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Plasma turbulence plays a key, governing role in determining the spatial-temporal evolution of plasmas in astrophysical, geophysical and laboratory contexts. In particular, turbulence on disparate spatial and temporal scales limits the level of confinement achievable in magnetic confinement fusion experiments and therefore limits the viability of sustainable fusion power 1 . The TDoTP project* (Turbulent Dynamics of Tokamak Plasmas) aims to advance understanding of plasma turbulence coupling across a wide range of scale sizes. As part of this effort, a mm-wave based scattering diagnostic is being designed for the MAST-U spherical tokamak, to measure binormal oriented high-k (electron scale) turbulence in the core plasma. We present the results of Gaussian wave optics and beam-tracing calculations 2 that demonstrate the predicted spatial and wavenumber resolution of the diagnostic, as well as estimates for the sensitivity of measurement. Current specifications for the diagnostic include an operating frequency of 260GHz, a turbulence wavenumber measurement range of k ⊥ ρ e = 0.1 -> 0.5 (where k ⊥ is the poloidal turbulence wavenumber and ρ e the electron gyroradius) and a minimum spatial localisation of ~3cm along the primary beam path.

Non-monotonic plasma density structures such as blobs and magnetic islands give rise to trapped upper hybrid (UH) waves. Trapped UH waves which satisfy Bohr–Sommerfeld quantization can be thought of as eigenmodes of a cavity. Using fully kinetic particle-in-cell simulations, we verify the existence of these UH eigenmodes and demonstrate their significance as only eigenfrequencies become unstable to three-wave interactions. The eigenmodes can be excited through parametric decay instabilities (PDIs) of an X-mode pump wave at approximately twice the UH frequency, as could be the case for a gyrotron beam traversing a blob in a magnetically confined fusion plasma. We derive a closed expression for the wavenumber of UH waves, which is accurate both close to the UH layer and to the electron cyclotron resonance. This allows for fast analysis of eigenmodes in a non-monotonic structure. An expression for the amplification of PDI daughter waves in an inhomogeneous plasma is extended to a decay region where the first several derivatives vanish. From the amplification in a convective PDI, we estimate the growth rate of the absolute PDI involving the trapped waves. We show that the excitation of eigenmodes through PDIs in our simulations are indeed absolute rather than convective due to the trapping of the daughter waves. Additionally, we show that only eigenmodes get excited through the PDIs, and that we are able to predict the growth rates of the daughter waves and how they scale with the pump wave intensity. This is evidence supporting a fundamental assumption of analytical theory describing low threshold strong scattering observed in magnetically confined fusion experiments during second harmonic electron cyclotron resonance heating (ECRH). Such low threshold instabilities can degrade ECRH performance but also offer novel uses for ion heating or as diagnostics.

Microwave heat pulse propagation experiments have demonstrated a correlation between millimeter-scale turbulence and deposition profile broadening of electron cyclotron (EC) waves on the DIII-D tokamak. In a set of discharges in DIII-D, a variation in edge density fluctuations on the mm-scale is associated with 40%–150% broader deposition profiles, expressed in terms of normalized minor radius, as compared with equilibrium ray tracing. The 1D power profile is determined from transport analysis of the electron temperature response to EC power modulation using perturbative analysis with a square wave power modulation at 20–70 Hz, producing a series of Fourier harmonics that are fit collectively to resolve transport. Fitting an integrated heat flux expressed in the Fourier basis of the modulation to diffusive, convective, and coupled transport terms in a linear model can resolve the broadened EC deposition width from the power perturbation to resolve a broadening in each case. The best fit degree of beam broadening observed scales approximately linearly with the Doppler backscattering measured fluctuation level in the steep gradient region. Quantifying the effect of edge fluctuation broadening on EC current drive power needs of future devices will require 3D full-wave codes that can be validated on the current generation of machines. These DIII-D experiments provide a quantitative measure of fluctuation effects and a dataset to benchmark full-wave simulations that can model and eventually predict nonlinear effects neglected by 1D equilibrium beam and ray tracing.

