Table of contents

The well-known radical and ion scavenger techniques of application in amorphous hydrogenated carbon film deposition studies are investigated in relation to the mechanism of tritium and deuterium co-deposition in carbon-dominated fusion devices. A particularly successful scheme results from the injection of nitrogen into methane/hydrogen plasmas for conditions close to those prevailing in the divertor region of present fusion devices. A complete suppression of the a-C : H film deposition has been achieved for N₂/CH₄ ratios close to one in methane (5%)/hydrogen DC plasma. The implications of these findings in the tritium retention control in future fusion reactors are addressed.

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.

An original method is presented to solve the linearized heat transport equation for a general class of χ models, of the form χ = χ₀T^μG(∇T/T), where χ₀ is a constant and G an arbitrary function which depends only on ∇T/T. These solutions allow one to address the propagation of heat and cold pulses in a tokamak plasma. By looking for solutions of the problem as functions of ∇T/T instead of the usual radial coordinates, the linearized transport equation is reformulated into a much simpler second-order differential equation. In this new form, it may be solved directly, if an analytical solution of the problem exists. The calculations are carried out both in slab and cylindrical geometry, and can be generalized to other geometries. For slab geometry, the exact solutions of the linearized transport equation are found in the case G = (|∇T|/T)^α. An approximate solution is given in the case with critical gradient length G = (|∇T|/T)^α(|∇T|/T−κ)^β, valid for strong profile stiffness (∇T/T≈κ). In cylindrical geometry, the Wentzel–Kramers–Brillouin solutions are found in the case G = (|∇T|/T)^α. These solutions are validated by comparison with numerical simulations. Their dependence on the modulation frequency and the model parameters is investigated. Finally, a method is proposed to identify the model parameters (e.g. χ₀, α and μ) which best fit given temperature modulation data, as an original application of these analytical calculations to experimental transport studies.

The instability that arises during the expansion of a plasma with negative ions into a vacuum is considered. The dispersion relation, its solutions, energy exchange between waves, and a heating of ions are studied. Effect of dispersion on the instability is discussed. Comparison of analytical solutions with simulation data gives a good agreement.

The paper deals with the operation of Hall plasma thrusters and the transversal to the magnetic field current in such systems. The problems of the transverse conductivity and related processes are treated in the framework of the well-known Morozov's model; the difference is in the addition of the mechanism of plasma recombination on the walls of the thruster and further volume ionization of the neutrals created at the walls. The distribution functions of the neutrals and secondary electrons generated by ionization are found, as well as the expression for the transverse current. The obtained result contains an additional correcting factor compared to the conventional Morozov's equation for this current and permits a better quantitative agreement of the theoretical expression and experimental results.

Axisymmetric MHD simulations have revealed a new driving mechanism that governs the vertical displacement event (VDE) dynamics in tokamak disruptions. A rapid flattening of the plasma current profile during the disruption plays a substantial role in dragging a single null-diverted plasma vertically towards the divertor. As a consequence, the occurrence of downward-going VDEs predominates over the upward-going ones in bottom-diverted discharges. This dragging effect, due to an abrupt change in the current profile, is absent in up–down symmetric limiter discharges. These simulation results are consistent with experiments in ASDEX-Upgrade. Together with the attractive force that arises from passive shell currents induced by the plasma current quench, the dragging effect explains many details of the VDE dynamics over the whole period of the disruptive termination.

The equilibrium currents and flow velocities of species are calculated with the guiding-field line (GFL) model for the plasma in tokamaks with a radial electric field, including the case of large gradients of the field. In the model, all quantities such as the particle position and distribution function are defined on the basis of the GFL—a field line that goes through the centre of the particle's drift orbit and moves at the bounce-averaged drift rate. The distribution function is formed by all orbits that have their GFLs at a given magnetic surface. When the orbits are being squeezed by large-gradient electric field, their position is not changed so that the GFL distribution function remains unchanged; the modification of the current is explicitly given by the wobble-magnetization term that is related to the orbits' shape in the model. The gradient of electric field is shown to affect the parallel component of the current or flow velocity of the ions, rather than the perpendicular one. The effect of the electric field gradient on the electrons is negligible. The results obtained with the model match well with the fluid equations and close to the results of neoclassical theory, though different in detail. It is shown that for the typical conditions of the Tokamak Fusion Test Reactor, the presence of radial electric field enhances the toroidal flow velocity of plasma species up to 20–100 km s⁻¹, opposite to the Ohmic current when the electric field is directed inward. The poloidal flow velocity of ions is of the order of 1–2 km s⁻¹, and is irrelevant to the electric field unless the electric field has a large gradient.

