The technical basis of this proposal pertains to the Neutron Transport Equation (NTE), which is used to describe neutron density in a physical environment where nuclear fission is taking place, such as a reactor core. This equation is of prime importance in the nuclear industry as it is used to construct models of reactor cores, nuclear medical equipment (e.g. for proton therapy) and other industrial scenarios where irradiation occurs. Primarily these models are used to assess safety and inform regulatory procedure when handling radioactive materials. Although the NTE can be derived through physical considerations of mass transport, it can also be derived using entirely probabilistic means. To be more precise, the NTE can be derived from the stochastic analysis of a spatial branching process. The latter models the evolution of neutron particles as they behave in reality, incorporating the features of random scattering and random fission, with increasing numbers of particles as time evolves. The derivation using spatial branching processes has been known since the 1960/70s, however, since then, very little innovation in the literature has emerged through probabilistic analysis. This mirrors a general lull in fundamental mathematical research contributing to modelling of nuclear fission after the 1980s. In recent years, however, the nuclear power and nuclear regulatory industries have a greater need for a deep understanding the spectral properties of the NTE. Such analytical quantities help e.g. engineers model the criticality and density of nuclear fission activity within a reactor core. In turn this informs optimal reactor design from several different view points (safety, energy production, efficiency etc.) as well as address regulatory constraints. With the decommissioning of old and the construction of new, more efficient and environmentally friendly nuclear power stations the demand for mathematical modelling using the NTE was never greater. The inhomogeneous nature of the NTE as it is used in practice has seen industry turn to Monte-Carlo techniques based on the underlying probabilistic treatment from 40-50 years ago. Many of the associated algorithms can only be run on supercomputers as they boil down to costly Monte-Carlo cycles of the entire fission processes, in essence replicating a virtual physical reality in a computer. This has the huge drawback that computational parallelization is not possible. In the decades that new probabilistic developments have been absent from the treatment of the NTE, there has been a significant evolution in the mathematical theory of spatial branching processes and related stochastic processes. The research in this proposal aims to re-align the understanding of the NTE with the modern theory of spatial branching processes. This is principally motivated by the implication that a whole suite of completely new Monte-Carlo techniques can be developed, as desired by industry, which are, fundamentally, of a lower order of complexity than existing algorithms. The overall aim of this project is to develop a `proof of concept' for this completely new approach, providing the theoretical basis and a stochastic numerical analysis that quantifies relative efficiency. In particular, the most important feature of the new algorithms that will emerge is the ability to parallelize computations. The project will be carried out in close scientific collaboration with industrial partner Amec-Foster-Wheeler, a major UK-based energy consultancies and one of the global leaders in servicing the nuclear energy and nuclear medical industries with simulation software for safety and regulatory purposes. All research output will be made open source on a webpage dedicated to the project.

The project aims to bring a step change improvement to the sensitivity of ultrasonic array imaging for Non Destructive Evaluation (NDE) to address the needs of the power generation industry. This will be based on the processing of the Full Matrix Capture (FMC) set of signals between all pairs of transducer elements, as is already established for state-of-the-art Beam-Forming (BF) imaging, but the approach for treating the signals will be entirely different. Instead of calculating a direct image from the FMC measurements, an inverse scattering approach will be pursued: this will involve iterations of unknowns in an integrated forward model of the array configuration, material properties and geometry, to find a best match to the measured signals. This approach has been shown to overcome conventional BF limitations in the context of the imaging of biological tissues, achieving intensified sensitivity and sub-wavelength resolution. This project will develop the concept for NDE, employing a specific, but commonly encountered, critical inspection task as a realistic example to focus the work. The proposal is being submitted within the UK Research Centre in NDE (RCNDE) to its targeted research programme. The proposal has been reviewed internally by the RCNDE, approved by the RCNDE board, and supported financially by two RCNDE industrial members.

