Abstract

Nuclear fusion is a promising candidate for the generation of clean energy in future societies. This is an exciting research area which shares an intersection with other fields of academia, including but not limited to engineering, computer science and environmental science. The method to achieving fusion of primary interest to
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us is known as magnetic confinement fusion (MCF). In particular, we will focus on a certain branch of toroidal MCF devices, known as stellarators. These are lesser known but quickly catching up to the more ubiquitous tokamaks. A problem still facing all MCF devices is plasma heat loss due to particle and energy transport from the hot core to the cold edge. This reduces confinement, which inhibits our plasma reaching the necessary fusion-temperatures. A primary cause of transport is turbulent behaviour due to plasma micro- instabilities. The instability mode of interest to this project is the trapped-electron mode (TEM). This mode has a critical threshold for when it first becomes manifest, and it subsequently becomes problematic. For the TEM, this threshold is known as the critical density gradient. The nature and behaviour of this instability mode is heavily dependent on the geometry in which it exists, and thus, it is desirable to create an optimal geometry that extends this threshold. This would in turn delay the onset of unwanted TEM-driven turbulence. Technically, gyrokinetic simulations could be run for a myriad of different geometries which vary in configuration space. This would involve starting with a simple tokamak geometry and gently deforming it until the optimum configuration was found. However, this approach is easier said than done, and would be far too costly in terms of time and money to be realistically feasible. Thus, we turn to the theoretical framework which describes these micro-instabilities, and seek to find an analytical expression predicting their behaviour. This expression will be dependent on the geometrical characteristics of the stellarator configuration. In particular, we require a geometry-dependent expression for the critical density gradient of the mode - which we wish to maximise. This is the end goal of the project. Beyond this work, our results would be utilised in a stellarator optimisation code (STELLOPT) to see if an optimal geometry can be found in configuration space which maximises the critical density gradient. Further investigation would then be required to see if turbulent transport is indeed reduced by this newly TEM-optimised geometry.
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