Electron density and electron temperature profiles are reconstructed from Thomson scattering data on the stellarator Wendelstein 7-AS by means of systematic statistical modelling employing the Bayesian probability theory (BPT). The BPT allows for systematic combination of all information entering the measurement descriptive model considering all uncertainties of the measured data, calibration measurements, physical model parameters and measurement nuisance parameters. The BPT results are consistent with the ratio-evaluation method (REM) which is used to determine the electron temperature from the ratios of scattering signals. If compared to the sequential REM, the Bayesian error analysis is much more informative because it yields probability density functions of the quantities of interest. Moreover, systematic consideration of all the obtainable raw data, in particular those data suffering from low signal levels, results in an improved evaluation for weakly informative data. Sensitivity analysis of model parameters allows for finding crucial uncertainties which has impact on both diagnostic improvement and design.

Ion cyclotron heating and current drive at ω≈2ω_cH in JET deuterium plasmas with a hydrogen concentration n_H/(n_D+n_H) in the range of 5–15% are analysed, comparing results of numerical computer modelling with experiments. Second harmonic hydrogen damping is found to be maximized by placing the resonance on the low-field side (LFS) of the torus, which minimizes competing direct electron damping and parasitic high-harmonic D damping in the presence of D beams. The shape of the calculated current perturbation and the radial localization of the heating power density for the LFS resonance are consistent with the experimentally observed evolution of the sawtooth period when the resonance layer moves near the q = 1 surface. Since the calculated driven current is dominated by a current of diamagnetic type caused by finite orbit widths of trapped resonating ions, it is not too sensitive to the ICRF phasing. Control of sawteeth with ion cyclotron current drive using the LFS ω≈2ω_cH resonance in the present experimental conditions can thus be best obtained by varying the resonance location rather than the ICRF phasing. Due to differences in fast ion orbits, collisional electron heating and fast ion pressure profiles are significantly more peaked for a LFS resonance than for a high-field side (HFS) resonance. For the HFS ω≈2ω_cH resonance, an enhanced neutron rate is observed in the presence of D beam ions, which is consistent with parasitic D damping at the ω≈5ω_cD resonance in the plasma centre.

The utility of ICRF heating in the LHD was demonstrated in the third campaign carried out in 1999. This paper summarizes the investigations made in 2000 with a focus on the optimization of ICRF heating. The flexibility of the LHD magnetic configuration was fully utilized as a key factor in the investigations. The experiments include (a) scan of magnetic field intensity, (b) scan of aspect ratio, (c) scan of magnetic axis shift, (d) scan of quadrupole magnetic field, and (e) cancellation of magnetic island. The performance of the ICRF heating was thus optimized with respect to magnetic parameters, while optimization was achieved mainly with respect to heating regime and wall conditioning in the third campaign. Some of these parameters are directly related to the orbit of trapped particles. Therefore, the relation between particle orbits and the performance of ICRF heating is also addressed in this paper based on analyses of the high-energy tail of ions.

The probability density function (PDF) of turbulent transport has been investigated in the plasma edge region of tokamak (JET) and stellarator (TJ-II) fusion devices. PDFs can be re-scaled using a functional form, PDF(Γ_E×B) = L⁻¹g(Γ_E×B/L), where L is directly related with the level of fluctuations in the turbulent flux. This kind of re-scaling holds at different timescales in which the functional form of the PDF changes. The empirical similarity in the PDF of turbulent transport in the edge region in both the JET tokamak and the TJ-II stellarator supports the view that turbulent transport displays universality in fusion plasmas. These results emphasize the importance of the statistical description of transport processes in fusion plasmas as an alternative approach to the traditional way to characterize transport based on the computation of effective transport coefficients (i.e. diffusion coefficients) and on average quantities (i.e. average correlation lengths).

