Michal Kuczynski

• This work explores the theory of stellarator plasmas with an outward-pointing elecric field, so-called core electron-root confinement plasmas, by means of numerical simulations and analytical theory. The numerical simulations were carried out with the global, gyrokinetic, particle-in-cell code EUTERPE, which was used to solve the drift kinetic equation for electrons and ions whilst self-consistently calculating the electric field. Electron roots hold significance for stellarator research due to the following factors: the positive radial electric field can aid in the removal of heavy impurities from the plasma core; the interplay between magnetic and electric poloidal drifts causes significant radial transport of low-energy α-particles, which can be utilised to expel helium ash in a stellarator reactor; and the highly-sheared E × B flow occurring at the transition from electron roots to ion roots has the capability to mitigate turbulence. Turbulent transport accounts for the majority of energy losses in both tokamaks and stellarators. With recent technological advancements in high-performance computing, full-device (global) numerical simulations of turbulent transport can now be performed. The calculated heat fluxes depend on the structure of the electric field, which for stellarators is predominantly determined by neoclassical transport theory. Thus, for accurate turbulence simulations, a consistent radial electric field is essential, and its determination is the main objective of this thesis. The goal of obtaining reliable calculations of the electric field in EUTERPE has been achieved, providing a crucial foundation for further research in turbulence simulations. On the other hand, routine transport calculations for comparison with experimental data typically use a local diffusion-type model to calculate the electric field, because it requires significantly fewer computational resources than a global kinetic simulation. In this work, the validity of this approach is verified. This is achieved by numerous benchmarks of the global EUTERPE results against calculations performed with local codes. Consequently, plasma regimes for which global theory is necessary are identified. Moreover, for the Wendelstein 7-X stellarator, an improved model of the electric-field diffusion coefficient is proposed. It allows for a quick estimation of a model electric field with the maximum shearing rate of the E × B flow that matches the global solution. The interpretation of numerical results is supported by analytical work, achieved through a collaborative effort. Most notably, on the basis of local theory, a criterion for the electron-to-ion temperature ratio required for the existence of electron-roots is derived. Further, it is proved that adequately optimised magnetic fields can produce electron-roots even when this ratio is close to unity. Consequently, this leads to the possibility of designing reactors exhibiting electron-root plasmas. Secondly, it is shown that in the limit of vanishing gyroradius, several generalisations of the electric-field diffusion model result in the same prediction of the electric-field transition location. This location is however in quantitative disagreement with global simulation, further highlighting their importance for the study of core electron-root confinement plasmas in both existing stellarators and future reactors.