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A model and code ("TIFF") for isothermal gyrofluid computation of quasi-two-dimensional interchange and drift wave turbulence in magnetized plasmas with arbitrary fluctuation amplitudes ("full-f") and arbitrary polarization wavelengths ("full-k") is introduced. The model reduces to the paradigmatic Hasegawa-Wakatani model in the limits of small turbulence amplitudes ("delta-f"), cold ions (without finite Larmor radius effects), and homogeneous magnetic field. Several solvers are compared for the generalized Poisson problem, that is intrinsic to the full-f gyrofluid (and gyrokinetic) polarization equation, and a novel implementation based on a dynamically corrected Fourier method is proposed. The code serves as a reference case for further development of three-dimensional full-f full-k models and solvers, and for fundamental exploration of large amplitude turbulence in the edge of magnetized plasmas. [ABSTRACT FROM AUTHOR]

Abstract The pullback scheme is implemented in the global gyrokinetic particle-in-cell code ORB5 (Jolliet et al., 2007[1]) to mitigate the cancellation problem in electromagnetic simulations. The equations and the discretisation used by the code are described. Numerical simulations of the Toroidal Alfvén Eigenmodes are performed in linear and nonlinear regimes to verify the scheme. A considerable improvement in the code efficiency is observed. For the internal kink mode, it is shown that the pullback mitigation efficiently cures a numerical instability which would make the simulation more costly otherwise. [ABSTRACT FROM AUTHOR]

Abstract We have implemented the Sugama collision operator in the gyrokinetic Vlasov simulation code, GKV, with an implicit time-integration scheme. The new method is versatile and independent of the details of the linearized collision operator, by means of an operator splitting, an implicit time integrator, and an iterative Krylov subspace solver. Numerical tests demonstrate stable computation over the time step size restricted by the collision term. An efficient implementation for parallel computation on distributed memory systems is realized by using the data transpose communication, which makes the iterative solver free from inter-node communications during iteration. Consequently, the present approach achieves enhancement of computational efficiency and reduction of computational time to solution simultaneously, and significantly accelerates the total performance of the application. [ABSTRACT FROM AUTHOR]

We implement the multi-species linearized model collision operator, based on the approach proposed by Kolesnikov [1] , in the full-f continuum gyrokinetic code COGENT [2]. We describe the operator and use it in several COGENT simulations of highly collisional plasmas. We analyze simulation results with the Braginskii fluid model [3] to illustrate that COGENT recovers both friction and thermal forces. Finally, we simulate the neoclassical transport of heavy impurities with COGENT and illustrate agreement with previously published [4] theoretical results. [ABSTRACT FROM AUTHOR]

A toroidal gyrokinetic full-f code GKNET (GyroKinetic Numerical Experimental Tokamak) with field solver in real space has been developed recently to simulate micro-turbulence dynamics in the circular cross-section tokamak plasmas (Obrejan et al., 2015). In this work, we introduce a new high accuracy Zonal Flow (ZF) equation solver which makes use of a parametrisation of the D-shaped magnetic flux surfaces to diagonalise the ZF equation. In addition to being more rigorous near the magnetic axis of the poloidal plane compared to methods based on local approximations, the ZF solver here allows to properly take into account the shape of magnetic flux surfaces independently of the coordinate system used in the rest of the code. The upgraded GKNET code is applied to study the collisionless damping of the Geodesic Acoustic Modes (GAMs) in elliptic and both positive and negative D-shaped magnetic configurations. We found that in addition to the influence of elongation, triangularity is effective in increasing the damping rate of GAMs, independently of the sign of the triangularity. [ABSTRACT FROM AUTHOR]

This paper presents the numerical methods for the nonlinear simulations of cyclokinetic [Waltz and Zhao Deng (2013)] equations in Fourier harmonics of the gyro-phase. A parallel processed, implicit time advanced, Eulerian (or continuum) code (rCYCLO) is developed. A novel numerical treatment of the magnetic moment velocity space derivative operator guarantees accurate conservation of the incremental entropy. By comparing the cyclokinetic simulations with the corresponding gyrokinetics, we quantitatively test the breakdown of gyrokinetics at high turbulence levels over a range of large relative ion cyclotron frequency ( 10 < Ω ∗ < 100 where Ω ∗ = 1 / ρ ∗ , and ρ ∗ is the relative ion gyroradius). As an important code verification, the rCYCLO gyrokinetic transport recovers cyclokinetic transport at high relative ion cyclotron frequency ( Ω ∗ ⩾ 50 ) and low turbulence levels. In the case of linearly stable ion cyclotron modes, the cyclokinetic transport is lower (not higher) than the gyrokinetic transport at high turbulence levels and low- Ω ∗ values. [ABSTRACT FROM AUTHOR]