Three methods to study the effect of density fluctuations on the reflected signal, based on a 2D full-wave analysis and Born approximation numerical and analytical calculations, are developed. The explicit analytical expression for the signal produced by an island-like perturbation running in poloidal direction is obtained and shown to be in nice agreement with results of numerical techniques for small level density perturbations. It is shown, both numerically and analytically, that due to small-angle scattering effects, fluctuations far from the cut-off layer may produce a significant and, in some realistic cases, dominant response. The conditions under which the fluctuation reflectometry signal is generated only in the cut-off vicinity are given.

At certain values of the edge rotational transform _a, the confinement quality of plasmas in the Wendelstein 7-AS (W7-AS) stellarator is found to react very sensitively to small modifications of the edge rotational transform _a. As _a can be reproducibly changed either by external fields or by a small plasma current, these transitions offer a precise way to systematically analyse differences in plasma turbulence between bad and good confinement cases. This paper presents results of the study of electron density fluctuations associated with confinement changes. Wavenumber and frequency spectra and radial profiles are compared. A slow and reproducible transition is induced by a small plasma current and the sequence of events leading to bad confinement is investigated. The laser scattering core plasma density fluctuation measurements are complemented by edge beam emission spectroscopy results and magnetic fluctuation measurements with Mirnov coils.

Clear correspondence between plasma fluctuations and confinement degradation is observed: the weight of larger structures increases, fluctuations increase in the plasma core, the poloidal flow velocity decreases and regions of mode-like activity move radially in the plasma. These changes occur gradually and controllably if the magnetic configuration is steered by a small plasma current.

Experiments performed on the PF-1000 plasma focus (PF) facility have shown that a stable corona plasma is created when PF current sheath interacts with an Al wire positioned on the PF electrode axis and attached to the anode face. Soft x-ray line radiation of highly ionized Al atoms was registered by a FSSR mica spectrometer with two-dimensional space resolution. These spectra are emitted by the entire surface of the corona but not from hot spots like as in usual PF discharges.

A transient behaviour is observed in the plasma core of TJ-II stellarator with fast drops in the electron temperature. Changes in the line-averaged density are observed synchronized with temperature drops. This phenomenon appears in plasmas created and heated using 300 kW of electron cyclotron heating with high power density. The transient behaviour resembles both, the electric pulsation discovered in CHS and the `electron root' feature reported by the W7-AS team. The flexibility and low magnetic shear of TJ-II have permitted the identification of the plasma current as the control parameter for the appearance of this phenomenon. The results obtained during the magnetic configuration scans carried out in TJ-II points to the hypothesis that the transient behaviour is connected with the presence of a rational surface close to the plasma centre. Equilibrium calculations performed with the VMEC code reinforce this hypothesis.

An extensive investigation of the global confinement properties in different operating scenarios in the rebuilt EXTRAP T2R reversed-field pinch (RFP) experiment is reported here. In particular, the role of a fast gas puff valve system, used to control plasma density, on confinement is studied. Without gas puffing, the electron density decays below 0.5×10¹⁹ m⁻³. The poloidal beta varies between 5% and 15%, decreasing at large I/N. The energy confinement time ranges from 70 to 225 μs. With gas puffing, the density is sustained at n_e≈1.5×10¹⁹ m⁻³. However, a general slight deterioration of the plasma performances is observed for the same values of I/N: the plasma becomes cooler and more radiative. The poloidal beta is comparable to that in the scenarios without puff but the energy confinement time drops ranging from 60 to 130 μs. The fluctuation level and the energy confinement time have been found to scale with the Lundquist number as S^{−0.05±0.07} and S^0.5±0.1, respectively. Mode rotation is typical for all the discharges and rotation velocity is observed to increase with increasing electron diamagnetic velocity.

Spontaneous improvements in particle and energy confinement have been observed in TJ-II plasmas with ≈300 kW of electron cyclotron resonance heating. Density and temperature profiles broaden giving rise to energy content enhancement up to a factor of 1.4. The transport analysis on one of these discharges describes the evolution of the profiles via a sudden reduction (∼50%) of the thermal and particle diffusivities inside the main plasma. A brief comparison with transition phenomena in other devices is given.

