Table of contents

The influence of finite orbit width effects and wave induced spatial diffusion on the resonant ion distribution function in the presence of ion cyclotron resonance heating (ICRH) is studied. In particular, it is found that the toroidal wavenumber spectrum affects the fast ion energy density and the local formation of the high energy tail. For high energy ions interacting with waves having a large toroidal wavenumber, the wave induced spatial diffusion plays an equal or even more important role than the finite orbit width. Only in the limit of artificially high plasma current and low toroidal wavenumber are results from two dimensional (2-D) orbit averaged Fokker-Planck models recovered. The finite orbit width and the wave induced spatial diffusion also produce ions that follow loss orbits, resulting in localized high energy ions losses to the wall

An artificial neural network, combining signals from a large number of plasma diagnostics, was used to estimate the high- beta disruption boundary in the DIII-D tokamak. It is shown that inclusion of many diagnostic measurements results in a much more accurate prediction of the disruption boundary than that provided by the traditional Troyon limit. A trained neural network constitutes a non-linear, non-parametric model of the disruption boundary. Through the analysis of the input-output sensitivities, the relative statistical significance of various diagnostic measurements (plasma parameters) for the determination of the disruption boundary is directly assessed and the number of diagnostics used by the neural network model is reduced to the necessary minimum. The neural network is trained to map the disruption boundary throughout most of the discharge. As a result, it can predict the high- beta disruption boundary on a time-scale of the order of 100 ms (much longer than the precursor growth time), which makes this approach ideally suitable for real time application in a disruption avoidance scheme. Owing to the relative simplicity of the required computations, the neural network is easily implemented in a real time system. A prototype of the neural network disruption alarm was installed within the DIII-D digital plasma control system, and its real time operation, with a typical time resolution of 10 ms, was demonstrated

To alleviate the plasma-wall interaction problems in magnetic confinement devices, a stochastic layer is used at the edge of the Tore Supra tokamak (ergodic divertor). A very important point is to determine the power deposition on the plasma facing components. Two different kinds of transport can be identified in such a configuration: stochastic transport surrounding the confined plasma, with a random walk process, and scrape-off layer (SOL) like transport, a laminar transport, near the plasma facing components. The laminar regime is investigated in terms of a simple criterion, namely that the power deposition is proportional to the radial penetration of the laminar zone flux tubes over a finite parallel length. The magnetic connection properties of the first wall components are then determined. The connection lengths are quantified with two characteristic scales. The larger corresponds to one poloidal turn and appears to be the characteristic parallel length for laminar transport. A field line tracing code MASTOC (magnetic stochastic configuration) is used to compute the complex topology and the statistics of the connection in the real tokamak geometry. The numerical simulations are then compared with the experimental heat deposition on the modules and neutralizer plates of the Tore Supra ergodic divertor. Good agreement is found. Further evidence of laminar transport is also provided by the tangential view of such structures revealed from H_alpha structures in detached plasma experiments

A database containing global energy confinement data for JET ohmic plasmas in the campaigns from 1984 to 1992 has been established. An analysis is presented of this database and the results are compared with data from other tokamaks, such as the Axially Symmetric Divertor Experiment (ASDEX), Frascati Tokamak Upgrade (FTU) and Tore Supra. The trends of JET ohmic confinement appear to be similar to those observed on other tokamaks: a linear dependence of the global energy confinement time on density is observed up to a density value where a saturation is attained; this density value defines the border between the linear and the saturated ohmic confinement regimes; this border is shifted towards higher density values if the q value of the discharge is decreased; the global confinement time in the saturated ohmic regime increases less than linearly with the value of the magnetic field

The results of a three dimensional (3-D) (in constants of motion space) Fokker-Planck simulation of the steady state collisional behaviour of fusion alphas in an axisymmetric TFTR-like tokamak plasma are presented. The distribution function of confined fusion products is shown to be strongly anisotropic and non-uniform in the radial co-ordinate. The influence of pitch angle scattering on distribution function anisotropy is investigated. It is shown that the distribution function of fast ions in the range where the cosine of the pitch angle is small is strongly influenced by this scattering. A qualitative comparison of numerical results and predictions of alpha particle distributions from previous studies is presented

