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.

The research project will study the physics and mechanics of creep cavity nucleation and the reverse process of healing by sintering in polycrystalline materials for energy applications using both modelling and experimental approaches. The experimental work will focus on a model single phase material (commercially pure Nickel), a simple particle strengthened material (Nickel with addition of Carbon), a commercial austenitic stainless steel (Type 316H), a superalloy (IN718) and a martensitic steel P91/92. An array of state-of-the-art experimental techniques will be applied to inform the development of new physics-based cavity nucleation and sintering models for precipitation hardening materials. Once implemented in mechanical analyses, and validated, such models will form the basis for development of improved life estimation procedures for high thermal efficiency power plant components.

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.

Power generation and petrochemical plant and civil structures require regular inspection and monitoring to ensure continued safe and reliable operation. The various ways that metal structures are routinely tested includes visual inspection, electromagnetic and radiographic methods and ultrasonic inspection, each technique having its own strengths and weaknesses, often being used in a complementary approach. Of all these methods, ultrasonic inspection is most prolific as it is inherently safe, portable and can be used to detect a wide range of defects down to sub-millimetre sizes. In recent years there has been significant and sustained progress in the fundamental scientific research of guided wave non-destructive evaluation (NDE). The majority of existing guided wave technology uses contacting transducers that must be clamped around the circumference of a pipe in the form of a ring of transducers. Typically a particular mode at a particular frequency is selected with suitable properties for being able to propagate over tens of metres, whilst having sensitivity to defects of interest. Target defect sizes are usually around 25% wall loss or more, which is perfectly acceptable for many applications. Guided waves can be used over shorter distances, and in general there is a trade-off between propagation distance and sensitivity.There is a need to maintain the current power generation plant, particularly within the nuclear industry and with an increase in our reliance on nuclear power anticipated, we need to ensure that we have suitable methods for inspecting critical components. As such, this project focuses on the ultrasonic inspection of stainless steel using ultrasonic transducers called EMATs that can generate or detect ultrasonic waves in metals without being in good mechanical contact with the sample. The advantages of using non-contact methods are that the automation of scanning is easier to implement as contact is not required and the EMATs have a unique set of characteristics that enable them to generate a wide range of wavemodes over a wide range of frequencies, unlike contacting piezoelectric transducers that are usually used at a particular fixed frequency. Note though that EMAT inspection does have some limitations, most principally because they are fairly inefficient when compared to piezoelectric transducers, and so the methods developed in this project are designed to complement the existing technology, providing new inspection capability through fundamental research of the transduction process and the wave propagation in the target sample.To realise fully the potential of EMAT based inspection we need to be able to model the problem scientifically from the bottom up, starting with the shape of the component and the target defect. Target components may be pipes, but will often be components with more complex geometries or problematic material properties as is often the case with stainless steel welds. Modelling how ultrasound propagates through such components can now be reasonably tackled on a high specification desktop PC using methods such as finite element (FE) analysis. Computation time obviously depends on the complexity and size of the model, and the range of frequencies being modelled, but typically one would expect models to take several hours to run on representative components. This needs to be complemented by modelling the behaviour of the transducers, again using FE modelling of the electromagnetic behaviour of sample and transducer. In some cases it is appropriate to combine these FE models with analytical models to improve computation time. Rather than simply providing solutions to a limited number of inspection issues, we will develop a scientific methodology for designing techniques to inspect components of any geometry, equipping both researchers and industrial users with an approach for making the right tool for a specific job rather than providing a limited range of tools.