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Abstract
The study of pure electron plasmas confined on magnetic surfaces has only recently begun, with much of the work being conducted by the Columbia Non-neutral Torus (CNT) group. This thesis describes a computational model used to solve the equilibrium equation of such plasmas, some general properties of the equilibrium predicted by the model, reconstructions of the equilibrium of experimental plasmas in the CNT and in the Compact Helical System (CHS), and some relevant experimental contributions to the CNT experiment.
The first three-dimensional equilibrium solver, the PBS (Poisson-Boltzmann Solver) code, was designed to model the equilibrium of these plasmas. The nonlinear equilibrium equation for the electrostatic potential is solved using an iterative pseudo-spectral method, and a flexible singular value decomposition (SVD) method is used to enforce boundary conditions.
This code was first used to model a variety of simple geometries and boundary conditions. The results of these calculations show an outward major radial shift of the plasma, a shift toward conductors, and an increase in plasma ellipticity with respect to the magnetic surfaces. Dependence of the equilibrium on Debye length has also been explored.
The complicated CNT magnetic surface configuration has been implemented and the equilibrium of CNT plasmas modeled. Results show a factor of five axial variation in density, more than twice as large as expected for a Penning trap with similar mirror fields. A simple analytical expression has been derived that describes this variation. Reconstructions of CNT equilibria have been performed and agree well with experiment, while CHS reconstructions differ somewhat from experimental measurements, but in a consistent with known problem associated with the diagnostic techniques employed.
Some experimental work done for the CNT is also described in this thesis. This includes the experimental verification of the CNT magnetic surface configuration, necessary for proper equilibrium reconstructions, and the construction of a copper mesh torus that conforms to the CNT outer magnetic surface, the implementation of which should improve confinement according to computational predictions.
