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Since the advent of modern-day computation, the size of electronic devices has been dramatically reduced, resulting in vast increases in computational power. As the size of these electronic devices approaches the nanoscale, the current densities transported through them can be many orders of magnitude higher than in a typical copper coil to heat the water in your kettle. These large current densities can lead to violent dynamics of the atoms in a nanodevice. The resultant momentum and energy transfer can lead the atoms within the nanowire migrating or fleeing the wire altogether. This process is known as electromigration and depending on the structure and size of the nanowire can lead to the loss of contact between source and sink. Originally electromigration was thought to be a process initiated by Joule heating. However, experiments carried out on one-atom-thick wires by our collaborators in Leiden showed that the wires were breaking at low bias. This bias was too small for localised Ohmic heating to be the cause of the breakdown. Years earlier it was proposed by Sorbello that the current-induced force experienced by an atom in a conductor could be nonconservative. That is, around closed paths, net work could be done on the nuclei. After a series of revolutions, the nucleus can pick up enough kinetic energy to change its position within the wire resulting in instabilities. This thesis involves a marriage between theory and simulation to take forward our present understanding, the role the electron wind force plays in electromigration in both the time independent and dependent case.

1 in 2 people will suffer from cancer during their lifetime and, in the UK, around a third of patients will be treated with radiotherapy, primarily with X-rays. Three decades of research and development into high-gradient linear accelerator technology has resulted in Very High Energy Electrons (VHEE) in the range 100-250 MeV being a potentially viable radiotherapy modality. Advantageous characteristics of VHEE include sufficient penetrative range to treat deep-seated tumours, measured relative insensitivity to inhomogeneities, reduced lateral penumbra and improved dose distribution. VHEE beams can be delivered and controlled rapidly using scanning magnets, making it a candidate for FLASH radiotherapy, a technique involving treatment at ultra-high dose rates - in vitro and in vivo studies present strong evidence of a normal tissue sparing effect. For successful translation of VHEE theory to the clinic, we must understand the effects of VHEE on fundamental biological structures and how these effects compare with well-established modalities. To achieve this, a dose conversion known as Relative Biological Effectiveness (RBE) is required. The primary aim of this project was to quantify the characteristics of VHEE RBE and to compare with other radiotherapy modalities. Traditionally, cell survival is used to measure RBE in vitro, however survival is the end-point of a damage and repair process. To gain fundamental understanding of the biological difference between VHEE and other modalities, it is necessary to separate the nanodosimetric physics qualities of VHEE by looking directly at how damage is induced. DSB yield was therefore selected as the endpoint for RBE calculation, determined following a series of pBR322 plasmid irradiation experiments, the first of their kind for VHEE, at the CLEAR user facility (CERN, 100-200 MeV) and the Christie NHS Foundation Trust (6-15 MeV). 60Co X-ray irradiation provided a reference point for RBE calculations. VHEE RBE varied from 1.1-1.2 over 100-200 MeV, indicating that physical effects of VHEE are similar to that of established modalities. This provides confidence that biological effects including cell death will also be similar - a key step on the road to clinical implementation. Experimental DSB yields were compared with GEANT4-DNA plasmid irradiation simulations of electron track structure, with the aim of producing an accurate Monte Carlo model of VHEE-induced DNA damage. This involved the adaptation of GEANT4-DNA physics constructors to allow modelling of electron track structure above 1 MeV. Parameter optimisation resulted in good agreement between GEANT4-DNA and experimental DSB yields. These damage mechanisms could then be applied to the modelling of biological effects such as DNA damage repair and cell death, with predictions informing treatment planning for clinical cases. As VHEE has been highlighted as a compatible modality for FLASH, a dose-rate variation study was carried out at the CLEAR facility to determine whether a FLASH effect could be observed when irradiating pBR322 DNA at ultra-high dose rates, presenting as a significant decrease in DSB yield. As plasmid irradiation experiments lack many key features causing a FLASH effect (primarily well-oxygenated water), variation between Conventional and FLASH-irradiated samples was not expected. No statistically significant difference between DNA damage yields was observed, it can be suggested that a FLASH effect is not present at the nanoscale under these conditions. A secondary aim of the research was to investigate the range of VHEE beams in various tissues. As part of the steps towards clinical implementation of VHEE, an understanding of the behaviour of treatment beams inside the patient is vital from a treatment planning point of view. As part of this research, a semi-empirical expression for VHEE beam range was produced, dependent on beam energy and the composition of the material through which it travels, using data from simulations of VHEE beams travelling through different media using TOPAS.

The electron radiation belts are regions of geomagnetically trapped electrons, surrounding the Earth, presenting hazards to operational satellites. On the timeframe of hours, both the energy and particle flux of the radiation belts can change by orders of magnitude. Variations in the high energy relativistic electron flux depend on transport, acceleration, loss processes, and importantly, on the lower energy seed (10s - 100s keV) population. Seed population electrons are supplied to the radiation belt region during geomagnetically active periods and can be accelerated to higher energies via a range of processes. Unlike the higher energy, > 1 MeV electrons, the azimuthal drift of the seed population is strongly affected by the convection electric field. Using fourteen years of electron flux data from low Earth orbit (LEO) satellites, a statistical study was performed on the magnetic local time distribution of three seed population energies, across a range of activity levels, defined by the geomagnetic indices AE, AE*, Kp, the solar wind velocity, and VswBz. During periods of high activity, dawn-dusk flux asymmetries of over an order of magnitude were observed for > 30 and > 100 keV electrons, due to increased flux in the dawn sector. For > 300 keV electrons, magnetic local time asymmetries were also present, but arose primarily due to a decrease in the average dusk-side flux beyond L* ~ 4.5. A novel method was developed that utilizes measurements from low altitude, polar orbiting POES and MetOp satellites to retrieve the seed population at a pitch angle of 90°. The resulting dataset offers a high time resolution, across multiple magnetic local time planes, and was used to formulate event-specific low energy boundary conditions for the British Antarctic Survey Radiation Belt Model (BAS-RBM). This new low energy boundary condition from LEO data has a higher spatial and temporal resolution, and a broader L* coverage, than previous work. The impact of variations in the seed population on the 1 MeV flux level was explored using the 3-D BAS-RBM to solve a diffusion equation for the electron phase space density. For some periods, an enhancement in the seed population was vital to recreate observed 1 MeV flux enhancements. A series of idealised experiments with the 2-D BAS-RBM were performed which highlight a careful balance between losses and acceleration from chorus waves. Our results show that seed population enhancements alter this balance by increasing the phase space density gradient, and consequently, the rate of energy diffusion, allowing acceleration to surpass loss. Additionally, pre-existing energy gradients in the phase space density and the duration of chorus wave activity determine whether > 500 keV electrons were enhanced due to local acceleration.

This thesis explores the theoretical representation of localised electrons in magnetic systems, using Majorana fermions. A motivation is provided for the Majorana fermion representation, which is then developed and applied as a mean-field theory and in the path-integral formalism to the Ising model in transversal-field (TFIM) in one, two and three dimensions, on an orthonormal lattice. In one dimension the development of domain walls precludes long-range order in discrete systems; this is as free energy savings due to entropy outweigh the energetic cost of a domain wall. An argument due to Peierls exists in 2D which allows the formation of domains of ordered spins amidst a disordered background, however, which may be extended to 3D. The forms of the couplings to the bosons used in the Random Phase Analysis (RPA) are considered and an explanation for the non-existence of the phases calculated in this thesis is discussed, in terms of spare degrees of freedom in the Majorana representation. This thesis contains the first known application of Majorana fermions at the RPA level.