Collisional transport in edge transport barriers and stellarators

Abstract: Nuclear fusion has the potential to generate abundant and clean energy. In magnetic confinement fusion, the temperatures needed to achieve fusion are obtained by confining a hot plasma with magnetic fields. To maintain these hot temperatures and realize the potential of fusion, an understanding of transport mechanisms of particles and energy in these plasmas is needed. This thesis theoretically investigates two aspects of collisional transport in magnetically confined fusion plasmas: the collisional transport in tokamak transport barriers and of highly-charged impurities in stellarators. The tokamak and the stellarator are the two most developed solutions to magnetically confining a plasma. Tokamaks frequently operate in a regime (the \emph{H-mode}) with a transport barrier near the edge of the plasma, in which turbulence is spontaneously reduced. This leads to reduced energy and particle transport and sharp temperature and density gradients. These sharp gradients challenge the modeling capabilities based on the conventional theory of collisional transport, which relies on the assumption that the density, temperature, and electrostatic potential of the plasma do not vary strongly over a particle orbit. This thesis explores an extension of the conventional theory that accounts for these effects, by means of numerical simulations. Another limit that challenges the conventional assumptions is when the density of an impurity varies along the magnetic field. This happens for heavy impurities, such as iron or tungsten, which can enter the plasma from interactions with the walls of the reactor. Due to their high charge, these impurities are sensitive to even slight variations in electrostatic potential in the plasma, which causes their density to vary along the magnetic field. This density variation can qualitatively affect how the impurities are transported. This is explored in the latter half of this thesis, with an eye towards how this effect could be used to prevent impurities from accumulating in the core of stellarators, where they are detrimental.