Nuclear energy will play a critical role in the future of secure, affordable and low-carbon power generation. The UK is committed to a greenhouse emissions target of 80% of pre-1990 levels by 2050 and as part of this, between now and then, it is likely that the percentage of power generation via nuclear will have to increase by somewhere between two- and three-times. The vast majority of nuclear power is generated by light water nuclear reactors. These use cladding made from various types of zirconium alloy to contain ('clad') nuclear fuel, creating a barrier between highly active fuel/fission products and the coolant. Zirconium is considered an ideal material for this purpose, as it has excellent corrosion resistance properties and a small neutron cross section, meaning that it has a low rate of neutron absorption. These properties make zirconium alloys fundamentally more suitable than many other materials in reactor conditions. There is still much more to be learnt about the behaviour and durability of zirconium alloys, in order to enhance their performance and the efficiency of nuclear power generation. If we gain further understanding about how these materials behave in a nuclear reactor, we can more accurately predict the 'life' of the clad and even develop new, more sophisticated alloys - advancements which can minimise new nuclear waste production and further enhance fuel and reactor safety. Zirconium alloy research is therefore at the heart of nuclear power generation and safety. Within this context, this project aims to develop increased understanding in the field of zirconium processing and its relationship to in-reactor performance. The UK-India Civil Nuclear Collaboration is an on-going initiative to promote cooperative research in the area of nuclear energy, and this Phase III project builds upon a highly successful project undertaken in Phase I. The previous collaboration, between the University of Manchester and the Bhabha Atomic Research Centre (BARC) in India, made significant developments in the understanding of zirconium alloys, through both experimental and modelling work. This work has already had direct relevance to, and application by, the nuclear industry. This project aims to directly follow-on from this work, adopting a 'cradle-to-grave' approach intended to gain further understanding about the in-reactor performance of zirconium, including how the initial 'processing' of the material might impact on its properties. The proposed work will again be carried-out with partners at BARC, as well as at the Indira Gandhi Centre for Atomic Research (IGCAR). Once new hypotheses about zirconium are developed, including potential new alloy compositions, these must be thoroughly tested in reactor conditions before real-world application. This is a costly and time-consuming process, with few test reactors available to researchers and the costs/experimental difficulties associated with working on radioactive material. Partly in response to this, nearly £30m has been invested into the development of the University of Manchester's Dalton Cumbrian Facility (DCF), designed to allow research on irradiated and activated materials. DCF will enable the other key aspect of this project: the development of novel experimental set-ups (pioneered at the University of Michigan) at both DCF and IGCAR. These experiments will allow the investigation of material degradation during irradiation, mimicking the conditions experienced in reactors without producing radioactive samples, and so drive forward accurate, practical understanding of zirconium performance, enhancing efficient, safe nuclear power generation. This project brings together outstanding capabilities and expertise from the UK (Manchester and Sheffield) and India (BARC and IGCAR), enabling a unique research programme that will have impact for the nuclear industry and research, as well as helping to develop new experimental techniques for the field.

This project aims to provide a predictive model for creep deformation of in-core nuclear components in the presence of irradiation damage. Creep deformation is time-dependent permanent deformation of materials under load nominally at temperatures higher than half the material melting point. Creep deformation plays a crucial role in the structural integrity of engineering components that work at high temperature such as those in aerospace propulsion and energy generation. It is one of the main life limiting factors of nuclear power plants that work at high temperature. This includes fusion reactors, Gen IV fission nuclear reactors, and UK's unique Advanced Gas-cooled Reactors. The context of this project is nuclear. UK's energy mix currently is and planned to continue to benefit from substantive contributions from nuclear. In addition, UK is the only country in the world that has in-depth and knowledge of designing, building, and operating high temperature nuclear power plants with many of its structural components working in the creep regime. The immediate new build reactors at Hinckley Point, Wylfa, and Moorside do not work at temperatures that induce creep. However, fusion reactors and Gen IV fission nuclear reactors are envisaged to be working at much higher temperatures to increase their thermal efficiency and as such they are susceptible to creep deformation and damage. Therefore, there is a high risk that UK loses its current unrivalled authority on high temperature structural integrity by the time the next generation of nuclear power plants are built, currently planned for 2050. One of the objectives of this proposal is to maintain UK lead in high temperature structural integrity of nuclear industry by developing new knowledge and new skilled scientists in the field. The current creep engineering structural integrity codes are based on empirical equations extracted from tests in certain standard conditions. They ignore the material microstructure, which evolves during a 60 years' service of a power plants. An important limiting factor that is currently ignored in the engineering codes and will be highly influential in the mechanical response of components for next generation power plants is irradiation damage. One of our objectives is therefore to include the effects of irradiation damage on the macro-scale mechanical response of materials by including the changes it makes on the material microstructure in their constitutive laws. To this end our main objective is to develop a predictive, multi-scale, microstructurally informed creep deformation model. The model spans from the fundamental physical equations that govern the dislocation mobility at high temperature (dislocations are imperfection in material crystal structure and their movements under load account for most the material permanent deformation) to the behaviour of engineering components with complex geometries and varied loading history and conditions made from homogenised material. The model will help engineers to predict the behaviour of critical components in a nuclear reactor and make informed decision on their fitness for service which is a crucial safety decision. Once our creep model is validated and verified by experiments across three mico, meso, and macro length scales, it will provide the foundation for a new generation of engineering structural integrity codes that are based on a mechanistic understanding the material and its microstructure and therefore is predictive, more accurate and not confined to the test conditions it is based on. This will be an invaluable asset for the UK to play a major role in designing, building, and operating future nuclear power plants.

The objective of this project is to obtain a step-change improvement in the detection and characterisation of defects in safety-critical components across a range of industries including nuclear power generation and the defence sector. This will be achieved through data-fusion of the multiple views of a component's interior that can be obtained through modern ultrasonic array imaging techniques. Previous work by the team has demonstrated a two-order-of-magnitude improvement in detection performance when data fusion was applied to ultrasonic data obtained from separate scans performed with single-element probes. This was in a case where the expected defects were small, point-like inclusions that scatter roughly uniformly in all directions. The proposed project will develop the data-fusion philosophy for improving defect detection performance from multi-view array data in the much more complex case where the defect morphology cannot be assumed in advance and the scattering pattern may be strongly directional. Therefore, the project will necessarily address the critical challenges of applying data fusion to defect classification and sizing from multi-view array data. Demonstrator software will be produced that will show an image of the test component with indications ranked by the probability of them being produced by a defect; it will then be possible to probe any of these indications to show detailed classification (e.g. crack, void, inclusion etc.) and sizing information. The project is supported by EDF, Hitachi, BAE Systems and AMEC Foster Wheeler.