## Doctoral Thesis

This dissertation focusses on the numerical modelling of resonant destabilization of AlfvÃ©n eigenmodes by fast ions in fusion plasmas. It especially addresses non-linear simulations of stellarator plasmas in which particle collisions are retained. It is shown that collisions are required for a realistic description of AlfvÃ©n waves in plasmas relevant to nuclear fusion.
We start by carefully verifying the implementation of the collision operators into the electromagnetic version of the gyro-kinetic delta-f particle-in-cell code EUTERPE. After these initial benchmarks are completed successfully, the code is in a position to be applied to realistic tokamak and stellarator scenarios.
Since every collision operator needs to fulfil conservation laws, a momentum-conserving version of the pitch-angle scattering operator is implemented. This is in particular important for neoclassical transport simulations aimed at computing flux-surface variations of the electrostatic potential in stellarators.
Using the simplified CKA-EUTERPE model (employing a fixed-mode-structure approximation), we perform non-linear simulations in tokamaks and stellarators. We show that the non-linear dynamics of fast-ion-driven AlfvÃ©n eigenmodes is significantly influenced by collisions. They have the potential to enhance the saturation level and to affect the frequency chirping of the modes.
It is thus concluded that collisions play an essential role in determining AlfvÃ©n-eigenmode-induced fast-ion transport - an important issue for future fusion devices. In order to address this issue the CKA-EUTERPE model is extended to evolve multiple modes at the same time. First results of this multi-mode version (which enhances the level of realism of the simulations) are shown in the Appendix of the thesis.

In this Ph.D. project a method is developed to measure the magnetic field and to derive variations in the total plasma pressure due to (dia-) magnetic effects. For this purpose a plasma diagnostic has been set up at the fusion experiment ASDEX Upgrade to measure spectroscopically polarized light. The light is emitted from fast beam-particles excited by the plasma. Since the fast atoms travel through a magnetic field at high velocity, a strong Lorentz field is seen in the moving frame. This electric field gives rise to the so-called motional Stark-effect (MSE) and it is possible to conclude from the Stark-spectrum on the magnetic field.

The present experimental work investigates plasma turbulence in the edge region of magnetized high-temperature plasmas. A main topic is the turbulent dynamics parallel to the magnetic field, where hitherto only a small data basis existed, especially for very long scale lengths in the order of ten of meters. A second point of special interest is the coupling of the dynamics parallel and perpendicular to the magnetic field. This anisotropic turbulent dynamics is investigated by two different approaches. Firstly, spatially and temporally high-resolution measurements of fluctuating plasma parameters are investigated by means of two-point correlation analysis. Secondly, the propagation of signals externally imposed into the turbulent plasma background is studied. For both approaches, Langmuir probe arrays were utilized for diagnostic purposes. The main findings can be summarized as follows: Greatly elongated fluctuation structures exist in plasma edge turbulence. The structures are aligned along the confining magnetic field (k|| = 0). The correlation degree of fluctuations for a short connection length of 0.75m is greater than 80%. For much longer connection lengths of 23m and 66m, the correlation degree is reduced to approximately 40%. A conceptual interpretation of these observations is the coexistence of two different fluctuation components. One component has a correlation length parallel to the magnetic field below 20m and the other component a correlation length greater than 70m. Sine signals in the frequency range 1-100 kHz were injected into the turbulent plasma background. The propagation parallel and perpendicular to the magnetic field of the signals was studied. In poloidal direction, an asymmetry is observed, that can be explained by a copropagation of the signal with the background E Ã— B-rotation of the plasma. The signal propagation parallel to the magnetic field shows no such asymmetry. As an advanced approach, spatio-temporal wave patters were injected into the edge plasma. The waves launched that way can be seen as test waves' in a turbulent background. The coupling strength of the imposed wave patterns to the background turbulence relies on the match of the imposed waves to the dynamics of turbulent structures. If the propagation direction of the imposed waves is parallel to the propagation direction of the background plasma, improved coupling is observed. This finding underlines the importance of the background plasma rotation for future attempts of controlling the plasma edge turbulence. Further optimization of frequency and wave vector of the imposed waves is probably a promising approach for achieving a significant and systematic influence of turbulence. Taking into account the present experimental state-of-the-art, for a deeper insight into the mechanism of the plasma edge turbulence of magnetized high-temperature plasmas a joint effort of numerical modeling and experimental results is a valuable approach. Such a cooperation should cover the explanation of the correlation observations as well as the experiments on signal injection into background turbulence. A quantitative comparison between the results presented in this work and a dedicated numerical drift wave simulation would be a significant step forward to a better understanding of plasma edge turbulence.