Recent results on feedback control of the global shape of the current density profile in discharges with lower hybrid current drive (LHCD) on Tore Supra are presented. The global shape of the current density profile is characterized by its internal inductance l_i, and feedback controlled through the LH power or the launched LH wave spectrum. Feedback control of the flux on the plasma boundary has allowed for exploration of regimes with partial current drive (constant loop voltage) and full current drive (zero loop voltage). In stationary, steady state discharges at 0.8 MA (qa=7), the current profile shape is characterized by an l_i between 1.5 and 1.7 and a safety factor on-axis (q₀) between 1 and 1.4. The energy confinement is 1.3 to 1.6 times higher than the value predicted by the Rebut-Lallia-Watkins scaling law

A series of experiments, examining the confinement properties of ion cyclotron range of frequencies (ICRF) heated H mode plasmas, has been carried out on the Alcator C-Mod tokamak. Alcator C-Mod is a compact tokamak that operates at high particle, power and current densities at toroidal fields up to 8 T. Under these conditions the plasma is essentially thermal with very little contribution to the stored energy from energetic ions (typically no more than 5%) and with T_i~T_e. Most of the data were taken with the machine in a single null `closed' divertor configuration with the plasma facing components clad in molybdenum tiles. The data include those taken both before and after the first wall surfaces were coated with boron, with emphasis on the latter. H modes obtained from plasmas run on boronized walls typically had a lower impurity content and radiated power and attained a higher stored energy than those run on bare molybdenum. Confinement enhancement, the energy confinement time normalized to L mode scaling, for discharges with boronized walls, ranged from 1.6 to 2.4. The unique operating regime of the Alcator C-Mod device provided a means for extending the tests of global scaling laws to parameter ranges not previously accessible. For example, the Alcator C-Mod edge localized mode (ELM)-free data were found to be 1.1 to 1.6 times the ITERH93 scaling and the ELMy data almost 2.0 to 2.8 times the ITERH92 ELMy scaling law, suggesting that the size scaling in both scalings may be too strong. While both ELM-free and ELMy discharges were produced, the ELM characteristics were not easily compared with observations on other devices. No large, low frequency ELMs were seen despite the very high edge pressure and temperature gradients that were attained. For all of our H mode discharges, a clear linear relationship between the edge temperature pedestal and the temperature gradient in the core plasma was observed; the discharges with the `best' transport barriers also showing the greatest improvement in core c

In nearly all hot ion H modes in JET, a magnetohydrodynamic (MHD) event is clearly observed just before the time the stored plasma energy saturates and the neutron yield starts to decline. The results of a systematic analysis of MHD observations for a large number of discharges is reported. The relationship between MHD phenomena and the onset of confinement limitation is discussed, as are aspects of the three main types of performance limiting MHD: (a) low-n modes in the outer regions of the plasma, (b) sawteeth and (c) giant edge localized modes (ELMs). Model simulations indicate how the transport is affected and allow an assessment of how much the neutron yield would be improved if the MHD activity were absent

The radiative cooling coefficient for molybdenum (Z=42) in a low density (n_e ≲ 10¹⁵ cm^-3) plasma is calculated. First, the molybdenum charge state distribution (CSD) is computed using the best available atomic physics data for ground state recombination and ionization, including the rates of excitation-autoionization for Mo⁶⁺ to Mo¹³⁺ and Mo²³⁺ to Mo³²⁺. The emissivities of Mo⁴⁺ to Mo⁴¹⁺ are then found using a collisional-radiative model such that the contributions from metastable levels to an ion's emissivity are taken into account. The CSD and the radiative emissivity for all molybdenum ions are combined to yield the total radiative cooling coefficient for molybdenum in a low density plasma. A radiative loss coefficient over 2 orders of magnitude smaller than that predicted by an `average ion' model for temperatures relevant to tokamak divertor and scrape-off layer plasmas (T<sub>e</sub> ≲ 50 eV) is found. The cooling coefficient of the present work varies from a factor of 2 smaller to a factor of 2 larger than that predicted by the `average ion' model for all other plasma temperatures. The coefficient calculated in the present work is benchmarked against the measured bolometric loss profile from a molybdenum dominated shot in the Frascati Tokamak Upgrade (FTU)