The Synthetic Aperture Microwave Imager-2 (SAMI-2) is a 2D Doppler backscattering (DBS) diagnostic designed for multiple high quality simultaneous measurements of the edge pitch angle on the Mega-Ampere Spherical Tokamak Upgrade (MAST-U). The specification, design and testing of the SAMI-2 microwave front end, predominantly antennas and mixer circuitry, are described in this thesis. Dual-polarisation sinuous antennas are designed and shown to fulfil their performance criteria over the 20-40 GHz range. A four-channel microwave in-phase and quadrature (IQ) downconverter is designed to mix the radio frequency (RF) signals from each antenna in the SAMI-2 phased array to a lower frequency, for digitisation. The down-converter is tested and found to achieve its performance specifications over the entire frequency range of the antennas. The 2D DBS technique was demonstrated by Synthetic Aperture Microwave Imager (SAMI) on the Mega-Ampere Spherical Tokamak (MAST) to measure the edge magnetic pitch angle. A radial profile of the edge pitch angle enables calculation of the edge current density, a difficult quantity to measure, which is valuable for the validation of models and understanding of pedestal dynamics and edge plasma instabilities, e.g. ELMs. In active probing mode, the SAMI-2 diagnostic is designed to make the first measurements of the edge current density by a DBS diagnostic. In passive mode, SAMI-2 will measure Bernstein wave mode conversion, to inform spherical tokamak microwave heating systems.

Parametric decay instabilities (PDIs) are nonlinear processes by which energy from a strong pump wave may be directed into other waves at other frequencies, in particular natural modes of the medium, provided that energy and momentum are conserved. The particle-in-cell (PIC) code EPOCH is used to simulate PDIs in a magnetically confined fusion plasma converting a 105 GHz microwave X-mode pump wave into electrostatic daughter waves at the upper hybrid (UH) layer. Modes associated with the PDIs as well as a linearly converted electron Bernstein wave (EBW) are identified in f- and k-space. The PDI daughter modes are found to agree with experimental observations from ASDEX Upgrade as well as with analytical predictions, showing a nonlinear increase in power above a predicted threshold.

