Table of contents

A new kind of plasma diagnostics, geodesic acoustic mode (GAM) spectroscopy, is proposed. Radial eigenmodes of GAMs with discrete eigenfrequencies in toroidal plasmas are analysed. The eigenmode has a wavelength of the order of (ρ_i the ion gyroradius, L_T the temperature gradient scale length) and has the highest peak near the radius where the eigenfrequency coincides with the local GAM frequency. Therefore, observing the radial position of the highest peak of the eigenmode provides a method to measure the local ion sound velocity. A novel method to measure the ion composition is given, combined with densities and temperatures.

During the last decade, significant progress has been made in the field of pellet injection with (1) the identification of the drift of the deposited material in the inhomogeneous magnetic field that opened the possibility of fuelling efficiently the plasmas from the high-field side of the torus, (2) the technique to mitigate ELMS in H-mode discharges with shallow pellet injection at high frequency and (3) with the development of high density, high performance scenarios close to the ITER requirements. Both the experimental and theoretical aspects of this domain are reviewed in this paper.

Recent gyrokinetic stability calculations have revealed that the spherical tokamak is susceptible to tearing parity instabilities with length scales of a few ion Larmor radii perpendicular to the magnetic field lines. Here we investigate this 'micro-tearing' mode in greater detail to uncover its key characteristics and compare it with existing theoretical models of the phenomenon. This has been accomplished using a full numerical solution of the linear gyrokinetic–Maxwell equations. Importantly, the instability is found to be driven by the free energy in the electron temperature gradient as described in the literature. However, our calculations suggest it is not substantially affected by either of the destabilizing mechanisms proposed in previous theoretical models. Instead the instability is destabilized by interactions with magnetic drifts and the electrostatic potential. Further calculations reveal that the mode is not significantly destabilized by the flux surface shaping or the large trapped particle fraction present in the spherical tokamak. Its prevalence in spherical tokamak plasmas is primarily due to the higher value of plasma β and the enhanced magnetic drifts due to the smaller radius of curvature.

In this article we investigate the physics and develop a theoretical model to perform computations of the Rosseland and Planck mean and multi-group opacities of weakly non-ideal Flibe plasma generated in the inertial fusion energy chamber. Ionization equilibrium and partition functions of all Flibe plasma species are modelled considering the plasma environmental influence (non-ideal effects) on the electronic structure in a static way within the chemical picture. A recently developed reduced formulation and efficient algorithm is used to solve the resulting set of equations and to determine the detailed plasma composition and partition functions for non-ideal Flibe plasma systems. The algorithm considerably reduces the computational efforts required to determine the plasma composition and allows, with considerable simplicity, the determination of all population densities of all plasma species (neutrals, ionized and excited) up to maximum ionization states equal to the atomic numbers of the involved chemical elements and considers an extensive database of energy levels of the excited states and line spectra. The calculated detailed composition is used along with the above mentioned theoretical opacity model to calculate the radiative properties of the Flibe plasma. Optical characteristics such as multi-frequency absorption coefficient, Planck's and Rosseland's mean and muli-group opacities of weakly non-ideal Flibe plasmas are calculated over a wide range of the density-temperature phase space and are presented as a set of isochors.

The Richardson–Lucy (RL) method of decoding used for x-rays code-aperture imaging (RAM) is proposed in this paper. The Wiener filter method cannot get the ideal result because of a lack of prior knowledge about the signal-noise ratio while the RL method gets a very good decoding result because it is based on the maximal probability estimation of the Poisson noise. We held experiments at the XingGuang II laser facility using an x-ray ring-code-microscope. The Wiener filtering method and the RL method are both used to decode the coded image. Compared with the Wiener filtering method, the RL method gets more ideal results, in good agreement with the pinhole image. This method can also be applied to penumbral imaging and other coded imaging techniques in ICF research.

Experiments were performed on an x-pinch using a pulsed power current generator capable of producing an 80 kA current with a rise time of 50 ns. Molybdenum wires with and without gold coating were employed to study the effect of high z coating on the low-density (<5 × 10¹⁸ cm⁻³) coronal plasma dynamics. A comparison of images from XUV frames and optical probing shows that the low density coronal plasma from the wires initially converges at the mid-plane immediately above and below the cross-point. A central jet is formed which moves with a velocity of 6 × 10⁴ ms⁻¹ towards both electrodes forming a z-pinch column before the current maximum. A marked change in the low density coronal plasma dynamics was observed when molybdenum wires coated with ∼ 0.09 µm of gold were used. The processes forming the jet structure were delayed relative to bare Mo x-pinches, and the time-resolved x-ray emission also showed differences. An m = 0 instability was observed in the coronal plasma along the x-pinch legs, which were consistent with x-ray PIN diode signals in which x-ray pulses were observed before x-ray spot formation. These early time x-ray pulses were not observed with pure molybdenum x-pinches. These observations indicate that a thin layer of gold coating significantly changes the coronal plasma behaviour. Two dimensional MHD simulations were performed and qualitatively agree with experimental observations of low density coronal plasma.

