Table of contents

The energy confinement properties of JT-60 during Ohmic and neutral beam heated discharges are analysed on the basis of the heat pinch model proposed by Callen and Cordey. The feature of temperature profile consistency during variation of the density profile sets an important constraint for the heat pinch term. A heat pinch term proportional to n_eB_p seems to be consistent with the experimental observation. A transport model is proposed which reproduces quite well the parameter dependence of the JT-60 experimental data. The formation of an edge temperature pedestal during the H-mode is observed with this model when the edge convective energy loss is significantly reduced.

The authors identify intensive low frequency (ω ≪ ω_ci) fluctuations of density (ñ/n ≳ 0.1) and potential (e_LF/T_e ≳ 1) in the peripheral plasma of the URAGAN-3 torsatron during plasma production and heating by RF fields with a frequency ω₀ ∼ ω_ci. Given their space-time characteristics, these fluctuations would normally be attributed to the development of natural drift oscillations on the density gradient; however, the energy source which maintains the abnormally high level of these oscillations lies in the waves generated by the antenna. It has been demonstrated that the low frequency oscillations occur as a result of parametric instability of these waves. Low frequency fluctuations may give rise to appreciable ion heating in the peripheral plasma (T_i ≳ 100 eV), and also help set up an ion flux onto the surface intersected by the divertor magnetic flux.

Using the outside launch with vertical polarization, electron cyclotron heating (ECH) experiments in DIII-D were carried out at 60 GHz at fundamental and second harmonic frequencies. The results are consistent with wave absorption theory for accessibility. For fundamental heating with a cut-off layer between the launch location and the resonant surface, good absorption efficiency was obtained. A process for mode conversion at the wall from the extraordinary mode to the ordinary mode is postulated to explain this result. For most efficient heating it was important to avoid the presence of a locked mode. For low density plasmas at the fundamental, the global energy confinement exceeds Kaye-Goldston scaling by about a factor of 1.4. However, heating at the second harmonic agrees numerically with the Kaye-Goldston scaling formula, for ECH alone or for ECH combined with neutral beam injection (NBI), and shows a mass dependence consistent with T_E ∼ √A_i. The global energy increase was insensitive to the resonance location for q_res < 2–3. Comparing data at both harmonics in the low density range, where the energy confinement of Ohmic plasmas satisfies neo-Alcator density scaling and P_rf/P_ohm > 1, global energy confinement scales as T_E ∼ B_t^−0.3. Since plasma current and plasma geometry were not varied for these discharges, a scaling with safety factor q is also consistent. Using ECH alone, H-mode confinement was achieved for second harmonic heating in the central core of the plasma at a power threshold of ∼0.75 MW for plasma parameters I_p = 0.5 MA, and _e = 1.1 × 10¹⁹ m⁻³. The energy confinement times during the H-mode are similar to Ohmic values with a normalized confinement time τ_E/I_p ∼ 200 ms/MA. For ECH and NBI H-mode plasmas, the transition from the L-mode to the H-mode was correlated with reduced magnetic fluctuations in the divertor region. For ECH H-mode plasmas, transport analysis shows that (1) the H-mode obtained with ECH is accompanied by an improvement of the electron thermal diffusivity χ_e relative to the L-mode over at least part of the plasma, (2) the ion thermal diffusivity χ_i is larger than predicted by neoclassical theory for the L- and H-modes, and (3) χ_e is approximately equal to χ_i for the ohmically heated discharge and for the L-mode and H-mode discharges heated by ECH discussed in the paper.

The paper presents ideal MHD stability calculations to show the effect of triangularity δ on the beta limit for plasmas of the NET/ITER type with ellipticity κ = 2 and aspect ratio A = 3.7. Two different types of beta optimizations have been made to clarify the influence of the equilibrium profiles. In the first set of optimizations, current profiles that are flat in the central region are prescribed and the pressure profile is optimized. The resulting pressure profiles are broad, and triangularity has only a weak influence on the beta limit. In the second set, more peaked pressure distributions are prescribed and the current profile is optimized. For peaked pressure profiles, triangularity has a clear, positive effect on the beta limit, and for δ ≥ 0.4 the peaked pressure profiles give about the same beta limit as the broad profiles. For cross-sections of small triangularity, peaking of the pressure profile is clearly unfavourable, and reasonably high beta values can be reached only if the current profile has strong gradients in the central region or if the central safety factor is significantly above unity. This is required for stability of Mercier and ballooning modes. The beta limit is found to be rather weakly dependent on the plasma current for safety factors at the plasma edge in the range of 2.2–5.