The mega amp spherical tokamak (MAST) was a low aspect ratio device (R/a = 0.85/0.65 ~ 1.3) with similar poloidal cross-section to other medium-size tokamaks. The physics programme concentrates on addressing key physics issues for the operation of ITER, design of DEMO and future spherical tokamaks by utilising high resolution diagnostic measurements closely coupled with theory and modelling to significantly advance our understanding. An empirical scaling of the energy confinement time that favours higher power, lower collisionality devices is consistent with gyrokinetic modelling of electron scale turbulence. Measurements of ion scale turbulence with beam emission spectroscopy and gyrokinetic modelling in up-down symmetric plasmas find that the symmetry of the turbulence is broken by flow shear. Near the non-linear stability threshold, flow shear tilts the density fluctuation correlation function and skews the fluctuation amplitude distribution. Results from fast particle physics studies include the observation that sawteeth are found to redistribute passing and trapped fast particles injected from neutral beam injectors in equal measure, suggesting that resonances between the m = 1 perturbation and the fast ion orbits may be playing a dominant role in the fast ion transport. Measured D–D fusion products from a neutron camera and a charged fusion product detector are 40% lower than predictions from TRANSP/NUBEAM, highlighting possible deficiencies in the guiding centre approximation. Modelling of fast ion losses in the presence of resonant magnetic perturbations (RMPs) can reproduce trends observed in experiments when the plasma response and charge-exchange losses are accounted for. Measurements with a neutral particle analyser during merging-compression start-up indicate the acceleration of ions and electrons. Transport at the plasma edge has been improved through reciprocating probe measurements that have characterised a geodesic acoustic mode at the edge of an ohmic L-mode plasma and particle-in-cell modelling has improved the interpretation of plasma potential estimates from ball-pen probes. The application of RMPs leads to a reduction in particle confinement in L-mode and H-mode and an increase in the core ionization source. The ejection of secondary filaments following type-I ELMs correlates with interactions with surfaces near the X-point. Simulations of the interaction between pairs of filaments in the scrape-off layer suggest this results in modest changes to their velocity, and in most cases can be treated as moving independently. A stochastic model of scrape-off layer profile formation based on the superposition of non-interacting filaments is in good agreement with measured time-average profiles. Transport in the divertor has been improved through fast camera imaging, indicating the presence of a quiescent region devoid of filament near the X-point, extending from the separatrix to ψ n ~ 1.02. Simulations of turbulent transport in the divertor show that the angle between the divertor leg on the curvature vector strongly influences transport into the private flux region via the interchange mechanism. Coherence imaging measurements show counter-streaming flows of impurities due to gas puffing increasing the pressure on field lines where the gas is ionised. MAST Upgrade is based on the original MAST device, with substantially improved capabilities to operate with a Super-X divertor to test extended divertor leg concepts. SOLPS-ITER modelling predicts the detachment threshold will be reduced by more than a factor of 2, in terms of upstream density, in the Super-X compared with a conventional configuration and that the radiation front movement is passively stabilised before it reaches the X-point. 1D fluid modelling reveals the key role of momentum and power loss mechanisms in governing detachment onset and evolution. Analytic modelling indicates that long legs placed at large major radius, or equivalently low at the target compared with the X-point are more amenable to external control. With MAST Upgrade experiments expected in 2019, a thorough characterisation of the sources of the intrinsic error field has been carried out and a mitigation strategy developed.

The Synthetic Aperture Microwave Imaging diagnostic (SAMI) has been operating on the MAST experiment since 2011. It has provided the first 2D images of B-X-O mode conversion windows and showed the feasibility of conducting 2D Doppler back-scattering experiments. The diagnostic heavily relies on field programmable gate arrays (FPGAs) to conduct its work. Recent successes and newly gained experience with the diagnostic has led us to modify it. The enhancements will enable pitch angle profile measurements, O and X mode separation and the continuous acquisition of 2D DBS data. The diagnostic has also been installed on the NSTX-U and is acquiring data since May 2016.

A cutting-edge standalone data acquisition system has been developed using Field Programmable Gate Arrays (FPGAs). It has 16 ADC channels operating at 250 MSPS, at 14-bit resolution acquiring continuously at 8 GB/s for 0.5 s. The system uses the Virtex 6 FPGA running embedded Linux on the MicroBlazeTM soft processor. We propose the development of a standard FPGA architecture, based on a methodology which has enabled us to develop this system using commercial-off-the-shelf (COTS) components. This architecture can easily be modified for a variety of applications, both high and low performance at a competitive cost in terms of hardware, engineering and development.

Optimization of antenna array configurations specifically designed to reduce side-lobes was carried out by using a simulated annealing algorithm to find a good approximation to the optimum of a modified array beam efficiency function. The optimization was carried out for the wide field synthetic aperture microwave imaging (SAMI) radiometer, which has the ability to switch between two configurations of eight antennas. This approach enables us to find configurations which simultaneously complement each other.

The Berk–Breizman augmentation of the Vlasov–Maxwell system is widely used to model self-consistent resonant excitation and damping of wave fields by evolving energetic particle populations in magnetic fusion plasmas. The key model parameters are the particle annihilation rate νa, which drives bump-on-tail structure, and the linear wave damping rate γd. A code, based on the piecewise parabolic method, is used to integrate the fully nonlinear Berk–Breizman system of equations across the whole (νa,γd) parameter space. The results of this code show that the system’s behavior can be classified into one of four types, each of which occurs in a well-defined region of parameter space: chaotic, periodic, steady state, and damped. The corresponding evolution in (x,v) phase space is also examined.