A hydrogen pellet is injected into a plasma in the Large Helical Device (LHD). Strong radiation from a dense plasma formed around the pellet, the so-called 'pellet cloud', is observed and its spectrum is analysed. Emission lines of neutral hydrogen exhibit Stark broadening profiles and the electron density is evaluated through comparison with theoretical data (e.g. 2.1 × 10²³ m⁻³). The continuum radiation is dominated by two components which correspond to radiative recombination and radiative electron attachment, respectively, the latter of which yields negative ions. From the absolute intensity and its dependence on the wavelength of the continuum radiation, the electron temperature (1.02 eV), the atom density (1.7 × 10²⁵ m⁻³) and the observed plasma volume (1.6 × 10⁻⁵ m³) are determined. These results indicate that the plasma state is close to complete LTE (local thermodynamic equilibrium). The Balmer-α line profile is deformed owing to the reabsorption effect. With the help of one-dimensional radiation transport calculation, the plasma thickness in the direction of the observation (2.4 × 10⁻³ m) is estimated. The result suggests that the pellet cloud is extended anisotropically in the direction perpendicular to the observation.

The local and global fluid magnetohydrodynamic stability properties of anisotropic pressure plasmas are investigated with the Kruskal–Oberman and rigid hot particle Johnson et al energy principles. A Heliotron configuration that models the Large Helical Device with finite pressure anisotropy driven by neutral beams at ⟨β⟩ = 4% shows that the Kruskal–Oberman model predicts stability when ⟨β^h⟩/⟨β⟩ ∼ 1/3 provided that the hot particle pressure profile is sufficiently peaked. The rigid hot particle model, on the other hand, is stable to local and global modes for broad and peaked profiles. For central deposition, the marginal pressure profiles are somewhat broader for p_|| > p_⊥ than for p_⊥ > p_||. Global n = 3 modes produce stricter stability criteria than n = 1, 2 and 4 modes. Off-axis hot particle deposition yields more unstable conditions with respect to global and local modes than on-axis deposition. The mode structures localize near the plasma periphery according to the Kruskal–Oberman model and near the plasma core according to the Johnson et al model. This observation could help resolve the appropriate model to apply to the experimental conditions in Heliotron devices.

The influence of a weak magnetic field (B) on the ion current collected by a spherical electrode is studied by means of the 2v-3d particle in cell code SCEPTIC in the limit of zero Debye length. The ion current dependence on B for low fields, shown to be linear, is compared with analytic expressions valid in the magnetized free-flight limit. In the flow-free regime, expressions for the angular distribution of current at different ion temperatures are provided. The configuration in which the plasma is drifting in the B-direction is investigated as well, and a Mach-probe calibration valid for equal temperature ions and electrons is given.

This work reports on numerical studies of small-scale electron-temperature-gradient (ETG) turbulence embedded in large-scale turbulence driven by both ion-temperature-gradient (ITG) modes and trapped-electron modes. To begin with, we find that the simplified adiabatic-ion model of ETG turbulence does not always saturate nonlinearly, suggesting that corrections to the purely adiabatic ion response are required for robust saturation. Our results also qualitatively confirm a prediction of Holland and Diamond that the back-reaction of ETG on ITG turbulence is insignificant. For the parameters studied, we find that ETG turbulence levels are reduced as ion driving gradients are increased. This result is at least partially explained by linear physics. An important practical result of this work is the finding that most of the electron energy transport arises from ion scales (k_θρ_i < 1) in cases for which ion-scale instabilities are not suppressed. Specifically, for the Cyclone base case parameters, only 16% of the energy diffusivity, χ_e, arises from the spectral region k_θρ_i > 1.0.

The success the Weiland model has had in reproducing modulation experiments prompted this in-depth investigation into its behaviour as a critical gradient model (CGM). The critical gradient properties of the Weiland model is examined analytically and numerically and compared with the empirical CGM commonly used in experiment. A simplified Weiland CGM is derived in which the height-above-threshold dependence is not necessarily linear. Simultaneously, the validity of the empirical CGM was examined. It is shown that an effective threshold, which is higher than the instability threshold, can be obtained if pinches influence the diffusivity.

A fast (⩽0.1 ms) and compact 'multi-colour' soft x-ray array has been developed for time and space-resolved electron temperature (T_e) measurements in magnetically confined fusion (MCF) plasmas. The electron temperature is obtained by modelling the slope of the continuum radiation from ratios of the available 1D-Abel inverted radial emissivity profiles over different energy ranges, with no a priori assumptions of plasma profiles, magnetic field reconstruction constraints or need of shot-to-shot reproducibility. This technique has been used to perform fast T_e measurements in the National Spherical Torus Experiment (NSTX), avoiding the limitations imposed by the well-known multi-point Thompson scattering, electron cyclotron emission and electron Bernstein wave mode conversion diagnostics. The applicability of this 'multi-colour' technique for magnetohydrodynamic (MHD) mode recognition and a variety of perturbative electron and impurity transport studies in MCF plasmas is also discussed. Reconstructed 'multi-colour' emissivity profiles for a variety of NSTX scenarios are presented here for the first time.

