| dc.description.abstract | The equilibrium and stability of physical systems are fundamental topics with applications throughout physics.
To realize a practical magnetically confined fusion power plant, it is essential to establish and maintain plasma equilibrium during periods of operation required for energy production.
Moreover, this equilibrium must remain stable in the presence of perturbations.
The work presented here is framed around the two leading magnetic confinement concepts: stellarators and tokamaks.
Within this dissertation, the stellarator studies focus primarily on equilibrium, whereas the tokamak studies focus on plasma stability.
These topics were chosen to address research questions of particular interest for each confinement concept.
For the equilibrium studies, we investigate three-dimensional plasma confined in stellarators.
To this end, two projects were undertaken.
The first was a verification study of equilibrium solvers, while the second was an in-depth investigation of a particular aspect of one equilibrium solver.
In the former, we investigated whether several different three-dimensional (3D) magnetohydrodynamic (MHD) equilibrium codes, DESC, SIESTA, SPEC, and VMEC, a would arrive at the same equilibrium given the same physical system.
Although the codes employ different numerical formulations, they are all based on the same MHD equations and should therefore converge to the same equilibrium solution.
This expectation was confirmed.
The latter project examined how SIESTA modeled magnetic islands, an important aspect of 3D equilibria.
This study sought to better understand the mechanism by which the code introduces perturbations that generate magnetic islands.
We show that increasing the magnitude of the perturbation parameter, which allows the islands to form, enlarges them and shifts their radial location in the plasma.
Furthermore, a relationship between the location of the island relative to the edge and its size was identified and investigated.
Regarding stability, motivated by previous tokamak equilibrium research, we investigated how a simplified version of this system of interest would respond to perturbations.
The initial system, containing discontinuities in both velocity and pressure, is susceptible to instability growth.
The former would lead to the development of a Kelvin-Helmholtz instability, and the latter could be modeled as a Rayleigh-Taylor instability.
Dispersion relations and asymptotic expressions for the growth rates were derived for compressible fluids subject to both instabilities, showing the instability persists beyond where the classical compressible Kelvin-Helmholtz instability would stabilize.
In the presence of flow-aligned magnetic fields, an approximate expression for the field strength required to suppress the instabilities was also obtained. | en_US |
