An arbitrary wavelength solver for global gyrokinetic simulations. Application to the study of fine radial structures on microturbulence due to non-adiabatic passing electron dynamics

The influence of the fine layers of the non-adiabatic passing electron response on electrostatic turbulent transport, previously studied systematically in flux tube geometry [Dominski et al., Phys. Plasmas 22, 062303 (2015)], is pursued in global geometry in conditions relevant for the TCV tokamak with a deuterium plasma (m(i)/m(e) = 3672). The spectral organization of the passing electron turbulent flux and its dependence on the radial profile of the safety factor are revealed. A radially dependent toroidal spectral analysis of the turbulent fluxes led to the key result that the particle and heat diffusivities of passing-electrons are proportional to the local density of low-order mode rational surfaces. To permit this study of the short radial scales associated with the passing electron dynamics, a new field solver valid at an arbitrary wavelength is implemented in ORB5, for the gyrokinetic quasi-neutrality equation. A benchmark is conducted against the global version of the gyrokinetic code GENE, showing very good agreement.

Collisions in Global Gyrokinetic Simulations of Tokamak Plasmas using the Delta-f Particle-In-Cell Approach

Thibaut Vernay

The present work takes place within the general context of research related to the development of nuclear fusion energy. More specifically, this thesis is mainly a numerical and physical contribution to the understanding of turbulence and associated transport phenomena occuring in tokamak plasmas, the most advanced and promising form of magnetically confined plasmas. The complexity of tokamak plasma phenomena and related physical models, either fluid or kinetic, requires the development of numerical codes to perform simulations of the plasma behaviour under given conditions defined by the magnetic geometry as well as density and temperature profiles. The studies presented in this work are based on electrostatic kinetic simulations, taking advantage of a reduced kinetic model (the gyrokinetic model) which is particularly suitable for studying turbulent transport in magnetically confined plasmas, in effect solving an approximate form of the Vlasov equation for the distribution function of each species (electrons, ions) along with a reduced form of the Poisson equation providing the self-consistent electric fields. The main tool of this work, the gyrokinetic ORB5 code making use of numerical particles according to the Particle-In-Cell (PIC) method, has been upgraded during this thesis with different linearized collision operators related to both ions and electrons. The BIRDIE code, enabling to study collisional effects on the evolution of Langmuir waves in an unmagnetized plasma, has been written in order to serve as a test-bed for the collision operators ultimately implemented in ORB5. Some essential algorithms related to collisional simulations have been jointly implemented, such as the two-weight scheme which is extensively described in this work. The collision operators in ORB5 have been further carefully tested through neoclassical simu- lations and benchmarked against other codes, providing reliable levels of collisional transport. Together with different procedures controlling the numerical noise, the collision operators have then been applied to the study of collisional turbulent transport in two different regimes, the Ion-Temperature-Gradient (ITG) regime and the Trapped-Electron-Mode (TEM) regime re- quiring a trapped electron kinetic response. Although not dominant in core tokamak plasmas, collisional effects nevertheless lead to interesting modifications in the turbulence behaviour which are not captured by the often considered collisionless gyrokinetic models. The so-called coarse-graining procedure, a noise-control algorithm which is suitable for collisional gyrokinetic simulations with particles, is shown to enable carrying out relevant simulations over many col- lision times. Consequently, reliable conclusions regarding turbulent transport in the presence of collisions could be drawn in this thesis. Namely, the turbulent transport in the ITG regime is found to be enhanced by ion collisions through interactions with so-called zonal flows as- sociated to axisymmetric modes, while it is reduced by electron collisions in the TEM regime through electron detrapping processes. The zonal flow dynamics in collisionless and collisional ITG turbulence simulations is studied, emphasizing the limitation of the zonal flow level due to Kelvin-Helmoltz-type instabilities. Additionally, some purely collisionless issues related to tokamak physics are discussed, such as the finite plasma size effects in TEM-dominated regime which are found to be important in non-linear simulations but unimportant in linear simu- lations. The role of zonal flows in temperature-gradient-driven TEM turbulence saturation is confirmed to be weak, in agreement with previous studies. Finally, a realistic global gy- rokinetic simulation, accounting for a proper TCV tokamak magnetic equilibrium and related experimental profiles, has been successfully carried out thus demonstrating the relevance of the ORB5 code for predictions related to physics of real tokamaks. A good agreement with GAM experimental measurements is indeed obtained.

