Table of contents

Mode conversion is studied in the ion cyclotron range of frequencies (ICRF), taking into account the toroidal geometry relevant for tokamaks. The global wavefields obtained using the gyrokinetic toroidal PENN code illustrate how the fast wave propagates to the neighbourhood of the ion-ion hybrid resonance, where it is converted to a slow wave that deposits the wave energy through resonant Landau and cyclotron interactions with the particles. The power deposition profiles obtained are dramatically different from the toroidal resonance absorption, showing that Budden's fluid model is not a good approximation in the torus. Radially and poloidally localized wavefield structures characteristic of slow wave eigenmodes are predicted, which could be used in experiments to form transport barriers and to interact with fast particles.

The expression for the Coulomb collision term in Fokker-Planck form is revised and generalized to the case of interaction of trace impurity ions with a fluid-like background plasma. The velocity distribution of the background ions is assumed as a Maxwellian in the 13 moment expansion, with parameters determined from a fluid consideration. The impurities are described in the framework of a linear drift kinetic test particle model. The new Coulomb term is suitable for linear Monte Carlo procedures and provides both a correct treatment of thermalization of the test particles and an accurate kinetic description of velocity distribution effects on the thermal and frictional forces. These features are missed out in existing codes for kinetic modelling of impurity transport, based on a reduced Coulomb term with these forces treated in the fluid approximation. Numerical results presented for TEXTOR specific edge plasma conditions emphasize the importance of the proposed more accurate treatment, in particular by consideration of the influence of thermal forces on low ionized impurities.

The `outer mode' is one of the MHD modes that limits the fusion performance of the hot ion H mode discharges in JET. It has previously been proposed that the outer mode is a non-linearly saturated external kink mode. This was based on the localization of the perturbation close to the edge as observed in soft X ray (SXR), electron temperature and electron density measurements. In addition, MHD stability calculations showed that the plasma edge is close to the ideal external kink stability boundary at the time when the outer mode is observed. The SXR data of the outer mode are compared with predictions based on the mode structure of the ideal n = 1 external kink mode. Excellent agreement is found, confirming the identification of the outer mode as an external kink mode.

Nickel has been injected into ohmic Tore Supra (TS) discharges with and without activation of the ergodic divertor (ED). The nickel ion transport is studied by means of an impurity transport code, and the radial profiles of the diffusion coefficient D and of the inward convection velocity V are obtained by simulating the soft X ray brightness and emissivity time evolutions. The simulations confirm two previously reported conclusions: the presence of a central core with reduced transport coefficients and, with the ED activated, the necessity of introducing a peripheral transport barrier (with increased inward convection and/or reduced diffusion). To make satisfactory simulations in both experimental conditions of the initial phase of the nickel ion inflow before the first inverted sawtooth, it is necessary to increase transiently the diffusion coefficient (by 1 order of magnitude or more) during the first few milliseconds after the injection. By comparison of the experimental and simulated bolometric signals, it is possible to verify quantitatively the available calculations of the global radiative losses for nickel. The observed discrepancy by a factor of 2 is discussed. The inward propagating cold wave, following the nickel injection, has been observed with a heterodyne radiometer (monitoring the electron temperature). Both with and without the ED, good simulations of the cold wave propagation are obtained using a predictive non-local transport model, previously successfully tested in JET during transient regimes. The model predicts large increases of the electron thermal diffusivity χ_e, by a factor of 5, immediately after the injection and describes well the electron temperature profile in the so-called heat transport dominated region outside the q = 1 surface. The experimental signals are smoothed with the `generalized singular value decomposition' technique, reducing the effect of the sawtooth modulation; the simulation can, therefore, be more clearly compared with the measurements. It is not possible, using present experimental data, to demonstrate the existence of an electron diffusivity transport barrier inside the q = 1 region, as done for the impurity transport, because the temperature profile is strongly affected by sawteeth in this region. Similarities have been found in the time evolutions of the electron temperature and of the Abel inverted soft X ray emissivities at fixed radii, implying similar time behaviour of D and χ_e outside the q = 1 surface.