The characteristics of the ion current driven by localized minority ion cyclotron heating in tokamaks in the presence of a well enhanced high energy tail are examined by fully toroidal Monte Carlo guiding centre simulations. The contribution of the diamagnetic current to the minority current drive has been found to be of importance as it dominates the resulting fast ion current in the presence of significant toroidal trapping of RF heated minority ions, and also because it is excited even with symmetric launching, thus requiring no directivity in the antenna system. The driven currents from the simulation are compared with a functional form approximating the trapped ion contribution to the minority ion diamagnetic current in the strong heating limit. The bidirectional current profile, the dependence on wave intensity and the increase of the current generation efficiency with electron temperature and with the inverse major radius as predicted by the Monte Carlo simulations are satisfactorily reproduced by the estimate

Results of magnetic surface mapping experiments over the whole operational range of the TJ-I U torsatron are reported. A theoretical model of the coil sets that includes internal and external error fields has been developed. It accounts for the main experimental features of the magnetic surfaces measured in the different magnetic configurations: size and shape of the surfaces, magnetic axis position and rotational transform dependence on the coil currents

A fast transport modelling code is applied to the transport profile database recently assembled by the ITER Transport Modeling and Database Group. Five published transport models currently in use are tested against a subset of DIII-D, JET and TFTR L and H mode discharges. The database provides little discrimination between the best fitting and the worst fitting models. Allowing for the fact that given experimental boundary conditions are critical elements of the models, it is shown that the present one dimensional transport models give only marginally better predictions than the ITER89P and ITER93H global scaling laws (GSLs). The difficulty of distinguishing the relative gyroradius ( rho *) scalings of transport models is discussed by focusing on the DIII-D dimensionally similar discharge pairs. There is a considerable difference in how the models project to ignition in ITER

The intrinsic impurity content of molybdenum and carbon was measured in the Alcator C-Mod tokamak using low resolution, multilayer mirror (MLM) spectroscopy ( Delta lambda ~1-10 AA). Molybdenum was the dominant high-Z impurity and originated from the molybdenum armour tiles covering all of the plasma facing surfaces (including the inner column, the poloidal divertor plates and the ion cyclotron resonant frequency (ICRF) limiter) at Alcator C-Mod. Despite the all metal first wall, a carbon concentration of 1 to 2% existed in the plasma and was the major low-Z impurity in Alcator C-Mod. Thus, the behaviour of intrinsic molybdenum and carbon penetrating into the main plasma and the effect on the plasma must be measured and characterized during various modes of Alcator C-Mod operation. To this end, soft X-ray extreme ultraviolet (XUV) emission lines of charge states, ranging from hydrogen-like to helium-like lines of carbon (radius/minor radius, r/a~1) at the plasma edge to potassium to chlorine-like (0.4<r/a<0.6) and magnesium- to sodium-like (r/a<0.4) lines of molybdenum in the main plasma, were measured using a novel, low resolution, photometrically calibrated polychromator with MLMs as dispersive elements. The MLM spectra were investigated in detail, and comparisons with high resolution spectroscopy were made. The utility of low resolution spectroscopy to diagnose tokamak plasmas is presented, and meaningful information about impurity behaviour was obtainable owing to the specific choice of the observed spectral regions. Ab initio physics rates from the HULLAC atomic physics package were input into the collisional radiative (CR) model and the multiple ionization state transport (MIST) code, and both MIST and the CR model were used in the interpretation of the molybdenum spectrum. The carbon spectrum was interpreted using the MIST code and the direct impact rates of Itikawa (Itakawa, Y., et al., At Data Nucl. Data Tables 33 (1985) 149), which were incorporated into the collisional radiative model. The intrinsic i

Corrections to Nuclear Fusion36 (1996) 1647.