## Doctoral 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.

Particle and heat transport in fusion devices often exceed the neoclassical prediction. This anomalous transport is thought to be produced by turbulence caused by microinstabilities such as ion and electron-temperature-gradient (ITG/ETG) and trapped-electron-mode (TEM) instabilities, the latter ones known for being strongly influenced by collisions. Additionally, in stellarators, the neoclassical transport can be important in the core, and therefore investigation of the effects of collisions is an important field of study. Prior to this thesis, however, no gyrokinetic simulations retaining collisions had been performed in stellarator geometry. In this work, collisional effects were added to EUTERPE, a previously collisionless gyrokinetic code which utilizes the δ f method. To simulate the collisions, a pitch-angle scattering operator was employed, and its implementation was carried out following the methods proposed in [Takizuka & Abe 1977, Vernay Master's thesis 2008]. To test this implementation, the evolution of the distribution function in a homogeneous plasma was first simulated, where Legendre polynomials constitute eigenfunctions of the collision operator. Also, the solution of the Spitzer problem was reproduced for a cylinder and a tokamak. Both these tests showed that collisions were correctly implemented and that the code is suited for more complex simulations. As a next step, the code was used to calculate the neoclassical radial particle flux by neglecting any turbulent fluctuations in the distribution function and the electric field. Particle fluxes in the neoclassical analytical regimes were simulated for tokamak and stellarator (LHD) configurations. In addition to the comparison with analytical fluxes, a successful benchmark with the DKES code was presented for the tokamak case, which further validates the code for neoclassical simulations. In the final part of the work, the effects of collisions were investigated for slab and toroidal ITGs and TEMs in a tokamak configuration. The results show that collisions reduce the growth rate of slab ITGs in cylinder geometry, whereas they do not affect ITGs in a tokamak, which are mainly curvature-driven. However it is important to note that the pitch-angle scattering operator does not conserve momentum, which is most critical in the parallel direction. Therefore, the damping found in a cylinder could be the consequence of this missing feature and not a physical result [Dimits & Cohen 1994]. Nonetheless, the results are useful to determine whether the instability is mainly being driven by a slab or toroidal ITG mode. EUTERPE also has the feature of including kinetic electrons, which made simulations of TEMs with collisions possible. The combination of collisions and kinetic electrons made the numerical calculations extremely time-consuming, since the time step had to be small enough to resolve the fast electron motion. In contrast to the ITG results, it was observed that collisions are extremely important for TEMs in a tokamak, and in some special cases, depending on whether they were mainly driven by density or temperature gradients, collisions could even suppress the mode (in agreement with [Angioni et al. 2005, Connor et al. 2006]). In the case of stellarators it was found that ITGs are highly dependent on the device configuration. For LHD it was shown that collisions slightly reduce the growth rate of the instability, but for Wendelstein 7-X they do not affect it and the growth rate showed a similar trend with collisionality to that of the tokamak case. Collisions also tend to make the ballooning structure of the modes less pronounced.

Impurity ions pose a potentially serious threat to fusion plasma performance by affecting the confinement in various, usually deleterious, ways. Due to the creation of helium ash during fusion reactions and the interaction of the plasma with the wall components, which makes it possible for heavy ions to penetrate into the core plasma, impurities can intrinsically not be avoided. Therefore, it is essential to study their behaviour in the fusion plasma in detail. Within the framework of this thesis, different problems arising in connection with impurities have been investigated. 1. Collisional damping of zonal flows in tokamkas: The effect of impurities on the collisional damping of zonal flows is investigated. Since the Coulomb collision frequency increases with increasing ion charge, heavy, highly charged impurities play an important role in this process. The effect of such impurities on the linear response of the plasma to an external potential perturbation, as caused by zonal flows, is calculated with analytical methods and compared with numerical simulations, resulting in good agreement. 2. Impurity transport driven by microturbulence in tokamaks: Fine scale turbulence driven by microinstabilities is a source of particle and heat transport in a fusion reactor. A semi-analytical model is presented describing the resulting impurity fluxes and the stability boundary of the underlying mode. The results are compared with numerical simulations. Both the impurity flux and the stability boundary are found to depend strongly on the plasma parameters such as the impurity density and the temperature gradient. 3. Pfirsch-SchlÃ¼ter transport in stellarators: Due to geometry effects, collisional transport plays a much more prominent role in stellarators than in tokamaks. Analytical expressions for the particle and heat fluxes in an impure, collisional plasma are derived from first principles. Contrary to the tokamak case, where collisional transport is exclusively caused directly by friction, in stellarators an additional source of transport exists, namely pressure anisotropy. Since this term is, contrary to the contribution from friction, non-ambipolar, it plays an important role regarding the ambipolar electric field. Furthermore, the behaviour of heavy impurities in the presence of strong radial temperature and density gradients is studied, which lead to a redistribution of the impurities on the flux surfaces. As a consequence, the radial impurity flux is decreased considerably compared with a plasma in which the impurities are evenly distributed on the flux surfaces.

The present work is the first work dealing with turbulence in the WEGA stellarator. The main object of this work is to provide a detailed characterisation of electrostatic turbulence in WEGA and to identify the underlying instability mechanism driving turbulence. The spatio-temporal structure of turbulence is studied using multiple Langmuir probes providing a sufficiently high spatial and temporal resolution. Turbulence in WEGA is dominated by drift wave dynamics. Evidence for this finding is given by several individual indicators which are typical features of drift waves. The phase shift between density and potential fluctuations is close to zero, fluctuations are mainly driven by the density gradient, and the phase velocity of turbulent structures points in the direction of the electron diamagnetic drift. The structure of turbulence is studied mainly in the plasma edge region inside the last closed flux surface. WEGA can be operated in two regimes differing in the magnetic field strength by almost one order of magnitude (57mT and 500mT, respectively). The two regimes turned out to show a strong difference in the turbulence dynamics. At 57mT large structures with a poloidal extent comparable to the machine dimensions are observed, whereas at 500mT turbulent structures are much smaller. The poloidal structure size scales nearly linearly with the inverse magnetic field strength. This scaling may be argued to be related to the drift wave dispersion scale. However, the structure size remains unchanged when the ion mass is changed by using different discharge gases. Inside the last closed flux surface the poloidal ExB drift in WEGA is negligible. The observed phase velocity is in good agreement with the electron diamagnetic drift velocity. The energy in the wavenumber-frequency spectrum is distributed in the vicinity of the drift wave dispersion relation. The three-dimensional structure is studied in detail using probes which are toroidally separated but aligned along connecting magnetic field lines. As expected for drift waves a small but finite parallel wavenumber is found. The ratio between the average parallel and perpendicular wavenumber is in the order of 10^-2. The parallel phase velocity of turbulent structures is in-between the ion sound velocity and the AlfvÃ¨nvelocity. In the parallel dynamics a fundamental difference between the two operational regimes at different magnetic field strength is found. At 500mT turbulent structures can be described as an interaction of wave contributions with parallel wavefronts. At 57mT the energy in the parallel wavenumber spectrum is distributed among wavenumber components pointing both parallel and antiparallel to the magnetic field vector. In both cases turbulent structures arise preferable on the low field side of the torus. Some results on a novel field in plasma turbulence are given, i.e. the study of turbulence as a function of resonant magnetic field perturbations leading to the formation of magnetic islands. Magnetic islands in WEGA can be manipulated by external perturbation coils. A significant influence of field perturbations on the turbulence dynamics is found. A distinct local increase of the fluctuation amplitude and the associated turbulent particle flux is found in the region of magnetic islands.