Studies of the pedestal characteristics and quantities determining edge-localized mode (ELM) energy losses in MAST are presented. High temperature pedestal plasmas have been achieved which have collisionalities one order of magnitude lower than previous results . A stability analysis performed on these plasmas shows them to be near the ballooning limit. The fraction of pedestal energy released by an ELM as a function of collisionality on MAST is consistent with data from other devices. The evolution of the filamentary structures observed during ELMs has been studied and has shown that they exist near to the last closed flux surface for the time over which the majority of particles and energy are being released from the pedestal region into the scrape off layer. A simple model has been developed, which is in reasonable agreement with the observed ELM energy losses and target profiles.

Relativistic effects on reflectometry density profile measurements have been evaluated for planned ITER operating scenarios. Standard X-mode, right-hand cutoff reflectometry reconstruction can produce large errors (up to 35% for T_e(0) = 24 keV plasmas) in high-temperature ITER plasmas if relativistic effects are ignored. It will therefore be essential to account for these effects in ITER. The errors created in density profile reconstruction have been analysed using simulated temperature profiles, including uncertainties, as an input to a standard inversion routine. Modelling using random errors with maxima of ±10% across the electron temperature profile leads to errors in the inverted density profile ranging from zero at the edge to a maximum RMS error of ∼1% at the magnetic axis. In addition to this, a novel iterative inversion technique is demonstrated which eliminates the dependence on external T_e information and allows T_e itself, and hence electron pressure P_e, to be extracted from the reflectometry measurement. The new technique utilizes phase data from both O- and X- mode propagation and has been successfully demonstrated numerically in peaked plasma profiles, as well as in the edge pedestal region. Integration of this novel approach with other planned measurement systems will serve to improve confidence in electron density and temperature measurements in ITER.

Improvement of the spatial resolution of the TCV Thomson scattering system has permitted measurements of the pedestal height and gradient of electron density and temperature profiles near the plasma boundary during ELMy H-mode. Measured profiles were fitted by a modified TANH function and characterized by pedestal height, width and gradient scale length. Taking advantage of an extended quasi-stationary phase with reproducible edge localized modes (ELMs), random sampling was used to reconstruct the time evolution during a typical ELM cycle. The measurements clearly reveal the influence of the ELM event on the edge profiles and have permitted quantification of the associated energy and particle losses. The experimental data, collected from a series of reproducible shots have provided the basis for an MHD stability analysis using the KINX code. The results confirm the type-III identification of the ELMs observed in ohmically heated H-mode plasmas in TCV.

Transient and non-transient changes to confinement properties of a tokamak equilibrium arise from several different plasma phenomena: a heat pulse triggered by a sawtooth; a cold pulse triggered by impurity injection or a giant ELM; the L ↔ H transitions triggered at the edge can produce a fast response in temperature towards the centre; MHD instabilities like sawtooth collapse, ELM or 'outer' mode cause negative-positive changes to the local energy density. Such changes to the confinement properties propagate through the plasma on timescales which are much smaller than the confinement time itself. A model to describe this based on turbulent guiding centre drift motion is developed. The theory for the non-linear model focuses on the propagation of perturbations to the plasma temperature and density. The model predicts a fluctuation-turbulence spectrum which agrees with that observed in experimental fluctuation measurements, apart from the predicted long wavelength part, which is not measured experimentally. A turbulence theory for the guiding centre velocity correlation function is developed in five steps, three of which have often been used in work on turbulence. Step 1 is the random phase approximation. Step 2 is the Markovian approximation. Step 3 is the discrete to continuum approximation. Step 4 is the solution of a prototype non-linear equation for one single harmonic. Step 5 is the solution of a non-linear equation for the entire spectrum of fluctuations using statistical techniques. The solution can be studied in two regimes. The long term or steady state regime has commonly been used in many turbulence theories. On the other hand the short term or ballistic regime predicts that perturbations propagate by advective or wave-like transport relevant to transient changes. The propagation speed is the characteristic guiding centre fluid drift velocity scaled by the ratio between the energy in the fluctuations and the thermal energy. Its magnitude agrees with experimental observations. The validity of the approximations in each of the five steps is discussed, together with how appropriate these are to a tokamak equilibrium with shear.

Experiments have shown that an overcritical density plasma is typically identified in some specific regions in conventional microwave (MW) discharges. The present work theoretically investigates this problem in a new and thorough way. By solving the wave equation, we treat the dynamic behaviour of the MW fields propagating through a gas slab. In this case, the gas is ionized and the density of the produced plasma grows consequently with time. Generalizing the results to a semi-infinite space case, we obtain the wave reflection index of the produced plasma. Comparison with the steady state case shows that the derived unsteady reflection index approaches its steady state value only at a very slow growth of the plasma density. This difference with the steady state values also leads to the deflection of the cut-off frequency from its usual value. At the critical plasma density, n_cr, the reflection index of the unsteady produced plasma is estimated to be much less than unity, which results in much more penetration of the wave and also ionization of the gas. We show that the density of the overcritical plasma, produced in this way, may reach approximately 15n_cr.