Simulation of Electron Bernstein Waves in FLiPS with various numerical methods

Abstract

The plasma generation and heating by microwaves is an important research topic in the field of controlled nuclear fusion. All modern fusion plasma devices such as Wendelstein 7-X use microwave heating. The microwave plasma-heating primarily occurs at the resonances, where the microwaves are efficiently absorbed. The heating scenario must be designed such that the microwaves can reach the resonance. When the plasma exceeds the cutoff density, the microwaves will be reflected, and the resonance becomes inaccessible. However, it is possible to perform heating by Electron Bernstein Waves (EBWs), since these electrostatic waves propagate even in overdense plasmas, unlike the electromagnetic plasma waves. EBWs cannot propagate in the vacuum and must be created through a coupling process. Both O- and X-mode can couple to EBWs. The thesis investigates the coupling of the O- and X-mode to EBWs as well as the EBW propagation with various numerical methods. The application of only one numerical method is not sufficient as the coupling involves very different wavelength scales. The optimal coupling scheme for the expected plasma parameters was determined using a Finite-Difference Time-Domain (FDTD) code. Since EBWs are not included in the code, a Boundary-Value Problem (BVP) code was developed. Using the BVP code, the effect of the collisions on EBWs was studied. The field amplification at the upper-hybrid resonance (UHR), where EBWs couple to the electromagnetic waves, and the effect of the magnetic field on EBWs could be directly visualized. The propagation of the EBW was investigated using the novel ray-tracing code RiP. The ray-tracing simulations provided a clear picture of the essential features of the wave propagation. For the O- and X-mode coupling, the importance of the axial plasma inhomogeneity was shown. For the first time, the method of the Wigner function was applied to calculate the intensity distribution of EBWs. Both, ray-tracing and the Wigner function simulations showed that the inhomogeneous magnetic can cause focusing of EBWs. The focusing effect can have practical applications e.g. for controlled local heating of the plasma. Additionally, the focusing effect can cause a parametric decay due to the field enhancement in the focal regions. In this thesis, the simulations were focused on excitation and propagation of EBWs in the geometry of the linear plasma device FLiPS located at the University of Stuttgart. Measurements were carried out to study the predicted focusing of the EBWs in the FLiPS plasma with monopole antennas. The measurements provided the density profile used in the simulations. The expected amplification of the signal at the UHR was not detected, indicating either the complete collisional absorption of the X-mode at the upper-hybrid resonance, or the turbulent plasma density oscillations that reduce the coupling efficiency to EBWs. These effects can be studied further using the developed tools since they provide a complete toolbox to study the full coupling process to EBWs in an actual experimental geometry.