Weak external helical fields can act as local resonant disturbances in a tokamak plasma. Such fields can therefore be used as 'active magnetic probes' in the study of MHD instabilities in tokamak plasmas. For this purpose, ℓ = 2/n = 1 and ℓ = 3/n = 1 helical windings have been installed on the HT-6B and HT-6M tokamaks. Diagnostic signals (using magnetic probes, soft X-ray detectors, spectroscopy, electron cyclotron emission, etc.) from MHD instabilities have been obtained and studied during discharges with programmed resonant helical fields (RHFs). It was found that an optimized value of the ℓ = 2 RHF strongly suppressed not only the m = 2/n = 1 magnetic perturbation but also the 3/1, 4/1 and 1/1 modes. It was unexpected that the ℓ = 3 RHF could suppress all m = 2,3,4 modes, as well as (and even more strongly) the m = 1 mode. The ℓ = 2 and ℓ = 3 RHFs could also substantially modify the sawtooth oscillation. During these processes, all MHD modes with different m numbers were tightly coupled, which indicates a global coherent mode structure over the whole plasma rather than individual mode behaviour.

The local energy and particle transport and density profile peaking in improved Ohmic confinement (IOC) discharges of ASDEX have been explored by computer simulations. It is shown that the observed improvement of the energy and particle confinement is due to a two to three times reduction of the electron heat diffusivity χ_e and the diffusion coefficient D that is correlated with the density scale length, while the ion heat diffusivity χ_i is constant. This result agrees with measurements of the diffusion coefficient and with the coupling between χ_e and D which was found in all confinement regimes. It is shown that there are lower limits for χ_e and D. Empirical relations for χ_e, χ_i D and the inward drift velocity v_in and their scalings in different confinement regimes are presented. The enhancement factor for χ_i with respect to the neoclassical value is found to be 1.4. Modelling of the measured density profiles requires a time independent ratio v_in/D and a feedback controlled decline of the fuelling rate. Simulations with a constant high particle source yield no density profile peaking (saturated Ohmic confinement, SOC). At a given line averaged density, two steady state solutions for the density profile are obtained which correspond to high (SOC) and low (IOC) refuelling rates.

The improved divertor confinement (IDC) phenomenon, observed in the JT-60 tokamak, is explained using collisional transport theory. The model successfully describes the correlation between the increase in radiated power at the divertor and the increase in line averaged density of the plasma, which is characteristic of the IDC. Other prominent features of IDC, such as the grad-B drift dependence, divertor heat flux asymmetries and carbon-oxygen impurity exchange, are also explained. The model predicts that IDC could be obtained in deuterium plasmas. The reduction in heat load to the divertor caused by IDC would be an important benefit for a fusion reactor.

Helium glow discharge conditioning of DIII-D is routinely used before every tokamak discharge to desorb hydrogen from the graphite tiles, which are the plasma facing surfaces for the floor, inner wall and top of the vessel. In addition to reducing hydrogen fuelling of the plasma by the graphite surfaces, helium glow discharges are also effective in removing low-Z impurities, primarily in the form of carbon monoxide and hydrocarbons, and this has permitted higher current divertor operation and more rapid recovery from tokamak disruptions. Since the implementation of repetitive helium glow wall conditioning, the parameter space in which tokamak discharges in DIII-D can be obtained has been expanded to include the first observations of limiter H-mode confinement, the Ohmic H-mode with periods of up to 150 ms that are free of edge localized modes, more reliable low q operation with volume averaged beta of up to 9.3%, improved control over locked modes and plasma discharges at lower electron density.

Eroded copper fluxes from the target plates in the ASDEX divertor have been measured spectroscopically. The measuring method is outlined and comprehensive experimental material for various modes of tokamak operation is presented. Assuming thermal sputtering to be the only erosion process, good agreement is found between the code predictions and the measurements.

The transport of particles and energy through a high recycling divertor scrape-off layer (SOL) in a tokamak is studied via a kinetic transport model. This model combines particle-in-cell (PIC) methods with Monte Carlo algorithms which simulate Coulomb collisions and charged/neutral interactions (charge exchange and electron impact ionization). The resulting transport code provides a fully kinetic description of transport and potential formation in a single spatial dimension (along the open field lines of the SOL) and two velocity components (parallel and perpendicular to those field lines). Plasma transport in the SOL system is modelled as a function of neutral particle recycling. The level of neutral recycling is varied by changing the average ionization frequency 〈ν_ion〉 relative to the average Coulomb collision frequency 〈ν_c〉 over the range 0 ≤ ν' ≤ 0.25, with ν' ≡ 〈ν_ion〉/〈ν_c〉. This study indicates that the plasma flow velocity, temperature and total kinetic energy flux decrease as the level of neutral particle recycling is increased. The variation of other transport quantities with neutral recycling intensity is presented, and the results are compared with those from other SOL transport models.

