Temperature gradient driven instabilities, structure, and transport in magnetized plasmas

Zielinski, Jeffery

Temperature gradient driven instabilities, structure, and transport in magnetized plasmas

dc.contributor.committeeMember	Tanaka, Kaori
dc.contributor.committeeMember	Bradley, Michael
dc.contributor.committeeMember	Bourassa, Adam
dc.contributor.committeeMember	Sowa, Artur
dc.creator	Zielinski, Jeffery
dc.creator.orcid	0000-0002-5683-9468
dc.date.accessioned	2021-09-23T17:39:06Z
dc.date.available	2021-09-23T17:39:06Z
dc.date.created	2021-09
dc.date.issued	2021-09-23
dc.date.submitted	September 2021
dc.date.updated	2021-09-23T17:39:06Z
dc.description.abstract	Turbulence presents one of the most interesting lasting challenges of classical physics. The vast universe of solutions, generated from such apparently simple constituent equations (e.g. the Navier-Stokes for neutral fluids), has yielded diverse fields of study which only consider particular parts of a given problem. In plasmas, particularly those which are magnetized, the equations become far more complex --- where the Navier-Stokes equations can be non-dimensionalized in terms of a single variable, the Reynolds number, plasmas require several. This work investigates small-scale turbulence in tokamak plasmas by developing understanding from an elemental perspective. The local properties of two distinct temperature-gradient driven instabilities are studied analytically, along with being elucidated pedagogically in terms of the physical processes. One of these instabilities, the Ion Temperature Gradient (ITG) mode, is studied using global numerical simulations which make up the vast majority of this dissertation. The technological capability for such simulations is relatively new, and the detailed investigation of eigenmode and turbulent structures presented here show numerous novel characteristic results. This provides insight into the potential nature of turbulent motion and transport with a clarity which cannot be measured in experiments. Once the simulations are well understood, they can be used to design experiments, in attempts to improve device performance, test the model, and further develop the theory. The simulations completed here use the JOREK code, which was originally designed to simulate large-scale tokamak phenomena. Nevertheless, the finite-volume method, with harmonic decomposition in the toroidal direction, is well suited to the ITG model under investigation, given the adaptations discussed within. Although using JOREK to simulate small-scale turbulence incurs some additional computational demands, due to the increased resolution, both the model and JOREK are fluid-based, which allow for significantly faster computations than comparable-scale kinetic simulations. In the subsequent approximation of kinetic effects like Landau damping, the results can be expected to omit the more nuanced nature of the instability and turbulence. Accepting this, the simulation portion of the dissertation endeavors to provide an understanding of global ITG fundamentals, identifying characteristic changes in structure and behavior by performing many simulations over a significant range of relevant parameters. In addition to considering the linear and nonlinear structures of the simulated variables, the ITG simulations enumerate a significant number of quantities and relationships. These vary from growth characteristics and the relationships in the energy spectra, to quantification of the nonlinear Reynolds stress (momentum transport) and heat flux (energy transport), to approximating the proportionality between radial and angular mode numbers during turbulence. Correlation coefficients between pairs of harmonics are also measured to establish an impression of how the overall energy spectra are formed from the coupling of particular harmonics. The simulations are shown to have a weak dependence on several numerical dissipation parameters, which are used to reproduce kinetic effects. The effect of these parameters is enumerated and described, throughout. The majority of this dissertation builds an understanding of how turbulence forms from the underlying instabilities. In contrast, the final portion of this work studies transport more abstractly. The focus is on electron transport by magnetic perturbations, and the starting point is a prescribed state of magnetic turbulence. The standard (diffusive) fluid heat flux equation is then expanded in terms of localized harmonics, and the highly anisotropic magnetic field is shown to drive significant higher-order (cubic) heat flux. In focusing on the relationship of structure to transport, this dissertation develops an elemental picture of how the turbulent motion of magnetized plasma can degrade energy confinement.
dc.format.mimetype	application/pdf
dc.identifier.uri	https://hdl.handle.net/10388/13606
dc.subject	Plasma, Turbulence, Transport, Fluid Modelling, Magnetic Geometry, Temperature Gradient, Instabilities
dc.title	Temperature gradient driven instabilities, structure, and transport in magnetized plasmas
dc.type	Thesis
dc.type.material	text
thesis.degree.department	Physics and Engineering Physics
thesis.degree.discipline	Physics
thesis.degree.grantor	University of Saskatchewan
thesis.degree.level	Doctoral
thesis.degree.name	Doctor of Philosophy (Ph.D.)