of energy of protons and boron ions take place in the plasma space. The presented scheme differs significantly from the conventional thermonuclear fusion. 'Fast' protons, which are the main energy component of plasma, have an almost monoenergetic spectrum. This makes it possible to realize the 'resonance' fusion.

In this paper we have investigated the effect of reversing the direction of the magnetic field and plasma current, hence the ion ∇B-drift direction, on the instability threshold of toroidal Alfvén eigenmodes with toroidal mode number (n) in the range |n| = 3–10. These modes are driven by MeV-energy protons produced by minority H(D) ion cyclotron resonance frequency heating. A larger fast ion drive is found to be required to destabilize the modes when the magnetic field and plasma current are reversed with respect to the usual JET configuration (i.e. when the ion ∇B-drift is directed away from the divertor), with the difference decreasing for increasing n.