The neutron emission from the JET tokamak is investigated using an extensive set of diagnostics, permitting the instantaneous neutron yield, the radial profile of the neutron emission and neutron energy spectra to be studied. Apart from their importance as an immediate indication of plasma fusion performance, the customary use for neutron measurements is as a test of the internal consistency of the non-neutron diagnostic data, from which the expected neutron production can be predicted. However, because contours of equal neutron emissivity are not necessarily coincident with magnetic flux surfaces, a fully satisfactory numerical analysis requires the application of highly complex transport codes such as TRANSP. In this paper, a far simpler approach is adopted wherein the neutron emission spatial profiles are used to define the plasma geometry. A two-volume model is used, with a core volume that encompasses about (2/3) of the neutron emission and the peripheral volume the remainder. The overall approach provides an interpretation of the measured neutron data, for both deuterium and deuterium–tritium (D–T) plasma discharges, that are as accurate as the basic non-nuclear plasma data warrant. The model includes the empirical assumption that particles, along with their energies and momenta, are transported macroscopically in accordance with classical conservation laws. This first-order estimate of cross-field transport (which, for D–T plasmas, determines the D : T fuel concentration ratio in the plasma core) is fine-tuned to reproduce the experimental ion and electron temperature data. The success of this model demonstrates that the observed plasma rotation rates, temperatures and the resulting neutron emission can be broadly explained in terms of macroscopic transport.

Nonlinear behaviour of resistive drift-Alfvén mode is described by a three-field model composed of vorticity equation, Ohm's law and continuity equation. Resistive drift-Alfvén instabilities occur in the cylindrical plasma where both resistivity and plasma β value are finite. The resistive drift-Alfvén instabilities assuming single helicity generate poloidal sheared flow via the Reynolds stress by nonlinear mode couplings. The poloidal sheared flow stabilizes several unstable modes including the most unstable mode and leads to saturation of the nonlinear resistive drift-Alfvén modes. It is noted that some harmonics are destabilized by this flow. The level of magnetic fluctuations is much smaller than that due to density and electrostatic potential fluctuations. Particle flux due to the magnetic fluctuations is also extremely small compared to that due to electrostatic fluctuations. However, it is shown that the effect of magnetic fluctuations on the poloidal flow is significant. The magnetic fluctuations play a role of suppressing the poloidal flow drive by convective nonlinearity.

Minimum dissipation states of a flux core spheromak sustained by helicity injection are presented. Helicity balance is used as a constraint and the resistivity is considered to be non-uniform. Two types of relaxed states are found: one has a central core formed by the flux that links the electrodes surrounded by a toroidal region of closed flux surfaces and the other has the open flux wrapped around the closed flux surfaces. The analysis includes two important features: a self-consistent calculation of the magnetic flux through the electrodes and a resistivity which depends upon the poloidal flux. Non-uniform resistivity effects can be very important because of the qualitative and quantitative changes they produce in the safety factor profile.

Opacity effects, in particular of Lyman lines, in divertors are believed to be relevant for plasma spectroscopy and for the overall divertor dynamics through possible redistribution of excited hydrogen atoms and radiation losses. Quite elaborate computational radiation transport tools have been developed, specialized for numerous applications. The task in fusion research has been adaptation to fusion edge plasma conditions. In this paper, we start from an existing kinetic neutral particle code already well adapted to divertor applications, and extend this from the `particle' simulation to an analogue `photon gas' simulation. It is shown how this can be achieved and that a quite flexible and detailed divertor radiation transport code can conveniently be obtained. We apply this to study Lyman opacity effects on population kinetics and hydrogen divertor radiation losses.

This article was scheduled to appear in issue 7 of Plasma Phys. Control. Fusion. To access this Special issue on advanced Tokamak research in EFDA-JET please follow this link: http://stacks.iop.org/0741-3335/44/7

Internal transport barriers (ITBs) can be produced in JET by the application of strong additional heating during the current rise phase of the plasma discharge. Using up to 3 MW of lower hybrid power to tailor the q-profile prior to the main heating phase, a large variety of q-profiles ranging from low positive to strong negative central shear have been obtained during the current rise (0.4 MA s⁻¹). With negative central magnetic shear s = (r/q)(dr/dq), the analysis of ITB triggering reveals a correlation between the formation of the ITB and q _min reaching an integer value (q = 2 or q = 3). This observation is confirmed by the analysis of the Alfvèn cascades. The minimum power required to access regimes with ITBs is probably related to the transport and magnetohydrodynamic properties of integer magnetic surfaces. Laser ablation and shallow pellet injection have also been attempted in recent JET ITB triggering experiments.