The operation of reversed shear plasmas in JT-60U has been extended to the low-q, high-I_p region keeping a large radius transport barrier, and a high fusion performance has been achieved. Record values of deuterium-tritium (DT)-equivalent power gain in JT-60U have been obtained: Q_DT^eq = 1.05, τ_E = 0.97 s, n_D(0) = 4.9 × 10¹⁹ m^-3 and T_i(0) = 16.5 keV. A large improvement in confinement resulted from the formation of an internal transport barrier (ITB) with a large radius, which was characterized by steep gradients in electron density, electron temperature and ion temperature just inside the position of q_min. Large negative shear regions, up to 80% of the plasma minor radius in the low-q_min regime (q_min∼2), were obtained by plasma current ramp-up after the formation of the ITB with the pressure and current profiles being controlled by adjustment of plasma volume and beam power. The ITB was established by on-axis beam heating into a low density target plasma with reversed shear that was formed by current ramp-up without beam heating. The confinement time increased with the radius of the ITB and the decrease of q_min at a fixed toroidal field. High H factors, up to 3.3, were achieved with an L mode edge. The effective one fluid thermal diffusivity χ_eff had its minimum in the ITB. The values of H/q₉₅ and β_t increased with the decrease of q₉₅, and the highest performance was achieved at q₉₅ ∼3.1 (2.8 MA). The performance was limited by disruptive beta collapses with β_N∼2 at q_min∼2.

During the initial experimental phase, LHD, a stellarator of the heliotron/torsatron variety presently under construction, will operate at a magnetic field lower than the nominal one. In this scenario, the frequency of the available gyrotrons (chosen in view of second harmonic heating at full field operation) will be resonant with the third or the fourth harmonic of the electron gyrofrequency. The aim of this article is to analyse the electron cyclotron resonance heating (ECRH) at these high harmonics. By using linear absorption theory, together with transport predictions, good absorption is found over a wide density range for third harmonic heating. In the case of the fourth harmonic, the conditions for absorption are considerably more critical, but non-negligible heating (single pass absorption ≳ 10%) is expected in very low density, high temperature target plasmas. Owing to the strong temperature dependence of the absorption mechanism, heating at higher harmonics presents some peculiar characteristics. Quasi-linear effects are found to improve the absorption properties (as compared with those of linear theory), and bifurcation phenomena, as well as a critical power threshold, might appear. The physical origin and the consequences of these effects are discussed.

First of a kind measurements of high-frequency ion temperature microturbulence in fusion-grade plasmas have been made in TFTR. The ion temperature fluctuations and carbon density fluctuations were found to have spectra similar to those of the ion density fluctuations across the plasma radius. The ratio of the relative fluctuation levels, (/T)/(ñ/n), is 2 ± 0.5 from r/a = 0.59 to r/a = 0.99. The fact that this ratio is greater than unity is consistent with the general expectations of ion temperature gradient driven turbulence theory and suggests that ion drift modes dominate trapped electron modes in the turbulent spectrum. The temperature fluctuation spectra were found to exhibit a narrow transition region between distinctive edge and core turbulent modes, as has been seen with ion density fluctuations. The ratio of the relative fluctuation levels is greater than unity across this transition, which suggests that, despite the different modes present, the underlying instability is driven by the ion temperature gradient.

A compact toroid (CT) penetrating into a tokamak discharge is modelled as a conducting solid sphere with an intrinsic magnetic moment. Equations of CT motion in tokamak discharges are derived and used to calculate the trajectory of a CT with parameters pertinent for penetrating the ITER tokamak. The advantage of tangential CT injection and the optimal direction of the initial magnetic moment are discussed.

