Table of contents

A system of plasma particle and parallel momentum balance equations is derived appropriate for understanding the role of drifts in the edge and for edge modelling, particularly in the scrape-off layer (SOL) of tokamaks, stellarators and other magnetic confinement devices. The formulation allows for strong collisionality—but also covers the case of weak collisionality and strong drifts, a combination often encountered in the SOL. The most important terms are identified by assessing the magnitude of characteristic velocities and fluxes for the plasma edge region. Explanations of the physical nature of each term are provided. A number of terms that are sometimes not included in edge modelling has been included in the parallel momentum balance equation after detailed analysis of the parallel component of the gradient of the total pressure-stress tensor. This includes terms related to curvature and divergence of the field lines, as well as further contributions coming from viscous forces related mainly to the ion centrifugal drift. All these terms are shown to be roughly of the same order of magnitude as convective momentum fluxes related to drifts and therefore should be included in the momentum balance equation.

Transport simulations of JET H-mode plasmas with different ν_eff have been performed in order to quantify the relative effect of the particle source and anomalous pinch on the gradient of the density profile. It is found that, in general, the wall ionization source and the Ware pinch velocity are not sufficient to explain the density peaking. Adding the particle source due to neutral beam injection (NBI) and an anomalous pinch proportional to D∇q/q gives results that are compatible with the experimental measurements. However, the effects of the two terms are comparable and difficult to separate. The presence of an anomalous pinch can only be clearly identified in shots heated mainly by ion cyclotron resonance heating (ICRH) where the NBI particle source is negligible.

Damaging effects of disruptions are a major concern for Alcator C-Mod, ITER and future tokamak reactors. High-pressure noble gas jet injection is a mitigation technique which potentially satisfies the operational requirements of fast response time and reliability, while still being benign to subsequent discharges. Disruption mitigation experiments using an optimized gas jet injection system are being carried out on Alcator C-Mod to study the physics of gas jet penetration into high pressure plasmas, as well as the ability of the gas jet impurities to convert plasma energy into radiation on timescales consistent with C-Mod's fast quench times, and to reduce halo currents given C-Mod's high-current density. The dependence of impurity penetration and effectiveness on noble gas species (He, Ne, Ar, Kr) is also being studied. It is found that the high-pressure neutral gas jet does not penetrate deeply into the C-Mod plasma, and yet prompt core thermal quenches are observed on all gas jet shots. 3D MHD modelling of the disruption physics with NIMROD shows that edge cooling of the plasma triggers fast growing tearing modes which rapidly produce a stochastic region in the core of the plasma and loss of thermal energy. This may explain the apparent effectiveness of the gas jet in C-Mod despite its limited penetration. The higher-Z gases (Ne, Ar, Kr) also proved effective at reducing halo currents and decreasing thermal deposition to the divertor surfaces. In addition, noble gas jet injection proved to be benign for plasma operation with C-Mod's metal (Mo) wall, actually improving the reliability of the startup in the following discharge.

Results from MAST concerning the effect of toroidal rotation driven by neutral beam injection (NBI) on sawteeth are presented. The sawtooth period is shown to increase as the co-NBI power, and thus the toroidal plasma rotation, is increased. As the counter-NBI power is increased, the sawtooth period decreases to a minimum that is shorter than in Ohmically heated plasmas, before lengthening at high toroidal flows. The sawtooth period reaches a minimum when the sawtooth precursor changes the direction of rotation. This can be interpreted as the counter-NBI inducing a toroidal flow which balances the intrinsic ion diamagnetic rotation of the plasma, at which point the mode precursor changes direction. Magnetohydrodynamic stability analyses of the ideal n = 1 internal kink mode with respect to toroidal rotation at finite ion diamagnetic frequency show good accordance with the experimental results. When MAST discharges are modelled at the experimental ion diamagnetic frequency, , the ideal n = 1 internal kink mode is stabilized completely by co-rotation approaching the ion sound speed. When the rotation is oriented in the counter- direction, the mode is initially driven more unstable, before being stabilized by high toroidal flows. Experimentally, the radial extent of the sawtooth crash, and hence the q = 1 surface, varies with respect to the sawtooth period. Stability analyses show that the marginally stable radial location of the q = 1 surface reaches a minimum at approximately the same counter-toroidal rotation as that which minimizes the sawtooth period experimentally. The magnitude of the toroidal rotation at the q = 1 surface determines the stabilizing effect of the toroidal flow upon the ideal n = 1 internal kink mode.