EPFL2013

Investigating profile stiffness and critical gradients in shaped TCV discharges using local gyrokinetic simulations of turbulent transport

Stephan Brunner, Yann Camenen, Alessandro Marinoni, Gabriele Merlo, Olivier Sauter, Laurent Villard

The experimental observation made on the TCV tokamak of a significant confinement improvement in plasmas with negative triangularity (delta < 0) compared to those with standard positive triangularity has been interpreted in terms of different degrees of profile stiffness (Sauter et al 2014 Phys. Plasmas 21 055906) and/or different critical gradients. Employing the Eulerian gyrokinetic code GENE (Jenko et al 2000 Phys. Plasmas 7 1904), profile stiffness and critical gradients are studied under TCV relevant conditions. For the considered experimental discharges, trapped electron modes (TEMs) and electron temperature gradient (ETG) modes are the dominant microinstabilities, with the latter providing a significant contribution to the non-linear electron heat fluxes near the plasma edge. Two series of simulations with different levels of realism are performed, addressing the question of profile stiffness at various radial locations. Retaining finite collisionality, impurities and electromagnetic effects, as well as the physical electron-to-ion mass ratio are all necessary in order to approach the experimental flux measurements. However, flux-tube simulations are unable to fully reproduce the TCV results, pointing towards the need to carry out radially nonlocal (global) simulations, i.e. retaining finite machine size effects, in a future study. Some conclusions about the effect of triangularity can nevertheless be drawn based on the flux-tube results. In particular, the importance of considering the sensitivity to both temperature and density gradient is shown. The flux tube results show an increase of the critical gradients towards the edge, further enhanced when d < 0, and they also appear to indicate a reduction of profile stiffness towards plasma edge.

Iop Publishing Ltd2015

Development and application of Eulerian and Particle-in-Cell gyrokinetic codes for studying the effect of non-adiabatic passing electron dynamics on microturbulence

Julien Stanislas Pierre Dominski

In tokamak fusion plasmas, micro-turbulence transport is known to be the cause of large losses of heat and particles. The present work deals with the study of electrostatic micro-turbulence transport driven by instabilities of essentially two types: the ion temperature gradient (ITG) modes and the trapped electron modes (TEM). The plasma is described within the gyrokinetic framework, which permits to save computational resources compared to the classical Vlasov kinetic description. In gyrokinetic simulations of fusion plasmas, the passing electrons are often assumed fast enough so that they respond instantaneously to the electrostatic perturbations. In this case, their response is computed adiabatically instead of kinetically. The main advantage is that this simplified model for the electron response is less demanding in computational resources. This assumption is nonetheless incorrect, in particular near mode rational surfaces where the non-adiabatic response of passing electrons cannot be neglected. This thesis work focuses on the study of this passing electron non-adiabatic response, whose influence on microturbulence is studied by means of numerical simulations carried out with the gyrokinetic codes GENE and ORB5. In the first part of this thesis work, the response of passing electrons in ITG and TEM microturbulence regimes is studied by making use of the flux-tube version of the GENE code. Results are obtained using two different electron models, fully kinetic and hybrid. In the hybrid model, passing particles are forced to respond adiabatically while trapped are handled kinetically. Comparing linear eigenmodes obtained with these two models enables one to systematically isolate fine radial structures located at corresponding mode rational surfaces, clearly resulting from the non-adiabatic passing-electron response. Nonlinear simulations show that these fine structures on the non-axisymmetric modes survive in the turbulent phase. Furthermore, through nonlinear coupling to axisymmetric modes, they induce radial modulations in the effective profiles of density, ion and electron temperature and zonal flows

E \times B

shearing rate. Finally, the passing-electron channel is shown to significantly contribute to the transport levels, at least in our ITG case. Also shown is that the passing electrons significantly influence the

E \times B

saturation mechanism of turbulent fluxes. Following this study in flux tube geometry, the influence of the non-adiabatic passing electron response near mode rational surfaces is further studied in global geometry with the global gyrokinetic code ORB5, in which a new field solver is implemented for the gyrokinetic quasi-neutrality equation valid at arbitrary wavelength, overcoming the former long wavelength approximation made in the original version of the code. A benchmark is conducted against the global version of the gyrokinetic code GENE, showing very good agreement. Nonlinear simulations are carried out with the new solver in conditions relevant to the TCV tokamak, with the physical deuterium to electron mass ratio (

m_i/m_e=3672

) and are compared to simulations carried out with heavy electrons (

m_i/m_e=400

). The particular spectral organization of the passing electron turbulent flux and its dependence on the radial profile of the safety factor are revealed. In particular, the formation of short-scale transport barriers is studied near low-order mode rational surfaces. Results show that quantitatively correct nonlinear fully-kinetic simulations of tokamak transport must be carried out in a full torus and with the physical mass ratio.

EPFL2016