First principles gyrokinetic analysis of electromagnetic plasma instabilities

A two-fold analysis of electromagnetic core tokamak instabilities in the framework of the gyrokinetic theory is presented. First principle theoretical foundations of the gyrokinetic theory are used to explain and justify the numerical results obtained with the global electromagnetic particle-in-cell code Orb5 whose model is derived from the Lagrangian formalism. The energy conservation law corresponding to the Orb5 model is derived from the Noether theorem and implemented in the code as a diagnostics for energy balance and conservation verification. An additional Noether theorem based diagnostics is implemented in order to analyse destabilising mechanisms for the electrostatic and the electromagnetic Ion Temperature Gradient (ITG) instabilities in the core region of the tokamak. The transition towards the Kinetic Ballooning Modes (KBM) at high electromagnetic $\beta$ is also investigated.Comment: 22 pages, 10 Figures, material form the ICPP conference 2018, invite

Effects of plasma shaping on tokamak scrape-off layer turbulence

The understanding of the plasma dynamics in the scrape-off layer (SOL) of tokamaks is of crucial importance as we approach the ITER era. In this region, particles and heat coming from the core, through turbulent transport, flow along the magnetic field lines and are exhausted to the vessel. The processes taking place in the SOL govern the performance of the entire device, as they determine the impurity dynamics, the recycling level, the peak heat loads at the vessel, and have an important role in setting the overall plasma confinement. In the recent past, a large effort has been devoted to improve the knowledge of plasma turbulent dynamics in the tokamak SOL, achieving significant progress. In the simplest circular limited configuration, electromagnetic fluid turbulence simulations carried out with the Global Braginskii Solver (GBS) [P. Ricci et al, PPCF 2012] have pointed out the mechanisms that regulate the SOL width, the plasma toroidal rotation, and the turbulence regime transition. In the present work we generalize the magnetic geometry of GBS, to perform simulations with elongated plasmas and non-zero triangularity, and we investigate the effects of plasma shaping on tokamak SOL turbulence. Nonlinear simulations are performed, with different values of elongation and triangularity. The turbulence properties are analyzed, and the gradient removal theory [P. Ricci et al, PoP 2013] is used to estimate the SOL width. Thanks to a linear study, we elucidate the mechanisms through which the plasma shaping affects the SOL turbulence

Linear and nonlinear excitation of TAE modes by external electromagnetic perturbations using ORB5

The excitation of toroidicity induced Alfv{\'e}n eigenmodes (TAEs) using prescribed external electromagnetic perturbations (hereafter ``antenna") acting on a confined toroidal plasma as well as its nonlinear couplings to other modes in the system is studied. The antenna is described by an electrostatic potential resembling the target TAE mode structure along with its corresponding parallel electromagnetic potential computed from Ohm's law. Numerically stable long-time linear simulations are achieved by integrating the antenna within the framework of a mixed representation and pullback scheme [A. Mishchenko, et al., Comput. Phys. Commun. \textbf{238} (2019) 194]. By decomposing the plasma electromagnetic potential into symplectic and Hamiltonian parts and using Ohm's law, the destabilizing contribution of the potential gradient parallel to the magnetic field is canceled in the equations of motion. Besides evaluating the frequencies as well as growth/damping rates of excited modes compared to referenced TAEs, we study the interaction of antenna-driven modes with fast particles and indicate their margins of instability. Furthermore, we show first nonlinear simulations in the presence of a TAE-like antenna exciting other TAE modes, as well as Global Alfv\'en Eigenmodes (GAE) having different toroidal wave numbers from that of the antenna

Hybrid OpenMP/MPI parallelization of the charge deposition step in the global gyrokinetic Particle-In-Cell code ORB5

Gyrokinetic simulations are computationally extremely demanding due to the high dimensionality of the physical phase space and the interplay between plasma particles and electromagnetic fields. It is thus essential to make full use of the available numerical resources to be able to simulate more complex physical problems. With the aim of optimizing the gyrokinetic Particle-In-Cell code ORB5 towards exascale computing, a particle sorting method is implemented to increase data locality. Furthermore, different algorithms are used to improve vectorization, and the MPI parallelization is complemented with OpenMP. More specifically, we shall focus on the particle to grid operations involved in the PIC charge deposition step. The latter is critical to parallelize using a shared memory paradigm due to the scatter operations involved. We will present the different algorithms and parallelization schemes implemented in the ORB5 charge deposition step and how they affect the speedup compared to the base MPI case

Porting a Legacy Global Lagrangian PIC Code on Many-Core and GPU-Accelerated Architectures

Modern supercomputer architectures are evolving towards embedding more and more cores per compute node, often making use of accelerators such as GPUs, in which thousands of threads can be executed concurrently. To make legacy codes profit efficiently from such resources usually requires a major refactoring effort. I will present the strategy that we adopted for the production code ORB5, a global gyrokinetic Particle-In-Cell (PIC) code for studying turbulence in tokamak plasmas, developed by many physicists over a period of 20 years, which clearly exceeds the timescale of HPC architecture evolution. Among others, the code now includes multiple kinetic species, electromagnetic effects, and collisions. The present refactoring work includes the restructuring of the main kernels, changing the data structure, multithreading with OpenMP on CPUs or OpenACC on GPUs, and optimization on different architectures. The modularity of the resulting code makes it more "future-proof", i.e. extensible to new physics features or computing architectures, and easier to maintain and develop in a collaborative fashion

Triangularity effects on global flux-driven gyrokinetic simulations

On the road to fusion energy production, many alternative scenarios have been investigated in order to address certain well-known problems of tokamak devices; among which, anomalous transport, ELMs and disruptions. The studies on plasma shaping fall into this effort. In particular, it has been experimentally observed that when operating in L mode, negative triangularity (NT) features better confinement properties than positive triangularity (PT). However, even though the trend is quite clear, a complete and satisfying theoretical explanation for this experimental findings is still lacking. With the aim of understanding and describing these improvements starting from first principles, we present the first comparison between PT and NT with global flux-driven gyrokinetic simulations performed with the ORB5 code. The numerical setup includes: electrostatic turbulence, kinetic trapped electrons, non-linear collisional operator, ECRH source, limiter and wall as boundary conditions. The simulations have been performed on ideal MHD equilibria and kinetic profiles inspired by TCV experiments, in a mixed ITG-TEM regime. First analysis reveal a strong reduction of transport in NT; while at the edge PT shows superdiffusivity, NT does not. The limiter plays an important role that has to be further clarified