Simulation of ion temperature gradient driven modes with 6D kinetic Vlasov code

With the increase in computational capabilities over the last years it becomes possible to simulate more and more complex and accurate physical models. Gyrokinetic theory has been introduced in the 1960s and 1970s in the need of describing a plasma with more accurate models than fluid equations, but eliminating the complexity of the fast gyration about the magnetic field lines. Although results from current gyrokinetic computer simulations are in fair agreement with experimental results in core physics, crucial assumptions made in the derivation make it unreliable in regimes of higher fluctuations and stronger gradient, such as the tokamak edge. With our novel optimized and scalable semi-Lagrangian solver we are able to simulate ion-temperature gradient modes with the 6D kinetic model including the turbulent saturation. After thoroughly testing our simulation code against analytical computations and gyrokinetic simulations (with the gyrokinetic code GYRO), it has been possible to show first plasma properties that go beyond standard gyrokinetic simulations. This includes the explicit description of the complete perpendicular energy fluxes and the excitation of high frequency waves (around the Larmor frequency) in the nonlinear saturation phase

Scaling and optimizing the Gysela code on a cluster of many-core processors

International audienceThe current generation of the Xeon Phi Knights Landing (KNL) processor provides a highly multi-threaded environment on which regular programming models such as MPI/OpenMP can be used. This specific hardware offers both large memory bandwidth and large computing resources and is currently available on computing facilities. Many factors impact the performance achieved by applications, one of the key points is the efficient exploitation of SIMD vector units, another one is the memory access pattern. Thus, vectorization and optimization works have been conducted on a plasma turbulence application, namely Gysela. A set of different techniques have been used: loop splitting, inlining, grouping a set of LU solve operations, removing conditionals and some loop nests, auto-tuning of one computation kernel, changing a key numerical scheme – Lagrange interpolation instead of cubic splines. As a result, KNL execution times have been reduced by up to a factor 3 in some configurations. This effort has also permitted to gain a speedup of 2x on Broadwell architecture and 3x on Skylake. Nice scalability curves up to a few thousands cores have been obtained on a strong scaling experiment. Incremental work for vectorizing the Gysela code meant a large payoff without resorting to writing assembly code or using low-level intrinsics

Flows and instabilities in low-temperature plasmas with ionization and charge-exchange processes

Plasma is rich with waves and instabilities, on scales ranging from the fastest electron plasma waves down to the slow fluctuations due to ion and atom inertial effects. The common theme of this study is flows, nonlinear waves and instabilities in low-temperature plasmas with atomic processes such as ionization and instabilities. Several nonlinear plasma problems related to applications in electric propulsion and open-mirror linear fusion devices are studied in this thesis. Hall thrusters, the devices for electric propulsion, are prone to many waves and instability phenomena, and the low-frequency ionization oscillations (propagating along its channel) stand as most commonly observed (so-called breathing mode). Though the ionization nature of the breathing mode is generally accepted, with the mode frequency scaling as the fly-by time of the slow neutral atoms, exact mechanisms remain poorly understood. In this study, we formulate a full fluid model for three species: atoms, ions, and electrons, and perform a comprehensive benchmark study between the fluid model and hybrid model (heavy kinetic species and fluid electrons). A novel result of this study is the identification of two different regimes of breathing modes. In one regime, the breathing mode co-exists with the higher frequency resistive mode, and the second - is clear breathing mode. The main features and characteristics of these regimes are identified and confirmed in both models. Generally, the benchmark study shows a good agreement between the fluid and kinetic models. A simple reduced fluid model is proposed for the solo regime. In this regime, the ion backflow region (the near-anode region with negative ion velocity) is identified as a driving mechanism for the breathing mode. The related theme of this work is the role of atomic physics effects (ionization and charge exchange) on plasma flow in the divertors of linear fusion devices. In open magnetic field configurations, the magnetic mirrors are placed at the ends both to confine the plasma in the core and to distribute output energy over a larger area, thus reducing the wall load. Direct interaction of plasma flow with the material wall results in the re-emission of neutrals into the plasma (recycling) due to particles' reflection, desorption, and other processes. This re-emitted neutral component can dramatically impact the whole system. It is found that the low-energy neutral component has the largest influence, generating ion sources (via ionization and charge exchange) in the region near the wall and resulting in strong modification of plasma potential and flow. To study these effects, we have developed a time-dependent hybrid drift-kinetic code with a detailed model of atom transport near the wall, including collision processes. This tool can be used for studying global quasineutral plasma flow dynamics and its interaction with atom components, such as in divertors of linear fusion devices. To illustrate its capabilities, we confirm previous findings (based on qualitative and steady-state analysis) that the ion temperature in the source generally reduces the transport of neutral atoms. Additionally, we show that an increase in the density of slow atoms above some critical value results in dramatic destabilization of plasma flow via ion streaming instabilities

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

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