A theoretical study of macroscopic wave activity in H-1 plasmas

A rich low-frequency wave phenomenology has been observed in plasmas generated on the H-1 heliac. A significant proportion of these fluctuations show Alfvenic characteristics. The strongly shaped magnetic geometry of H-1 presents a major obstacle to theoretical modelling of macroscopic wave physics, even under the simplifying assumptions of ideal MHD. An additional obstacle has been the dearth of literature on low-frequency Alfvenic oscillations in fusion plasmas in general, and stellarator plasmas in particular, until quite recently. A recent surge of interest in the low-frequency Alfvenic oscillations as well as the low equilibrium uncertainty of H-1 makes a physical theory of the dominant H-1 oscillations desirable. Apart from intrinsic scientific interest, the underlying driver of Alfven wave activity studies in the broader context of the physics of magnetically confined plasmas is the potential role such wave activity may have in achieving good plasma confinement. Interactions of Alfven waves with energetic particles can lead to reduced energetic ion confinement with consequent heating losses and vessel damage. MHD spectroscopy offers the prospect of using wave behaviour as a proxy for determining underlying plasma parameters and conversely, there is scope for active control of plasma parameters through excitation of Alfven waves. In this thesis, the three-dimensional, compressible ideal spectrum for H-1 is presented, based on numerical simulations with the CAS3D three-dimensional ideal MHD linear eigenmode solver. A significant mirror term in combination with a variety of strong field-strength modulations within a cross-section induces coupling of eigenmode Fourier harmonics in both toroidal and poloidal directions. It is shown that the conditions for convergence of the code in Fourier space are quite stringent for H-1 configurations, in the sense that shear Alfven frequencies dip sharply near the core unless the component of fluid motion along the field lines has a Fourier basis including at least two toroidal sidebands, even for high frequency modes with negligible acoustic interaction. The first two HAE gaps and the TAE gap are identified. A significant beta-induced gap is found, bounded above by the geodesic acoustic frequency, which is found to lie at around 30-40 kHz. Consequently, H-l fluctuations, which typically lie below 40 kHz, can be considered sub-GAM modes. Based on analytic estimates, it is proposed that H-1 fluctuations may include sub-GAM beta-induced Alfvenic eigenmodes reproducing a characteristic "whale tail" sloping in configuration space due to temperature gradients. Low frequency CAS3D spectra and quasi-discrete modes are presented. To provide context for the new results presented, a from-first-principles review of the ideal theory relevant to H-1 plasmas is given starting with a definition of the plasma state. A summary of the assumptions underlying ideal MHD and its reliability in a fusion plasma wave analysis context is given and linear ideal wave physics in three dimensional toroidal geometry is reviewed. Limitations of ideal-MHD in the sub-GAM frequency range are discussed