Abstract: Numerical techniques for parallel dynamics in electromagnetic gyrokinetic simulations are introduced to regulate unphysical grid-size oscillations in the field-aligned coordinate. It is found that a fixed boundary condition and the nonlinear mode coupling in the field-aligned coordinate, as well as numerical errors of non-dissipative finite difference methods, produce fluctuations with high parallel wave numbers. The theoretical and numerical analyses demonstrate that an outflow boundary condition and a low-pass filter efficiently remove the numerical oscillations, providing small but acceptable errors of the entropy variables. The new method is advantageous for quantitative evaluation of the entropy balance that is required for obtaining a steady state in gyrokinetic turbulence. [Copyright &y& Elsevier]

Abstract: A hybrid method of semi-Lagrangian and additive semi-implicit Runge–Kutta schemes is developed for gyrokinetic Vlasov simulations in a flux tube geometry. The time-integration scheme is free from the Courant–Friedrichs–Lewy condition for the linear advection terms in the gyrokinetic equation. The new method is applied to simulations of the ion-temperature-gradient instability in fusion plasmas confined by helical magnetic fields, where the parallel advection term severely restricts the time step size for explicit Eulerian schemes. Linear and nonlinear results show good agreements with those obtained by using the explicit Runge–Kutta–Gill scheme, while the new method substantially reduces the computational cost. [Copyright &y& Elsevier]

Abstract: In the case of adiabatic electrons the gyrokinetic field equation for the electrostatic potential includes an averaging operator acting on flux surfaces. For realistic three-dimensional configurations, as e.g. in stellarator devices, the discretisation of this integro-differential equation leads to very large nearly dense matrices (full matrix approach) which typically cannot be stored in computer memory explicitly. A low memory consuming partly matrix-free approach, based on a preconditioned iterative matrix solver, has been developed where the Helmholtz part of the field equation is used in a matrix formulation while the averaging term is treated matrix-free. For matrices which could still be stored in memory explicitly, it is demonstrated that this approach is also much faster than the full matrix approach. [Copyright &y& Elsevier]

Abstract: Non-physical effects of discretization schemes on simulations of plasma microturbulence are investigated, and different types of hyperdiffusion terms in the gyrokinetic Vlasov equation are employed to cancel or mitigate these effects. Widely applicable rules on how to operate parallel spatial and velocity space diffusion – to avoid numerically excited high- modes and recurrence phenomena, respectively – are presented. The impact of diffusion terms on and the applicability of these findings to results obtained in the context of a benchmark scenario are demonstrated. [Copyright &y& Elsevier]

Abstract: Fluctuating quantities in magnetic confinement geometries often inherit a strong anisotropy along the field lines. One technique for describing these structures is the use of a certain set of Fourier components on the tori of nested flux surfaces. We describe an implementation of this approach for solving partial differential equations, like Poisson''s equation, where a different set of Fourier components may be chosen on each surface according to the changing safety factor profile. Allowing the resolved components to change to follow the anisotropy significantly reduces the total number of degrees of freedom in the description. This can permit large gains in computational performance. We describe, in particular, how this approach can be applied to rapidly solve the gyrokinetic Poisson equation in a particle code, ORB5 (Jolliet et al., (2007) ), with a regular (non-field-aligned) mesh. [Copyright &y& Elsevier]

Abstract: We describe the parallel full-f gyrokinetic particle-in-cell plasma simulation code ELMFIRE and the issue of solving an electrostatic potential from particle data distributed across several MPI (Message Passing Interface) processes. The potential is solved through a linear system with a strongly sparse matrix and ELMFIRE stores data of the estimated non-zero diagonals of the whole matrix in every MPI process. We present and compare several memory efficient structures for gathering the matrix data while keeping only a local part of the matrix in each process. We also demonstrate that these alternative structures improve scalability, thus enabling ELMFIRE to use more MPI processes and a finer time and space scale than before without sacrificing performance. [Copyright &y& Elsevier]

Abstract: A global plasma turbulence simulation code, ORB5, is presented. It solves the gyrokinetic electrostatic equations including zonal flows in axisymmetric magnetic geometry. The present version of the code assumes a Boltzmann electron response on magnetic surfaces. It uses a Particle-In-Cell (PIC), δf scheme, 3D cubic B-splines finite elements for the field solver and several numerical noise reduction techniques. A particular feature is the use of straight-field-line magnetic coordinates and a field-aligned Fourier filtering technique that dramatically improves the performance of the code in terms of both the numerical noise reduction and the maximum time step allowed. Another feature is the capability to treat arbitrary axisymmetric ideal MHD equilibrium configurations. The code is heavily parallelized, with scalability demonstrated up to 4096 processors and 109 marker particles. Various numerical convergence tests are performed. The code is validated against an analytical theory of zonal flow residual, geodesic acoustic oscillations and damping, and against other codes for a selection of linear and nonlinear tests. [Copyright &y& Elsevier]