A general zero-dimensional modelling of implosion without thermonuclear reactions is presented, for standard indirectly driven capsules. It is not substantially a new theory, but new demonstrations and improvements of existing models. The model is derived directly from the gas dynamics conservation equations written in integral form for fluid domains with variable mass, in effect the whole non-ablated capsule, the hot spot and the dense shell. The necessary approximations which involve global or mean quantities are justifed theoretically and checked by comparisons with numerical simulations. Two different sets of approximations are developed, one for each of the acceleration and the deceleration phases of the implosion. An improved—in the sense that the time variation of the hohlraum temperature is fully taken into account as it is required for high gain capsules—rocket model is proposed for the acceleration phase. With further approximations, it gives the maximum implosion velocity and the initial capsule mass corresponding to a given final capsule mass, in terms of the initial outer deuterium–tritium radius and the maximum hohlraum temperature. For the deceleration phase, the present model gives an analytical solution for the time decrease in the implosion velocity up to stagnation. Assuming the invariance of PV^γ for the different media considered—a property only approximately verified—this model defines the state of these mediums in deceleration and at stagnation, in terms of the mean entropy parameters, the capsule mass, the mean implosion velocity at the end of acceleration and the initial gas mass filling the shell. A simple ODE, which can be easily integrated numerically, is derived for the hot spot mass which depends on the heat conduction wave ablating the fuel from the inside. All the numerical coefficients presently involved in the model can be calculated from the EOS, opacities and heat conduction parameters, except for the value of the supplementary energy transferred to the non-ablated capsule during deceleration which has been taken here, for simplicity, from simulations. Results obtained with this modelling are shown to be in reasonable agreement with numerical simulations for several different capsules.

Measured damping rates of stable toroidal Alfvén eigenmodes (TAEs) have been compared with damping rates calculated with the NOVA-K code for a number of experimental conditions on Alcator C-Mod to test the NOVA-K damping model. Very low amplitude ( 10⁻⁷ at the wall) stable TAEs are excited in Ohmic plasmas with a pair of active MHD antennas inside C-Mod. By sweeping the excited frequency of the antennas through the expected TAE frequency, the frequency width of a mode resonance can be measured with poloidal field pick-up coils on outboard limiters to determine the damping rate of that mode. The calculated equilibrium and main plasma parameters at the time of the resonance are input into the NOVA-K code to then calculate the expected damping rate for the measured toroidal mode number and compare with the experimental value. The calculations include continuum damping, Landau damping on both the electrons and the background and impurity ions and collisional damping on the electrons. Comparisons have been made for inner wall limited and diverted cases over a range of ITER-relevant moderate toroidal mode numbers (4 ⩽ |n | ⩽ 9). Good agreement between the experiment and theoretical calculations can be obtained with reasonable q profiles for the plasma conditions in which perturbative NOVA models are applicable, but the results are found to depend very sensitively on the assumed q profile.

Experiments in H-mode plasmas have shown that both heat and particle transport are sensitive to the ratio between electron and ion temperature (T_e/T_i). While decreasing T_e/T_i is beneficial for confinement, an increased electron heating in these so called 'hot ion plasmas' deteriorates the confinement. H-mode plasmas with low T_e/T_i are often accompanied by high toroidal rotation velocity (v_ϕ). Its gradient (∇v_ϕ) can destabilize the ion temperature gradient mode (ITG) through its parallel component in the parallel velocity shear, but it has also stabilizing effects since it produces an E × B shearing rate (ω_{E × B}). In this paper, the effects of electron heating on the ion heat transport is investigated in H-mode plasmas heated by neutral beam injection (NBI) and electron cyclotron heating (ECH). In particular, the correlation on T_e/T_i and ∇v_ϕ is studied and compared with calculations made with GLF23 and GS2. Experimentally it is shown that the normalized gradient length of the ions ( ) is correlated with both T_e/T_i and ∇v_ϕ: peaked ion temperature profiles are only obtained with low T_e/T_i and high ∇v_ϕ, and vice-versa. When ECH is added, both ion heat and momentum transport are enhanced, leading to a drop of both the T_i and v_ϕ profiles. The effective growth rate γ_eff = γ−ω_{E × B} is calculated, with the mode growth rate γ determined with GS2 and ω_{E × B} with GLF23. The ion transport is enhanced due to the decrease of the ITG threshold with increasing T_e/T_i. Comparison of the dependence of on T_e/T_i and ∇v_ϕ between experiments and modelling indicates that the deterioration of confinement cannot be explained by the changes in only T_e/T_i or ∇v_ϕ, but by the combined effects of both parameters. The changes in T_e/T_i act directly on the ITG threshold, while the ones in ∇v_ϕ modify the ω_{E × B} shearing rate leading to changes in the effective threshold.

The full text of this introduction is available in the PDF.

The PDF file provided contains web links to all articles in this volume.