Plasma turbulence underpins a wide range of phenomena, including the formation of stars and galaxies; the properties of the solar wind, and - the focus of this programme - the confinement of plasmas in tokamaks. It is complicated by feedback mechanisms that couple space and time scales spanning several orders of magnitude. The full problem is extremely challenging, and so to make progress for real world applications we must develop reduced models that capture the essential physics. The goal of our proposed programme is to address this by advancing our understanding of these multi-scale interactions at a fundamental science level. This will be achieved by coupling analytic theory, advanced computation and experimental capabilities, including the newly upgraded MAST-U tokamak. Plasma turbulence is complicated by the fact that there are at least two types of interacting "fluids" - electrons and ions - and these are charged. Fluctuations in density therefore drive charge separation and hence fluctuations in the electrostatic field, while fluctuations in velocity drive currents and hence fluctuations in the magnetic field. These fields then couple the relative motions of the electron and ion "fluids". The situation is further complicated by the rich variety of waves that a magnetised plasma supports, and the resonances that exist when the phase velocity of a wave matches the particle velocity. To properly treat these resonances requires knowledge of the particle velocity distribution; this, in turn, requires either a kinetic or an advanced fluid approach - a daunting task. Turbulence, typically at the millimetre-centimetre scale in tokamaks, interacts in a complex way with the global equilibrium profiles (density, temperature and flow gradients, for example), which are on the metre-scale. To quantify the complex, multi-scale feedback mechanisms between tokamak plasma turbulence and profiles, and so provide a predictive capability for the quasi-steady final states, we will address and integrate a number of topics. We will first learn how mean flows interact with electrostatic turbulence (ie neglecting fluctuations in the magnetic field), requiring coupling between fluctuations with characteristic scales ranging from the electron Larmor radius (sub-mm) through to the ion Larmor radius (few mm) and beyond (cm), to the system length scale of the profiles (m). Our new theory and simulations will inform experiments on MAST-U, exploiting two diagnostic instruments already planned for the device (beam emission spectroscopy and doppler back-scattering). It is likely there will be gaps in the wavelength range that these instruments can measure, so we anticipate a need to develop and install a new microwave imaging system. This will be designed using knowledge gained from the early phase of the programme, and deployed for further experiments towards the end. Understanding of electromagnetic turbulence is less developed and new theoretical models will be required. Building on the knowledge gained from the electrostatic turbulence, we will seek to again understand the multi-scale interactions and feedbacks, including flows. However, now the situation is more complicated as electromagnetic turbulence can drive large scale currents, modifying the magnetic field which confines the plasma, and coupling into large scale electromagnetic modes. A key motivation is to optimise tokamak plasmas for fusion performance, and this requires us to understand the impact of fast particles. These can drive turbulence directly through the instabilities they excite, or influence the turbulence driven by the thermal particles. Our simulations will assess the impact of the fast particles created by the neutral beam heating systems on MAST-U, and also the impact of energetic alpha particles from fusion reactions on future devices like ITER, as well as experiments planned on JET with the deuterium-tritium mix fusion fuel.

Exascale computing offers the prospect of running numerical models, for example of nuclear fusion and the climate, at unprecedented resolution and fidelity, but such models are still subject to uncertainty and we need to able to quantify such uncertainties (and for example use data on model outputs to calibrate the model inputs). Exascale computing comes at a cost. We will never be able to run huge ensembles go models on Exascale computers. Naive methods, such as Monte Carlo where we simply sample from the probability distribution of the model inputs, run a huge ensemble of models and produce a sample from the output distribution, are not going to be feasible. We need to develop uncertainty quantification methodology that allows us to efficiently, and effectively, perform sensitivity and uncertainty calculations with the minimum number of exascale model runs. Our methods are based on the idea of an emulator. An emulator is a statistical approximation linking model inputs and outputs in a fast non-linear way. It also includes a measure of its own uncertainty so we know how well it is approximating the original numerical model. Our emulators are based on Gaussian processes. Normally we would run a designed experiment and use these results to train the emulator. Because of the cost of exascale computing we use a hierarchy of models from fast, low fidelity versions through higher fidelity more computationally expensive ones to the very expensive, very high fidelity one at the apex of the hierarchy. Building a joint emulator for all the models in the hierarchy allows us to gain strength from the low fidelity ones to emulate the exascale models. Although such ideas have been around for a number of years they have not been exploited much for very large models. We will expand on the existing theory on a number of new ways. First we will look at the problem of design. To exploit the hierarchy to its fullest extent we need an experimental design that allocates model runs to the correct layer of the model hierarchy. We will extend existing sequential design methodology to work with hierarchies of model, not only finding the optimal next set of inputs for running the model but also which level it should be run in. We will also ensure that the sequential design is 'batch' sequential, allowing us to run ensembles rather than waiting for each run to return answers. Because the inputs and outputs of exascale models are often fields of correlated values we will develop methods for handling such high dimensional inputs and outputs and how to relate them to other levels of the hierarchy. Finally we will investigate whether AI methods other than Gaussian processes can be used to build efficient emulators.

