The role of the electric field in simulations of plasma microturbulence

The ultimate goal of magnetic confinement fusion research is to develop an electricity producing power plant based on thermonuclear fusion reactions. Among the most promising magnetic confinement devices, as leading concepts for future power plants, are tokamaks. Plasma turbulence typically produces much larger rates of particle and energy diffusion than one would otherwise expect (for example taking into account only collisions between particles), and is a main source of present-day difficulties in achieving controlled fusion. Large scale flows induced by radial electric fields (E × B flows) are known to act as a regulating agent on the plasma turbulence. This thesis focuses on the study of the effects of an E × B flow on plasma turbulence driven by microinstabilities. These plasma instabilities are characterized by small spatial scales compared to the size of the device. The corresponding plasma turbulence is named microturbulence. The gyrokinetic model has been derived to describe microinstabilities. The gyroaveraged potential allows for a dimensional reduction of the problem. A numerical computation of the solution of the full nonlinear electromagnetic gyrokinetic equations is still behind the computational capabilities of modern supercomputers. Further approximations have to be introduced. In this thesis two schemes are presented which include the effects of E × B flows into two different global gyrokinetic codes. The first is a linear electromagnetic code which solves the gyrokinetic equation with a spectral approach. The linear approximation excludes the self-generation of electric fields which have then to be imposed as external equilibrium fields. The second is a nonlinear electrostatic code which solves the gyrokinetic equations with a Particle in Cell scheme. The nonlinear model allows us to study the self-generated radial electric field and the corresponding axisymmetric flows, also known as zonal flows. In this thesis, a formulation of the gyrokinetic equations is derived which includes E × B terms in a form suited for numerical implementation in both the linear and nonlinear schemes. The code implementations are described together with several numerical optimizations, in particular devoted to the execution of the two codes on parallel machines. Simulations have been run on electrostatic and electromagnetic microinstabilities driven by temperature gradients (ITG, Ion Temperature Gradient, and AITG, Alfvén Ion Temperature Gradient modes). The main results include a linear stability analysis of the effects of an equilibrium E × B flow on AITG and ITG modes and a study of the nonlinear interactions of ITG turbulence, zonal flows and poloidally asymmetric zonal flow oscillations, known as GAMs. As a consequence of these linear and nonlinear effects, the radial ion heat flux is found to scale linearly with the total plasma current. Besides these main results, the implemented models allows for other interesting analyses of the microinstabilities which are also presented in this thesis.