The Mega Ampère Spherical Tokamak (MAST) programme is strongly focused on addressing key physics issues in preparation for operation of ITER as well as providing solutions for DEMO design choices. In this regard, MAST has provided key results in understanding and optimizing H-mode confinement, operating with smaller edge localized modes (ELMs), predicting and handling plasma exhaust and tailoring auxiliary current drive. In all cases, the high-resolution diagnostic capability on MAST is complemented by sophisticated numerical modelling to facilitate a deeper understanding. Mitigation of ELMs with resonant magnetic perturbations (RMPs) with toroidal mode number n RMP = 2, 3, 4, 6 has been demonstrated: at high and low collisionality; for the first ELM following the transition to high confinement operation; during the current ramp-up; and with rotating n RMP = 3 RMPs. n RMP = 4, 6 fields cause less rotation braking whilst the power to access H-mode is less with n RMP = 4 than n RMP = 3, 6. Refuelling with gas or pellets gives plasmas with mitigated ELMs and reduced peak heat flux at the same time as achieving good confinement. A synergy exists between pellet fuelling and RMPs, since mitigated ELMs remove fewer particles. Inter-ELM instabilities observed with Doppler backscattering are consistent with gyrokinetic simulations of micro-tearing modes in the pedestal. Meanwhile, ELM precursors have been strikingly observed with beam emission spectroscopy (BES) measurements. A scan in beta at the L–H transition shows that pedestal height scales strongly with core pressure. Gyro-Bohm normalized turbulent ion heat flux (as estimated from the BES data) is observed to decrease with increasing tilt of the turbulent eddies. Fast ion redistribution by energetic particle modes depends on density, and access to a quiescent domain with ‘classical’ fast ion transport is found above a critical density. Highly efficient electron Bernstein wave current drive (1 A W−1) has been achieved in solenoid-free start-up. A new proton detector has characterized escaping fusion products. Langmuir probes and a high-speed camera suggest filaments play a role in particle transport in the private flux region whilst coherence imaging has measured scrape-off layer (SOL) flows. BOUT++ simulations show that fluxes due to filaments are strongly dependent on resistivity and magnetic geometry of the SOL, with higher radial fluxes at higher resistivity. Finally, MAST Upgrade is due to begin operation in 2016 to support ITER preparation and importantly to operate with a Super-X divertor to test extended leg concepts for particle and power exhaust.

A generic model of a kinetic plasma formed from a source and sink is presented which without instability would form a strongly unstable state due to a single mode. Instead, the resulting wave-particle resonant interaction maintains the distribution near a marginally stable state through the continual production of fast frequency-sweeping modes that sweep unidirectionally (upward in our case) throughout the energy-inverted region of the distribution function. The energy of these modes can be channeled to the background plasma through wave dissipation and, in our particular example, one quarter of the injected energy is available to be channeled.

A novel microwave imaging system (SAMI) which utilizes an array of phase sensitive antennas to synthesize an optical aperture has been designed and deployed on MAST. The system requires no optical components for focusing and yet is able to image up to half of the plasma surface simultaneously. All image formation is done in post processing and SAMI can be refocused after the fact. SAMI is capable of imaging both passive thermal emission and scattered radiation from an active probing source simultaneously without compromising performance. We have used the diagnostic to observe highly anisotropic thermal emission characteristic of high β plasma devices which are overdense to regular ECE emission. This is an exciting emerging diagnostic field and we present our first observations here.