At the onset of neutral beam injection (NBI) in JET, the toroidal angular momentum is observed to rise rapidly in the outer regions of the plasma. The toroidal angular momentum in the plasma centre, where the fast ions are injected into passing orbits, and the thermal energy are found to rise on the slowing down time-scale of the fast ions. This behaviour can be explained by a model that incorporates three mechanisms for momentum transfer of fast ions to the bulk: (a) quasi-instantaneous, or first orbit, transfer which results mainly from particles that are injected into trapped orbits, (b) collisional transfer of momentum from passing ions during their slowing down process, (c) enhancement of the total angular momentum of the rotating plasma once the particles have thermalized. The model for the torque is applied to the study of toroidal angular momentum confinement in transient hot ion H mode plasmas in JET. In contrast to steady state conditions, such as L mode and ELMy H mode, where the toroidal angular momentum confinement time τ_L is approximately equal to the thermal energy confinement time τ_E, τ_L is found to be about a factor of 2 smaller than τ_E in the transient part of the ELM-free phase of the discharge.

Ion cyclotron range of frequencies (ICRF) heating experiments with the third harmonic deuterium resonance in the plasma centre have been carried out at JET. These experiments were the first to demonstrate third harmonic damping on initially Maxwellian plasmas. A record deuterium-deuterium (DD) fusion reaction rate for ICRF-only heating on JET was achieved. The discharges have been simulated with the PION code (a self-consistent calculation of the evolution of the distribution function and the ICRF power deposition). To obtain reasonable agreement between the measurements and the simulations, three additions to the PION code were necessary: (a) parasitic absorption at the plasma edge, (b) a particle loss term that removes particles above 4 MeV, i.e. the particles that were not confined in the discharges, and (c) a sawtooth model that accounts in a simplified way for the redistribution of fast ions at the sawtooth crashes. According to the simulations, high energy tail formation on the distribution function of the resonating ions plays a crucial role in the power absorption.

The effect of Z_eff on the runaway generation process by close collisions has been studied experimentally in the TEXTOR-94 tokamak in ohmic low density discharges. It is shown that the effective avalanching time increases with increasing Z_eff. This opens the possibility of controlling the runaway production in tokamaks by active impurity injection. Furthermore, the energy of the runaway electrons emitting the observed synchrotron radiation could be determined to be W_r ≈ 20 MeV. However, for ITER-like disruptions the runaway production will probably be reduced but not prevented by a Z_eff increase.

Electron cyclotron wave current startup has been investigated in a wide range of toroidal magnetic fields on the CT-6B tokamak. Two kinds of drive mechanisms of current startup have been identified experimentally, according to the dependence of the wave started current on the vertical field. Their contributions to the current have been estimated quantitatively for different resonance scenarios. The wave started current may occur at a downshifted resonance frequency even if the resonance layer is located outside the vacuum vessel.

Radiative mantle scenarios of the ignited ITER Engineering Design Activity (EDA) with argon and neon influxing are explored by computer experiments using special versions of the 1.5 dimensional (1.5-D) BALDUR predictive transport code. An empirical scaling law for the effective heat diffusivity, compatible with the ITERH92-P ELMy H mode scaling and validated against experiments, is applied. The prescribed flat density profiles, conductive heat loss across the separatrix of 200 MW and ratio τ*_He/ τ_E,r of 10 are reached in the simulations. Self-sustained thermonuclear burn is achieved for at least 485 s. The helium ash concentrations of up to 9.5% are found to cause significant fuel dilution. Owing to the high electron density, only small argon and neon fractions of 0.07 and 0.27%, respectively, are needed. In the argon scenario, the required radiation corrected thermal energy confinement time τ_E,r is 4.8 s. The confinement time predicted by the local scaling law is 1.4 times longer and agrees with the global scaling prediction. With argon, the design parameters are reached by radiating 128 MW within the separatrix, thus reducing the energy flow to the divertor to 73 MW. In the neon case with its more peripheral radiation, the radiative loss within the separatrix has to be diminished. Owing to the flat profile of the fuel ion density, the neoclassical drift velocities of argon and neon are directed outwards in the whole plasma. In the argon scenario, the sensitivity of transport to the density profile shape is studied. It is found that τ_E,r remains almost unchanged, varying between 4.5 and 4.8 s, which is explained by an analytic expression for the thermal energy. Peaking of the electron and impurity densities does not alter the required argon concentration but causes a peaking of the radiation profiles and reduction in the temperatures. Sufficiently narrow fuel ion density profiles are shown to cause inward directed neoclassical drift velocities of argon in the collisionless plasma. The minimum density for steady state operation at the designed alpha particle heating power, still compatible with the transport predicted by the heat diffusivity scaling, is found to be ⟨n_e⟩ = 9.1 × 10¹⁹ m^-3.