Je-S summary: Developing a portfolio of energy producing solutions is imperative to advance the economy, keep society functioning and to fight the advance of climate change. Commercial fusion will play an important role as part of that portfolio when technical challenges are overcome, having the ability to provide a low-carbon, essentially limitless, steady source of energy on a large scale, with a small land footprint. Arguably the biggest challenge to the magnetic fusion energy concept is how to safely channel the reactor heat exhaust to the surrounding material surfaces. The fusion reactions occur between ions in the hot fusion core that are at a temperature ~ 100 million oC. This provides enough energy for the positively charged nuclei to overcome their electrical repulsion and come close enough for the attractive nuclear force to take over. The two ions then bind to form a new nucleus with less mass than the original two ions, releasing energy. The hot plasma is contained within a magnetic 'bottle', called a tokamak, which has the shape of a torus. Exhaust energy and particles, which leak out of the magnetic bottle in steady state, are diverted away along magnetic field lines to remote material surfaces (termed 'divertor targets') designed to handle the resulting high power densities. The excellent confinement of energy within the magnetic bottle necessary for fusion energy production results in a narrow channel of exhaust power flowing to the divertor targets which, for a tokamak of radius ~ 5m, has a channel thickness of order 1 mm. The resulting heat flux flowing along the magnetic field to the divertor target likely approaching 25GigaWatts/m2. This is about 500x times the heat flux of an arc welder and 2500x what the engineering limits of steady state heat transfer to a solid material allows (10MegaWatts/m2). We employ several methods to reduce this heat flow to surfaces to below engineering limits: a) The simplest is to arrange the angle of the target to the heat flux to be small, spreading the divertor heat over a larger area, reducing the peak heat flux by x20; & b) More significantly, we encourage light (power) to be emitted from the plasma. We also utilise other atomic processes to remove energy, momentum and even particles from the plasma in a process we call 'detachment'. Detachment has been the main process to reduce the heat flux to the target, but more reduction is needed for a viable reactor-scale device. The goal of this research project is to evaluate how modifications of the magnetic fields and geometry in the divertor target ('alternative divertor configurations') region can further enhance the power removal properties of the plasma & reduce the heat fluxes reaching divertor surfaces below the engineering limit. In the research proposed we will: a) test our model predictions that alternative divertor configurations remove more heat from the plasma & better control the detachment processes using data from existing and new diagnostics we develop; and b) study both the dynamics of how the plasma is cooled through the processes mentioned and the sensitivity of the detachment process to external controls. This project will promote the UK into a world-leading role in the area of fusion reactor divertor physics research through development of key knowledge and research capabilities within the UK. Indeed, we will contribute unique results to the upcoming EU decision of what the appropriate divertor solution is for commercial reactors, reducing the time to a demonstration fusion power plant. The proposed work will also accelerate fusion research at the £50M upgrade to the MAST tokamak at Culham, where the first (worldwide) embodiment of the so-called 'super-x' alternative divertor topology will occur. By the UK playing a key role in achieving fusion the country will benefit economically from commercial applications as well as having an essentially limitless, steady source of clean energy into the future.

Robots with legs and arms are likely replace most manual labour, especially in environments that are dangerous for humans, and revolutionize multiple services domains in the long-term. One of the main advantages of legged robots is that they can discretely make and break contact with the environment, in contrast to wheeled or tracked systems that require continuous contact with the ground. This way, robots with legs can modify their area of support from step to step, a requirement when negotiating challenging terrain and environments primarily built for humans. Also, the use of legs decouples the body from the robot's foot-print. This allows for wide areas of support with only small footprints, a major advantage when navigating passages, tight spaces, cluttered environments, etc. The high articulation of legged systems also allows them to manipulate their center of mass, so that the system's dynamics can be exploited for the task at hand, and to dynamically reconfigure their workspace for the benefit of their payload, i.e., increase a manipulator arm's reach or position a sensor suite in a preferred pose. The autonomous locomotion framework that we will develop will enable current technology to be used in industrial scenarios, especially in hazardous environments that are primarily built for humans. Examples of such places are nuclear power plants, factories, oil & gas facilities, etc., where typically industrial stairs are used and a system will need to overcome various terrain difficulties, such as step over pipes, gaps, climb up/down stairs, manoeuvre through narrow passageways. Legged systems in such settings can have a large variety of roles; starting from inspection, automated monitoring of the condition of a facility; maintenance, periodic recurring tasks that need to be performed typically by a human, to intervention when an anomaly is detected.

There are many applications where infrastructure and machinery operate under extreme environmental conditions, such as very high temperatures, high pressures, high magnetic fields and exposure to radiation. The ability to obtain better measurement data within these environments has the potential to enable better control systems, leading to increased safety, increased efficiency and lower environmental impact. This project will therefore research new sensor technologies which can withstand these extreme environments, whilst allowing multiple measurements to be obtained. This project will aim to develop multi-point pressure sensors that operate up to 700C and multi-point temperature sensors that operate up to 1500C. The sensors will be in optical fibre, which can be routed around the infrastructure to allow measurements at defined points along its length. The measurement data is recovered by injecting light into one end of the optical fibre and monitoring the light which comes back. The sensors will be fabricated by exposing the optical fibre to high intensity, short pulse laser light from the side, to cause a permanent modification inside the optical fibre. A key novelty in the research is correcting for the distortion that occurs when focussing the short pulse laser light into the optical material, to enable higher precision sensor designs. The use of sapphire will be investigated to allow operation at temperatures in excess of 1000C. The work will be conducted at the Department of Engineering Science at the University of Oxford. There will be academic collaboration with the Osney Thermofluids Institute (University of Oxford) and Cranfield University. There are industrial collaborators in the aerospace, oilfield services and space industries. There is also collaboration with the UK Atomic Energy Authority.