Abstract: We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving 1 spatial and 2 velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams–Bashforth algorithm, where the parallel motion operator is treated implicitly and the field terms are treated with an Adams–Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms. [Copyright &y& Elsevier]

Particle simulation has played an important role for the recent investigations on turbulence transport in magnetically confined plasmas. In this paper, theoretical and numerical properties of a gyrokinetic plasma as well as its relationship with magnetohydrodynamics (MHD) are discussed with the ultimate aim of simulating microturbulence on transport time scale using massively parallel computers. [Copyright &y& Elsevier]

Understanding and predicting plasma turbulence in the scrape-off layer of a magnetic confinement fusion device is a key open problem in modern plasma physics. The transitional region between the core and scrape-off layer poses a difficult problem for turbulence simulations. The poloidal magnetic field vanishes at the X-point of a fusion device, which introduces a coordinate singularity in the commonly used field-aligned coordinates. In the present work, we present a full- f gyrokinetic code based on a locally field-aligned coordinate system that is flux-coordinate independent and free of singularities. The coordinate system, as well as the equations and numerical methods are described. In addition, careful numerical and physical verifications in closed magnetic flux surfaces are included. [ABSTRACT FROM AUTHOR]

Gyrokinetic codes in plasma physics need outstanding computational resources to solve increasingly complex problems, requiring the effective exploitation of cutting-edge HPC architectures. This paper focuses on the enabling of ORB5, a state-of-the-art, first-principles-based gyrokinetic code, on modern parallel hybrid multi-core, multi-GPU systems. ORB5 is a Lagrangian, Particle-In-Cell (PIC), finite element, global, electromagnetic code, originally implementing distributed MPI-based parallelism through domain decomposition and domain cloning. In order to support multi/many cores devices, the code has been completely refactored. Data structures have been re-designed to ensure efficient memory access, enhancing data locality. Multi-threading has been introduced through OpenMP on the CPU and adopting OpenACC to support GPU acceleration. MPI is further used in combination with the two approaches. The performance results obtained using the full production ORB5 code on the Summit system at ORNL, on Piz Daint at CSCS and on the Marconi system at CINECA are presented, showing the effectiveness and performance portability of the adopted solutions: the same source code version was used to produce all results on all architectures. [ABSTRACT FROM AUTHOR]

A new diagnostic has been developed to investigate the wave-particle interaction in the phase-space in gyrokinetic particle-in-cell codes. Keeping information about energy transfer terms in the velocity space, the technique has been implemented and tested in the global code ORB5 and it gives an opportunity to localize velocity domains of maximum wave–plasma energy exchange for separate species. Moreover, contribution of different species and resonances can be estimated as well, by integrating the energy transfer terms in corresponding velocity domains. This Mode-Plasma-Resonance (MPR) diagnostic has been applied to study the dynamics of the Energetic-particle-induced Geodesic Acoustic Modes (EGAMs) in an ASDEX Upgrade shot, by analysing the influence of different species on the mode time evolution. Since the equations, on which the diagnostic is based, are valid in both linear and nonlinear cases, this approach can be applied to study nonlinear plasma effects. As a possible future application, the technique can be used, for instance, to investigate the nonlinear EGAM frequency chirping, or the plasma heating due to the damping of the EGAMs. [ABSTRACT FROM AUTHOR]

A multi-species linearized collision operator based on the model developed by Sugama et al. has been implemented in the nonlinear gyrokinetic code, GENE. Such a model conserves particles, momentum, and energy to machine precision, and is shown to have negative definite free energy dissipation characteristics, satisfying Boltzmann's H-theorem, including for realistic mass ratio. Finite Larmor Radius (FLR) effects have also been implemented into the local version of the code. For the global version of the code, the collision operator has been developed to allow for block-structured velocity space grids, allowing for computationally tractable collisional global simulations. The validity of the collision operator has been demonstrated by relaxation and conservation tests, as well as appropriate benchmarks. The newly implemented operator shall be used in future simulations to study magnetically confined fusion plasma turbulence and transport in more extreme regions with higher collisionality. [ABSTRACT FROM AUTHOR]