The primary purpose of `Computational Atomic Structure' is to give a potential user of the Multi-Configuration Hartree-Fock (MCHF) Atomic Structure Package an outline of the physics and computational methods in the package, guidance on how to use the package, and information on how to interpret and use the computational results. The book is successful in all three aspects. In addition, the book provides a good overview and review of the physics of atomic structure that would be useful to the plasma physicist interested in refreshing his knowledge of atomic structure and quantum mechanics. While most of the subjects are covered in greater detail in other sources, the book is reasonably self-contained, and, in most cases, the reader can understand the basic material without recourse to other sources. The MCHF package is the standard package for computing atomic structure and wavefunctions for single or multielectron ions and atoms. It is available from a number of ftp sites. When the code was originally written in FORTRAN 77, it could only be run on large mainframes. With the advances in computer technology, the suite of codes can now be compiled and run on present day workstations and personal computers and is thus available for use by any physicist, even those with extremely modest computing resources. Sample calculations in interactive mode are included in the book to illustrate the input needed for the code, what types of results and information the code can produce, and whether the user has installed the code correctly. The user can also specify the calculational level, from simple Hartree-Fock to multiconfiguration Hartree-Fock.

The MCHF method begins by finding approximate wavefunctions for the bound states of an atomic system. This involves minimizing the energy of the bound state using a variational technique. Once the wavefunctions have been determined, other atomic properties, such as the transition rates, can be determined.

The book begins with an introduction to atomic structure. It covers single and many electron systems, how to set up a basis set of wavefunctions for a many electron system, LS coupling, single and multi-electron Hamiltonians, the elementary Hartree-Fock approximation and how variational methods are used to determine the ground state energy and wavefunctions. The computational methods used in the codes are outlined and there are exercises at the end of each chapter. For a number of candidate atomic configurations, explicit examples are given that illustrate the physics, the approximations and the computational methods involved, and which provide the reader with the opportunity to check that he is using the suite of codes correctly.

Relativistic effects are covered as perturbations with Breit-Pauli Hamiltonians. Isotope and hyperfine level splitting are also covered. A summary chapter covers allowed and forbidden bound-bound transitions. It describes how to set up the matrix elements for transition operators, and the determination of selection rules and computational aspects of the methods for allowed and forbidden lines. The last chapter provides a brief introduction to continuum transitions, including how to compute the necessary wavefunctions to calculate photoionization or photodetachment and autoionization processes.

Several appendices provide a summary of angular momentum theory, an introduction to the Dirac and Breit-Pauli theory for relativistic processes, and a description of the input parameters needed to run the programs.

In summary, the book is an almost essential guide to anyone planning to use the Multi-Configuration Hartree-Fock suite of codes. With this guide, even someone not thoroughly familiar with the details of the subject or the codes should be able to use them to obtain energy levels, wavefunctions and transition rates for any atomic system of interest. This book serves as a model example for the general computational physics community of how to document an important suite of codes for a wide number of researchers and really make the suite usable to the general physics community. The book would also be useful to someone seeking a survey of the physics of atomic structure and how it can be calculated. A limitation of the book is that it covers only isolated atoms and ions. Density effects are not covered. Plasma physicists, especially spectroscopists, interested in calculating line positions, line strengths and other atomic properties will find this book and suite of codes useful.