Turbulent and Collisional Transport in Optimized Stellarators

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The stellarator is a fusion energy concept that relies on fully three-dimensional shaping of magnetic fields to confine particles. Stellarators have many favorable properties, including, but not limited to, the ability to operate in steady-state, many optimizable degrees of freedom, and no strict upper limit on the plasma density. Due to the three-dimensional character of stellarators, theoretical and computational studies of stellarator physics are challenging, and they also possess some disadvantages compared with tokamaks. Namely, particle confinement and impurity control are problems in generic stellarator magnetic fields that must be addressed with optimized magnetic fields. Further, simulations will require a substantial increase in grid points because of the three-dimensional structure, leading to more expensive computations. This thesis will address both topics, by first exploring the behavior of impurity particle transport in optimized stellarators, and then introducing a boundary condition to reduce the cost of stellarator turbulence simulations.

Impurity temperature screening is a favorable neoclassical phenomenon involving an outward radial flux of impurity ions from the core of fusion devices. Quasisymmetric magnetic fields lead to intrinsically ambipolar neoclassical fluxes that give rise to temperature screening for low enough $\eta^{-1}\equiv d\ln n/d\ln T$. Here we examine the impurity particle flux in a number of approximately quasisymmetric stellarator configurations and parameter regimes while varying the amount of symmetry-breaking in the magnetic field. Results indicate that achieving temperature screening is possible, but unlikely, at low-collisionality reactor-relevant conditions in the core. Further, in configurations optimized for quasisymmetry, results suggest that neoclassical fluxes are small compared with a gyro-Bohm estimate of turbulent fluxes.

Calculating these turbulent fluxes is generally done by solving the gyrokinetic equation in a flux tube simulation domain, which employs coordinates aligned with the magnetic field lines. The standard ``twist-and-shift'' formulation of the boundary conditions was derived assuming axisymmetry and is widely used because it is efficient, as long as the global magnetic shear is not too small. A generalization of this formulation is presented, appropriate for studies of non-axisymmetric, stellarator-symmetric configurations, as well as for axisymmetric configurations with small global shear. The key idea of this generalization is to rely on integrated local shear, allowing one significantly more freedom when choosing the extent of the simulation domain in each direction. Simulations of stellarator turbulence that employ the generalized parallel boundary conditions allow for lower resolution to be used compared with simulations that use the (incorrect, axisymmetric) standard parallel boundary condition.