Development of a Global Version of the Gyrokinetic Microturbulence Code GENE

In order to address non-local effects in turbulent transport of magnetic-fusion devices, the gyrokinetic code GENE has been extended from a flux tube to a more global geometry. This global version of GENE includes radial variations of temperature and density profiles, as well as of magnetic equilibrium quantities. Non-periodic radial boundary conditions allow for profile evolution. Thanks to an interface with the MHD equilibrium code CHEASE, as well as the implementation of various types of source and sink terms, the global GENE version will provide a realistic model for carrying out gyrokinetic, quasi-stationary, microturbulence simulations over a major fraction of the core plasma. Validation of the code has in particular been ensured thanks to detailed comparisons with the global PIC codes GYGLES and ORB5.

Flux-tube and global grid-based gyrokinetic simulations of plasma microturbulence and comparisons with experimental TCV measurements

Gabriele Merlo

In magnetic fusion devices, the radial transport of heat and particle largely exceeds predictions based on collisional processes. This is widely understood as a consequence of small-scale turbulence which results from the nonlinear behaviour of so-called microinstabilities. The complexity of such nonlinear phenomena allows one to address microturbulence only with a numerical description, carried out here within the gyrokinetic framework. This reduced kinetic model describes the evolution of the particle distribution functions and of the self-consistently generated electromagnetic fields neglecting the fast gyromotion. In this work we applied the grid-based gyrokinetic code GENE, using both its local and global versions, to model some of the experimental observations made in the Tokamak à Configuration Variable (TCV) at the Swiss Plasma Center. All simulations are performed considering realistic magnetic geometries, in turn provided by the MHD equilibrium solver CHEASE. In order to verify the interface of GENE with CHEASE, a series of benchmarks have been developed and successfully carried out in the linear local limit. These tests have then been extended to the global version of the code and a good agreement found with results obtained with the gyrokinetic Particle In Cell code ORB5. A significant part of this work deals with the electron heat confinement improvement observed when the shape of the plasma is modified by changing the sign of the edge triangularity, from positive to negative. In the latter case, half the heating power is required to maintain the same electron profiles compared to the former, which was experimentally interpreted as a better confinement at all radial locations, even though triangularity has a finite radial penetration depth. A series of local runs were carried out to investigate the dependence of profile stiffness on shaping, failing at reproducing both the absolute level of transport as well as the ratio between the two shapes. Global gradient-driven simulations have then been performed, showing a very high sensitivity of the electron heat flux with respect to the density gradient. These runs, carried out neglecting carbon impurities, are compatible with the experiments when using parameters from an experimentally well diagnosed discharge. In this case, strong global effects which lower the heat flux compared to local runs are seen. Local and global simulations have then been performed looking at axisymmetric dynamics in the frequency range of the Geodesic Acoustic Mode (GAM). Experimentally, the GAM is almost always observed as a radially coherent mode, i.e. an oscillation at constant frequency over a main fraction of the plasma minor radius. The only exception is for very large values of the edge safety factor q, where the mode looses its coherence becoming dispersive. A density ramp-up was studied with local simulation, already obtaining a reasonable agreement with measurements of heat transport as well as GAM frequency and amplitude. The coherent GAM was then investigated with global runs. Simulations qualitatively agree with experiments and a good match is recovered with ORB5 results when the same physical model is used. Finally, the hypothesis of a coherent-dispersive GAM transition related to the safety factor profile is addressed. It is found that changing only q is not sufficient to induce a regime transition, which thus appears to be due to other parameters, including finite machine size effects.

EPFL2016

The role of the electric field in simulations of plasma microturbulence

Paolo Angelino

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.

EPFL2006

Gyrokinetic particle-in-cell global simulations of ion-temperature-gradient and collisionless-trapped-electron-mode turbulence in tokamaks

Sébastien Jolliet

The goal of thermonuclear fusion research is to provide power plants, that will be able to produce one gigawatt of electricity. Among the different ways to achieve fusion, the tokamak, based on magnetic confinement, is the most promising one. A gas is heated up to hundreds of millions of degrees and becomes a plasma, which is maintained – or confined – in a toroidal vessel by helical magnetic field lines. Then, deuterium and tritium are injected and fuse to create an α particle and an energetic neutron. In order to have a favorable power balance, the power produced by fusion reactions must exceed the power needed to heat the plasma and the power losses. This can be cast in a very simple expression which stipulates that the product of the density, the temperature and the energy confinement time must exceed some given value. Unfortunately, present-days tokamaks are not able to reach this condition, mostly due to plasma turbulence. The latter phenomenon enhances the heat losses and degrades the energy confinement time, which cannot be predicted by analytical theories such as the so-called neoclassical theory in which the heat losses are caused by Coulomb collisions. Therefore, numerical simulations are being developed to model plasma turbulence, mainly caused by the Ion and Electron Temperature-Gradient and the Trapped-Electron-Mode instabilities. The plasma is described by a distribution function which evolves according to the Vlasov equation. The electromagnetic fields created by the particles are self-consistently obtained through Maxwell's equations. The resulting Vlasov-Maxwell system is greatly simplified by using the gyrokinetic theory, which consists, through an appropriate ordering, of eliminating the fast gyromotion (compared to the typical frequency of instabilities). Nevertheless, it is still extremely difficult to solve this system numerically due to the large range of time and spatial scales to be resolved. In this thesis, the Vlasov-Maxwell system is solved in the electrostatic and collisionless limit with the Particle-In-Cell (PIC) ORB5 code in global tokamak geometry. This Monte-Carlo approach suffers from statistical noise which unavoidably degrades the quality of the simulation. Consequently, the first part of this work has been devoted to the optimization of the code with a view to reduce the numerical noise. The code has been rewritten in a new coordinate system which takes advantage of the anisotropy of turbulence, which is mostly aligned with the magnetic field lines. The overall result of the optimization is that for a given accuracy, the CPU time has been decreased by a factor two thousand, the total memory has been decreased by a factor ten and the numerical noise has been reduced by a factor two hundred. In addition, the scaling of the code with respect to plasma size is presently optimal, suggesting that ORB5 could compute heat transport for future fusion devices such as ITER. The second part of this thesis presents the validation of the code with numerical convergence tests, linear (including dispersion relations) and nonlinear benchmarks. Furthermore, the code has been applied to important issues in gyrokinetic theory. It is shown for the first time that a 5D global delta-f PIC code can achieve a thermodynamic steady state on the condition that some dissipation is present. This is a fundamental result as the main criticism against delta-f PIC codes is their inability to deal with long time simulations. Next, the role of the parallel nonlinearity is studied and it is demonstrated in this work that this term has no real influence on turbulence, provided the numerical noise is sufficiently low. This result should put an end to the controversy that recently occurred, in which gyrokinetic simulations using different numerical approaches yielded contradictory results. Finally, thanks to the optimization of the code, the gyrokinetic model has been extended to include the kinetic response of trapped-electrons, in place to the usual adiabatic (Boltzmann) approximation. For the first time, global TEM nonlinear simulations are presented, and the role of the zonal flow on heat transport is analyzed. This study will help in acquiring some knowledge on the less-known TEM turbulence (as compared to ITG). In conclusion, this thesis is one of the main steps of the development of ORB5, which is now a state-of-the-art gyrokinetic code for collisionless ITG and TEM turbulence, and has brought several contributions to the understanding of these phenomena.

EPFL2009