Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)




Allen H Boozer


The goal of nuclear fusion research is to confine a deuterium-tritium plasma at a sufficiently high temperature (15 keV) and density (3 $\times$ 10$\sp{20}$ m$\sp{-3}$) for a sufficient length of time (1 sec) to produce net fusion power. One means to attain the required plasma confinement is to embed the plasma within a magnetic field. The global structure of this magnetic field determines the variation of magnetic field strength within the surfaces of constant plasma pressure. This field strength variation in turn determines many of the stability and confinement properties of the plasma. This dissertation gives the first detailed exposition of the spectrum of possible forms for magnetic field strength corresponding to toroidal plasma equilibria, both within any three-dimensional volume and within any two-dimensional surface of constant plasma pressure. Constraints due to the toroidicity of the configuration and the divergence-free property of the magnetic field are found to limit the form of the field strength. Three-dimensional stellarator equilibria corresponding to a particular form of the magnetic field strength are especially interesting. These "quasi-helically symmetric" equilibria are non-axisymmetric, toroidal configurations in which the magnetic field strength depends on only one angular coordinate, instead of two, within the constant plasma pressure surfaces. Unlike conventional stellarator equilibria, these quasi-helically symmetric equilibria exhibit the favorable confinement properties of axisymmetric tokamak equilibria. We show that stellarators with exact quasi-helical symmetry do not to exist, but that good approximations can be found.



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