Experiments on the stabilization of highly elongated, vertically unstable plasmas were carried out on the DIII-D tokamak. Identification of the closed-loop transfer function showed that vertical stability could be usefully modelled as a second order dynamical system. The effect of varying the controller gains and the vertical field decay index was studied and found to be qualitatively as predicted by a low order model proposed previously. The implementation of a new hybrid inboard/outboard coil positional control with differing controller dynamics allowed operation of DIII-D up to 92% of the limiting equilibrium field decay index of the vacuum vessel for the plasmas used. This improved control allowed operation at a plasma elongation κ of up to 2.5.

Particle transport in JT-60 was investigated with a simple perturbation method. From an analysis of the sawtooth induced density perturbations, it was found that the particle diffusivity has an inverse dependence on the electron density and that the measured diffusion coefficients correspond to the values obtained from the analysis of pellet induced perturbations. Also, from an analysis of the density and the heat pulse propagations, the ratio of the electron thermal diffusivity and the particle diffusivity, χ_e/D, was estimated to be about four. These experimental results were compared with the drift wave transport models.

The origin of the reduced electron heat diffusivity χ_e and the diffusion coefficient D in the core of H-mode plasmas is investigated. From the evolution of many local parameters in the L- and H-phases of ASDEX it follows that only the density scale length r_n is a possible key parameter. The r_n values are larger in the H-phase, but the electron temperature scale lengths remain unchanged. A local transport law for χ_e and D based on the increase of r_n is tested by self-consistent transport simulations. It works for ASDEX H-mode discharges with edge localized modes, but is incompatible with the broad density profiles observed in other devices.

Enhanced density fluctuations associated with the rational q = 2 (ł = 0.5) surface have been observed by microwave reflectometry in currentless discharges heated by neutral beam injection, with pellet injection at an edge value of the rotational transform ł of 0.52. A radial scan of the MHD activity located the coherent density fluctuations at r/a = 0.7. The frequency and amplitude of these fluctuations have been estimated. The correlation between the level of the local density fluctuation and the ł value during ł modulation at 300 Hz leads to the conclusion that the broadband density fluctuation is enhanced at the points where the rational ł values are crossed. A phase jump in the turbulence modulation occurs for r/a = 0.7, indicating the location of the resonant ł = 0.5 surface. This effect can become the basis of a new method to analyse the evolution of the ł profile inside the plasma, with interesting applications to current control experiments, especially in low shear configurations.

Impurity transport coefficients were determined by means of sinusoidally modulated gas puffing. The principles of the method are outlined, and results for impurity diffusion coefficients, evaluated with respect to a simplified transport model, are presented for measurements on ASDEX during stationary phases. The dependence of the diffusion coefficient on various plasma parameters is found to be in striking contrast to neoclassical theory.

Studies of waves developed in a solid/gas layer driven by a two-step pressure pulse have been performed. The solid is treated with a realistic equation of state and the gas is considered to be ideal. An explicit analytical expression for the Lagrangian distribution of the entropy function p/ρ^γ is found.

In highly elongated DIII-D divertor discharges, it was found that the line integrated X-ray sawtooth inversion radius scales as r_inv/a = 1/q₉₅ for a wide range of plasma parameters including low q and high beta discharges. No density or elongation dependence was observed. The sawtooth inversion radius showed little dependence on injected beam power in H-mode discharges at full toroidal field (2.1 T). At lower fields, the sawtooth inversion radius was observed to increase somewhat with increasing input power. Also, it was found that the sawtooth mixing radius scales as r_mix/a = 1/q₉₅ + 0.3 and is independent of elongation.

An innovative fusion reactor suitable for D-³He fuel is proposed; it is based on a dipole magnetic field produced by a levitated superconducting coil. The equilibrium plasma, whose phase space density satisfies ∂f̑₀(μ,J,ψ)/∂ψ = 0, where ψ is the flux function, has a steep enough pressure profile for an efficient fusion reaction yet is stable to low frequency instabilities for local beta exceeding unity. At the outer wall, the plasma is stabilized by line tying or localized magnetic cusps which can be used for direct conversion. The fusion product confinement time can be controlled for ash removal by breaking the axisymmetry of the dipole magnetic field. A conceptual 70 MW reactor design is presented.

A three-dimensional non-linear toroidal MHD code, MH3D, has been used to study sawtooth oscillations in tokamaks. The simulation results at high temperature agree with the Kadomtsev model, but good agreement with experiment is obtained only if neoclassical resistivity is used. The result Δq₀ ≃ 0.2 is much larger than the value Δq₀ ≃ 0.01 obtained with classical resistivity. To understand this, a formula for q₀(t) is derived. A functional dependence of the sawtooth period and a semi-empirical scaling law are presented. There is some evidence that the fast crash time is due to enhanced resistivity at the singular current sheet.

The 9th International Workshop on Laser Interaction and Related Plasma Phenomena was held from 6 to 10 November 1989, at Naval Postgraduate School, Monterey, California. This series of meetings began in 1969 and it is the longest series of meetings in this field in the USA. It is, in fact, the longest series with published proceedings that document the advances and the growth of this dynamic field of physics and technology.