New diagnostic, modelling and plant capability on the Mega Ampère Spherical Tokamak (MAST) have delivered important results in key areas for ITER/DEMO and the upcoming MAST Upgrade, a step towards future ST devices on the path to fusion currently under procurement. Micro-stability analysis of the pedestal highlights the potential roles of micro-tearing modes and kinetic ballooning modes for the pedestal formation. Mitigation of edge localized modes (ELM) using resonant magnetic perturbation has been demonstrated for toroidal mode numbers n = 3, 4, 6 with an ELM frequency increase by up to a factor of 9, compatible with pellet fuelling. The peak heat flux of mitigated and natural ELMs follows the same linear trend with ELM energy loss and the first ELM-resolved Ti measurements in the divertor region are shown. Measurements of flow shear and turbulence dynamics during L-H transitions show filaments erupting from the plasma edge whilst the full flow shear is still present. Off-axis neutral beam injection helps to strongly reduce the redistribution of fast-ions due to fishbone modes when compared to on-axis injection. Low-k ion-scale turbulence has been measured in L-mode and compared to global gyro-kinetic simulations. A statistical analysis of principal turbulence time scales shows them to be of comparable magnitude and reasonably correlated with turbulence decorrelation time. Te inside the island of a neoclassical tearing mode allow the analysis of the island evolution without assuming specific models for the heat flux. Other results include the discrepancy of the current profile evolution during the current ramp-up with solutions of the poloidal field diffusion equation, studies of the anomalous Doppler resonance compressional Alfvén eigenmodes, disruption mitigation studies and modelling of the new divertor design for MAST Upgrade. The novel 3D electron Bernstein synthetic imaging shows promising first data sensitive to the edge current profile and flows. © 2013 IAEA, Vienna.

On MAST studies of the profile evolution of the electron temperature (Te), electron density (ne), radial electric field (Er) as well as novel measurements of the ion temperature (Ti) and toroidal current density (j) in the pedestal region allow further insight into the processes forming and defining the pedestal such as the H-mode access conditions and MHD stability. This includes studies of fast evolution of Te, ne and Er with ¿t = 0.2 ms time resolution and the evolution of pe and j through an edge-localized mode (ELM) cycle. Measurements of the H-mode power threshold, PL-H revealed that about 40% more power is required to access H-mode in 4He than in D and that a change in the Z-position of the X-point can change PL-H significantly in single and double null configurations. The profile measurements in the L-mode phase prior to H-mode suggest that neither the gradient nor the value of the mean Te or Er at the plasma edge play a major role in triggering the L–H transition. After the transitions, first the fluctuations are suppressed, then the Er shear layer and the ne pedestal develops followed by the Te pedestal. In the banana regime at low collisionality (¿) ¿Ti ˜ 0 leading to Ti > Te in the pedestal region with Ti ~ 0.3 keV close to the separatrix. A clear correlation of ¿Ti with ¿ is observed. The measured j (using the motional Stark effect) Te and ne are in broad agreement with the common peeling–ballooning stability picture for ELMs and neoclassical calculations of the bootstrap current. The j and ¿pe evolution ¿t ˜ 2 ms as well as profiles in discharges with counter current neutral beam injection raise questions with respect to this edge stability picture.

Results on edge turbulence in periods separating edge localised modes (ELMs), i.e. inter-ELM periods, in Mega-Amp Spherical Tokamak (MAST) are presented. It is shown through combined measurements of fast camera images and reciprocating Langmuir probes that filamentary structures contribute to transport during these periods. Analysis of Dα light emission reveals that inter-ELM filaments are the lowest amplitude fluctuations in the MAST scrape-off layer (SOL) relative to L-mode and ELM filaments. Physical properties such as size, density and mode numbers have also been characterized, along with measurements of the spatio-temporal evolution: inter-ELM filaments are found to rotate in the vicinity of the last closed flux surface and propagate radially outwards. Motion of these filaments is found to depend strongly on plasma density such that with increasing density, there is an enhancement of the radial transport manifested by an increased number of filaments which leave the edge and travel faster into the SOL. Camera images show that intermittent fluctuations in ion saturation current signals correspond to inter-ELM filaments passing the probe. Measured radial e-folding lengths indicate larger decay lengths at higher densities. Similar trends are also obtained in simulations of a filament propagating radially and losing particles on ion parallel loss timescales. Finally, a discussion is presented on how the radial velocity and Isat measurements reported in this paper are used to test the velocity scalings predicted by different theories.

