Publication
In magnetically confined fusion devices, the energy and particle transport is significantly larger than expected from purely collisional processes. This degraded confinement mostly results from small-scale turbulence and prevents from reaching self-sustained burning plasma conditions in present day experiments. A better understanding of these nonlinear phenomena is therefore of key importance on the way towards controlled fusion. The small-scale microinstabilities and associated turbulence are investigated for Tokamak plasmas by means of numerical simulations in the frame of the gyrokinetic theory. This model describes the evolution of the particle distribution functions in phase space together with self-consistent electromagnetic fields, while neglecting the fast motion associated with the Larmor orbit of particles around the magnetic field lines. In the course of this thesis work, substantial modifications to the existing Eulerian gyrokinetic code GENE have been carried out in collaboration with the Max-Planck-Institute für Plasmaphysik in Garching, Germany. The code has been extended from a local approximation, which only considers a reduced volume of a fusion plasma, to a global version which fully includes radial temperature and density profiles as well as radial magnetic equilibrium variations. To this end, the gyrokinetic equations have been formulated for general magnetic geometry, keeping radial variations of equilibrium quantities, and considering field aligned coordinates, suitable for their numerical implementation. The numerical treatment of the radial direction has been modified from a Fourier representation in the local approach to real space in the global code. This has in particular required to adapt the radial derivatives, the field solver, and to implement a real space dealiasing scheme for the treatment of the nonlinearity. A heat source was in addition introduced to allow for steady state global nonlinear simulations. An important part of this work also focused on the description of the magnetic equilibrium. A circular concentric flux surface model as well as an interface with an MHD equilibrium code were implemented. A detailed investigation concerning the s – α model, previously used in local codes, was also carried out. It was shown that inconsistencies in this model had resulted in misinterpreted agreement between local and global results at large ρ* = ρs/a values, with ρs the Larmor radius and a the minor radius of the Tokamak. True convergence between local and global simulations was finally obtained by correct treatment of the geometry in both cases and considering the appropriate ρ* → 0 limit in the latter case. The new global code was furthermore successfully tested and benchmarked against various other codes in the adiabatic electron limit in both the linear and nonlinear regime. A nonlinear ρ* scan was in addition carried out showing convergence to the local results in the limit ρ* → 0 and also providing further in
António João Caeiro Heitor Coelho