Beam tracing for stellarators

Abstract

Nuclear fusion presents a promising path to achieving clean, virtually limitless energy by replicating the processes that power the Sun. However, realising controlled fusion on Earth remains a significant challenge, particularly due to extreme temperatures and pressures of the plasma. One of the most promising approaches involves confining the plasma through the use of strong magnetic fields -- the main principle behind magnetic confinement fusion (MCF) -- and is the method adopted in two of the most popular designs: the tokamak and the stellarator. However, a key obstacle in MCF is plasma turbulence, which causes energy and particle outfluxes that degrade plasma confinement and is termed turbulent transport. As such, the study of turbulence is a high-priority goal in MCF, for which a collection of plasma diagnostic techniques have been employed. One such diagnostic is the Doppler backscattering (DBS) diagnostic, wherein a microwave is launched into the plasma and scattered by the plasma density fluctuations, with the signal from the backscattered waves being measured by an antenna. By using the beam model for DBS, an existing Python library called Scotty provides insights into how the signal is weighted along its trajectory, but only within axisymmetric tokamak-type configurations.

In this thesis, we develop a new computational Python mini-library, colloquially called Cartesian Scotty, to extend the simulation capabilities of the existing Scotty library to perform Doppler backscattering (DBS) analysis using the beam model for DBS in more complex and non-axisymmetric magnetic geometries. The code is extensively validated in three scenarios: in vacuum, the 2-D linear layer, and tokamak data obtained from DIII-D shot 189998. The results are benchmarked against analytical solutions (for the first two scenarios) and the Scotty code (for the tokamak). We find that the numerical results generated by Cartesian Scotty are in good agreement with known solutions for all three scenarios. Lastly, preliminary DBS simulations are conducted in a synthetic stellarator-type plasma generated using DESC using parameters based on the W7-X stellarator, where for all simulations we use two simple scaling laws for the turbulence spectra. For this, we find that the relation between the expected backscattered power vis-a-vis the turbulence spectrum does not globally follow the aforementioned turbulence scaling laws, which leads to the conclusion that this is a result of the signal localisation rather than the particular turbulence spectrum. This has a few implications, for which one example is that extra care must be taken when trying to solve the inverse problem -- wherein one tries to obtain a specific turbulence spectrum scaling law given an experimentally-measured backscattered power spectrum. Finally, using these results, we also give a brief exposition on the rationale behind optimising the mismatch angle and its importance in real-life DBS systems.