Verification of Gyrokinetic codes: theoretical background and applications

In fusion plasmas the strong magnetic field allows the fast gyro-motion to be systematically removed from the description of the dynamics, resulting in a considerable model simplification and gain of computational time. Nowadays, the gyrokinetic (GK) codes play a major role in the understanding of the development and the saturation of turbulence and in the prediction of the subsequent transport. Naturally, these codes require thorough verification and validation. Here we present a new and generic theoretical framework and specific numerical applications to test the faithfulness of the implemented models to theory and to verify the domain of applicability of existing GK codes. For a sound verification process, the underlying theoretical GK model and the numerical scheme must be considered at the same time, which has rarely been done and therefore makes this approach pioneering. At the analytical level, the main novelty consists in using advanced mathematical tools such as variational formulation of dynamics for systematization of basic GK code's equations to access the limits of their applicability. The verification of numerical scheme is proposed via the benchmark effort. In this work, specific examples of code verification are presented for two GK codes: the multi-species electromagnetic ORB5 (PIC) and the radially global version of GENE (Eulerian). The proposed methodology can be applied to any existing GK code. We establish a hierarchy of reduced GK Vlasov-Maxwell equations implemented in the ORB5 and GENE codes using the Lagrangian variational formulation. At the computational level, detailed verifications of global electromagnetic test cases developed from the CYCLONE Base Case are considered, including a parametric $\beta$-scan covering the transition from ITG to KBM and the spectral properties at the nominal $\beta$ value.Comment: 16 pages, 2 Figures, APS DPP 2016 invited pape

ORB5: a global electromagnetic gyrokinetic code using the PIC approach in toroidal geometry

This paper presents the current state of the global gyrokinetic code ORB5 as an update of the previous reference [Jolliet et al., Comp. Phys. Commun. 177 409 (2007)]. The ORB5 code solves the electromagnetic Vlasov-Maxwell system of equations using a PIC scheme and also includes collisions and strong flows. The code assumes multiple gyrokinetic ion species at all wavelengths for the polarization density and drift-kinetic electrons. Variants of the physical model can be selected for electrons such as assuming an adiabatic response or a ``hybrid'' model in which passing electrons are assumed adiabatic and trapped electrons are drift-kinetic. A Fourier filter as well as various control variates and noise reduction techniques enable simulations with good signal-to-noise ratios at a limited numerical cost. They are completed with different momentum and zonal flow-conserving heat sources allowing for temperature-gradient and flux-driven simulations. The code, which runs on both CPUs and GPUs, is well benchmarked against other similar codes and analytical predictions, and shows good scalability up to thousands of nodes

Transport in turbulent plasmas at the interface between different levels of description

Energetic ion dynamics play an important role in magnetic confinement fusion (MCF) plasmas, as well as in the solar wind. In the former case, energetic ions such as neutral beam injection (NBI) ions and fusion-born alpha-particles, can interact with global modes in tokamak plasmas leading to instabilities that might result in loss of confinement and energy. In the latter case, ion dynamics must be taken into account in order to explain in situ and remote observations of heating of the solar wind, which show the occurrence of anisotropic heating of ions, as well as magnetohydrodynamics turbulence and intermittency all at the same time. In this thesis we address two scenarios in plasma physics where ion dynamics play a key role modifying the mass and energy transport in the plasma, specifically, ion cyclotron emission (ICE) in MCF plasmas, and preferential ion heating due to intermittent magnetic fields in the solar wind. ICE results from a radiative instability, probably the magnetoacoustic cyclotron instability (MCI), driven by energetic ions in MCF plasmas. Understanding the underlying physics of ICE is important for the exploitation of ICE as a non-perturbative diagnostic for confined and lost alpha-particles in deuterium-tritium (D-T) plasmas in future thermonuclear fusion reactors [McClements et al., Nucl. Fusion, 55, 043013 (2015); Dendy and McClements, Plasma Phys. Controlled Fusion, 57, 044002 (2015)]. On the other hand, preferential ion heating in the solar wind, observed as the occurrence of an ion beam which drifts along the background magnetic field with a velocity close to the local Alfven speed, is still an open problem. Despite the large amount of studies conducted in this issue, none of them included intermittency self-consistently. Therefore, the relationships between preferential ion heating and intermittency have remained unknown, until now. We study in detail the previously mentioned scenarios through numerical simulations using the hybrid approximation for the plasma, which treat ions as kinetic particles and electrons as a neutralizing massless fluid. Our hybrid simulations of the MCI confirm predictions of the analytical theory of the MCI, and recover some features of ICE as observed in D-T plasmas in JET. Furthermore, by going deep into the nonlinear stage of the MCI, we recover additional features of ICE which are not predicted by the linear theory of the MCI but are present in the measured ICE signal, resulting in a good match between our simulation results and the measured ICE intensity in JET. On the other hand, we present the first study of preferential ion heating in the fast solar wind including intermittent electromagnetic fields in a self-consistent way. We find that the temporal and spatial dynamics of the mechanisms driving preferential ion heating in our simulations (gyrobunching and ion trapping by the electric field), the ion temperature anisotropy T=T (perpendicular temperature/parallel temperature), and the degree of correlation between velocity and magnetic field fluctuations, show strong dependence on the level of intermittency in the electromagnetic fields