A new generation plasma turbulence fluid code for tokamak scrape-off layer dynamics

Understanding the turbulent dynamics of the tokamak scrape-off layer (SOL) is critical for the safe operation of future fusion reactors. In this region of the tokamak device, the plasma exhausts particles and heat onto plasma facing hardware components, which may limit their lifetime if material constraints are not met. Recently, we have gained deep insights into SOL dynamics by means of electromagnetic fluid turbulence simulations carried out with the Global Braginskii Solver (GBS). GBS is currently capable of carrying out simulations of the SOL of medium-size tokamaks such as TCV or Alcator C-Mod. We present the new version of the GBS code, which is intended to address larger SOL plasmas using advanced two-fluid models. GBS has undergone major transformations, including (a) porting of the code kernel to F2008, (b) upgrading pure MPI parallelism to employ a 3D cartesian communicator, and (c) including a matrix-free parallel multigrid solver to address generalized Poisson and Ampere operators. There is also an ongoing effort to port this code to MIC/GPU architecture. The new GBS code achieves excellent parallel scalability up to 8192 cores for a C-Mod size plasma (e.g. weak/strong scalings), while at the same time it is possible to achieve a fast and scalable solution of time dependent operators. As an example, we discuss two new physics capabilities of GBS allowed by numerical advances. The first is the inclusion of electromagnetic fluctuations at realistic plasma sizes, which is now possible due to the reduced numerical cost and improved parallel scalability. Second, the Boussinesq approximation in the evaluation of the divergence of the polarization drift is not justified in the tokamak scrape-off layer, where dn/n ~ 1. The drift-reduced equations have been rederived, and we have implemented and benchmarked a non-Boussinesq Poisson operator in GBS. Finally, we present the latest GBS simulation results using realistic size and parameters from inner-wall limited discharges, which is the chosen scenario for ITER start-up. Our simulations reveal the presence of steep plasma gradients near the last closed flux surface, which implies that a large portion of the exhaust heat can be deposited in a very small area. The turbulent dynamics recovered show low frequency, large amplitude drift and ballooning modes with a 1cm radial and poloidal correlation lengths. Intermittent transport events are present, leading to strongly skewed fluctuation probability distribution functions. The simulations have been benchmarked against measurements from the same experiments, showing very good agreement in many observables.

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

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

Plasma turbulence in the tokamak scrape-off layer

Federico David Halpern, Sébastien Jolliet, Joaquim Loizu Cisquella, Annamaria Mosetto, Mario Podesta, Paolo Ricci, Fabio Riva, Christoph Wersal

In the tokamak scrape-off layer (SOL) the magnetic field lines are open, channeling particles and heat onto plasma facing components, and constraining their lifetime. This is a critical issue for ITER and future devices -- safe operation of fusion devices will require a better understanding of the SOL plasma dynamics \cite{Loarte2007}. The steady-state heat load onto the tokamak plasma facing components depends on the SOL width, which results from a balance between plasma injection from the core region, turbulent transport, and losses to the divertor or limiter. Recently, we have gained deep insights into the tokamak SOL dynamics in the inner-wall limited configuration (like the ITER start-up plasmas), by means of massively-parallel fluid electromagnetic turbulence simulations. SOL turbulence, in fact, is characterized by the presence of large amplitude meso-scale turbulence, which requires the use of a global, flux-driven approach. In order to address this turbulent system, we have developed GBS, a flux-driven global turbulence code implementing the drift-reduced Braginskii equations. Our investigations have pointed out, among the others, the mechanisms regulating the turbulence level and therefore the SOL width, the turbulent regimes, and the mechanisms driving the rotation in this region. GBS simulations at realistic size and plasma parameters display features normally observed in the SOL of limited discharges, for instance, low frequency drift-wave or ballooning turbulence, fluctuations with an amplitude of the order of 30 percent and a poloidal width of about 10 ion sound larmor radii. Moreover, we have recovered strongly skewed fluctuation PDFs revealing the presence of intermittent transport events. In the present talk, we address, in particular, (a) the mechanisms establishing the SOL width, which regulates the steady-state heat load and (b) the physics of coherent filamentary plasma structures (blobs) that can travel across the SOL carrying heat and particles. The simulated non-linear dynamics have been compared with analytical estimates, that have highlighted the key physics mechanisms at play in the SOL, and with experimental measurements taken in a number of tokamak worldwide, showing good agreement.

2014