Magnetic fluctuations at frequencies ω ωci driven by neutral-beam injection heating and identified as compressional Alfven eigenmodes (CAEs) have been observed on MAST. The measured toroidal mode numbers are in the range 4 < |n| < 10 and waves rotate in both co- and counter-current directions. The frequency variation is consistent with an Alfvenic scaling, and modes are elliptically polarized with a significant magnetic field component aligned parallel to the equilibrium field. Frequency clustering of modes occurs on three frequency scales. At the finest scale there are multiple modes each separated by a constant frequency ~10–20 kHz; this is shown to be a result of modulation by low-frequency tearing modes. A larger scale frequency splitting exists in the range 100–150 kHz; these have consecutive toroidal mode numbers and are in agreement with numerical modelling. Finally, modes exist at frequencies close to ω = ωci and ωci/2 consistently with previous observations on START and DIII-D suggesting that the CAEs exist in two distinct ranges of k∥. Calculations of CAEs suggest that the modes are localized at r/a ~ 0.5. The modes form within a potential well due to the variation of (nq/κρ)2, and are not directly influenced by variations in vA. This is distinct from observations based on ion cyclotron emission in conventional aspect ratio tokamaks which indicate that CAE modes occur closer to the plasma edge and that their existence relies on a competition between k⊥ and 1/vA.

The developments of advanced tokamak scenarios as well as the employment of a new neutral beam injection (NBI) source with higher power and beam energy up to ≈65 keV have significantly broadened the frequency range and the variety of Alfvén eigenmodes (AEs) excited by the super-Alfvénic NBI on the spherical tokamak MAST. During recent experiments on MAST, several distinct classes of beam-driven AEs have been identified, with different modes being most unstable in different MAST scenarios. In MAST discharges with elevated monotonicq(r)-profiles and NBI power ⩾3 MW, chirping modes starting in the frequency range ⩽150 kHz decreased in frequency down to ≈20 kHz asq(0) decreased and then smoothly transformed to long-living modes with a weakly-varying frequency and an= 1 kink-mode structure. The bolometer data suggest that the long-living modes can be responsible for fast ion losses on MAST, while the charge-exchange data show that a coupling between these modes and other low-frequency modes can cause a collapse of toroidal plasma rotation with a subsequent disruption. In MAST discharges with reversed magnetic shear, Alfvén cascade eigenmodes in the frequency range 40–180 kHz were observed at a moderate NBI power ⩽2 MW allowing an additional assessment ofq(r)-profile evolution in time. A robust reproducible scenario was found on MAST, in which the instability of high-frequency modes in the range 0.4–3.8 MHz and typically with negative toroidal mode numbers was dominating the spectrum of beam-driven AEs. Since the highest frequency of such modes is close to the on-axis ion cyclotron frequency and the polarization study of these modes show a significant parallel perturbed magnetic field, these modes are identified as compressional Alfvén eigenmodes. For investigating the AE spectrum in plasmas with high β, an active AE antenna has been installed on MAST. First measurements of stable AE modes in MAST have been performed successfully and are described here.

The Synthetic Aperture Microwave Imaging (SAMI) diagnostic is a Mega Amp Spherical Tokamak (MAST) diagnostic based at Culham Centre for Fusion Energy. The acceleration of the SAMI diagnostic data-processing code by a graphics processing unit is presented, demonstrating acceleration of up to 60 times compared to the original IDL (Interactive Data Language) data-processing code. SAMI will now be capable of intershot processing allowing pseudo-real-time control so that adjustments and optimizations can be made between shots. Additionally, for the first time the analysis of many shots will be possible.