This article was scheduled to appear in issue 7 of Plasma Phys. Control. Fusion. To access this special issue on advanced Tokamak research in EFDA-JET please follow this link: http://stacks.iop.org/0741-3335/44/7

With a high resolution visible light spectrometer the H_α emission at the RTP tokamak has been studied. Monitoring the H_α line (6562.8 Å) with a toroidal line of sight into the plasma shows spectra with intricate H_α line structures. These line profiles can be explained by the occurrence of three different velocity groups of excited hydrogen with relative line shifts of the order of 2 Å. The origin of these three groups results from collisional processes with species of hydrogen, namely neutral hydrogen, H⁺ and also H₂⁺ molecules.

The 4th Europhysics Workshop was organized in Funchal in Madeira as a Satellite Meeting of the 28th EPS Conference on Controlled Fusion and Plasma Physics, and attended by about 45 scientists from 15 countries. It was hosted by the Portuguese Association IST-Euratom, and organized by the Czech Association Euratom/IPP.CR. The scope of the workshop is broad and includes experiments, techniques, theory and modelling pertinent to the effects of electric fields on plasmas. After refereeing, 18 of the 27 (oral) contributions were published in the October 2001 issue of Czechoslovak Journal of Physics.

Books by scientists about science usually fall into one of two distinct types: technical or popularizations. The technical category includes texts, collections, and monographs where, in physics at least, equations and data are the meat. In popular books, by contrast, it is said that each equation halves the readership: these books are written to be intelligible to the non-scientist. Nuclear Fusion: half a century of magnetic confinement fusion research falls into neither of these categories. Its authors, C M Braams and P E Stott, are physicists whose distinguished careers span most of the past half-century of fusion research. They write with both a first hand experience of the history of the field and an intimate knowledge of the science. The book might be described as a scientific history. Equations are unhesitatingly included where they are necessary to describe the physics, but the main thread of the book is the description of how fusion research evolved. Introductions to the physics of various topics are described briefly in `boxes' alongside the historical narrative. To a plasma physicist these are helpful and often insightful reminders of the fundamentals. I think that any professional physicist could benefit from these pithy technical summaries. But clearly they are not intended as more than pointers to a systematic understanding of plasma physics; and for a non-physicist they are doubtless incomprehensible.

In giving a physicist's view of fusion history, the authors are careful to document their sources, with twenty seven pages of references. This scholarly approach greatly enhances the value of the work in describing the progress and achievements of fusion research. It also provides a much-needed reminder, to those who speak lightly about `innovation', of the tremendous breadth of ideas for plasma confinement that have already been studied. But it means that the book reads somewhat like a review article, and definitely not like earlier fusion popularizations. By comparison Robin Herman's Fusion: the search for endless energy (CUP 1990) stresses the human interest angle by using many quotes from interviews, and Ken Fowler's The fusion quest (Johns Hopkins 1997) is far more in the manner of personal recollections.

While lacking these populist touches, Braams and Stott's book gives mature and balanced opinions about the reasons and influences, scientific and social, that have governed fusion's development. They outline the roots of nuclear energy and plasma physics leading to the classification of fusion research and its declassification in 1958 at Geneva. Continuing from the profusion of ideas disclosed at that time, they deal in succeeding chapters with open systems, pulsed toroidal configurations and other alternatives, stellarators, and tokamaks. Each configuration is traced from its earliest ideas to its modern embodiment-or its demise. In succeeding chapters are described the development of important techniques and scientific understanding, from the 1980s on, especially in application to the big tokamaks. The concluding chapter, which is remarkably up to date, discusses the steps to a fusion reactor and the history and status of ITER.

As a student considering plasma fusion as a possible career, I recall reading the book by Artsimovich and it seeming the best available introduction to the scientific history of the field, although even then it was hopelessly out of date. Now, in this new work by Braams and Stott, I have a book to give to students today for a thoroughly modern introduction-not to the technical mastery of plasma physics, for which there are many introductory texts, but to the background of where fusion research has come from. This broader perspective is both fascinating and essential to our maturing discipline; so I warmly recommend this book to all readers of Plasma Physics and Controlled Fusion.

I H Hutchinson