Mitigation of the cancellation problem in the gyrokinetic particle-in-cell simulations of global electromagnetic modes

Mishchenko, A.; Bottino, A.; Hatzky, R.; Sonnendrücker, Éric; Kleiber, R.; Könies, A.

doi:10.1063/1.4997540

Cited by 22 publications

(24 citation statements)

References 27 publications

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“…0 < n < 40), which opens the way to the investigation of the interaction of AMs and turbulence, is not discussed here, and is left as the focus of a dedicated paper. The resolution of the Vlasov-Maxwell set of equations in a p formulation (also known as Hamiltonian formulation) with a δf (perturbed distribution function) particle-in-cell code is found to be affected by the cancellation problem, which can be mitigated with a control variate method, or with a pull-back scheme (Mishchenko, Hatzky & Könies 2004;Hatzky, Könies & Mishchenko 2007;Mishchenko et al 2017). The recent inclusion of the pull-back scheme greatly improved the efficiency of ORB5 (Mishchenko et al 2019), making these simulations feasible.…”

Section: Introductionmentioning

confidence: 99%

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

et al. 2020

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Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

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Section: Introductionmentioning

confidence: 99%

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

et al. 2020

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“…2016) and the reduction of the statistical error (Mishchenko et al. 2017). In the following, we will focus on the latter in the context of simulation of damped magnetohydrodynamics (MHD) modes.…”

Section: Introductionmentioning

confidence: 99%

“…In principle, it is possible to use the δf -method for electromagnetic gyrokinetic PIC simulation (Mishchenko, Hatzky & Könies 2004a), but the time-step size can be quite restrictive and the required number of markers can be so large that PIC simulations become unfeasible. Hence, in the past three decades, many attempts have been made to improve electromagnetic PIC algorithms in two respects: the increase of the timestep size (Kleiber et al 2016) and the reduction of the statistical error (Mishchenko et al 2017). In the following, we will focus on the latter in the context of simulation of damped magnetohydrodynamics (MHD) modes.…”

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confidence: 99%

Reduction of the statistical error in electromagnetic gyrokinetic particle-in-cell simulations

et al. 2019

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The $\unicode[STIX]{x1D6FF}f$-PIC method is widely used for electrostatic particle-in-cell (PIC) simulations. Its basic idea is the ansatz $f=f_{0}+\unicode[STIX]{x1D6FF}f$ ($\unicode[STIX]{x1D6FF}f$-ansatz) where the particle distribution function $f$ is split into a usually time-independent background $f_{0}$ and a time-dependent perturbation $\unicode[STIX]{x1D6FF}f$. In principle, it can also be used for electromagnetic gyrokinetic PIC simulations, but the required number of markers can be so large that PIC simulations become impractical. The reason is a decreasing efficiency of the $\unicode[STIX]{x1D6FF}f$-ansatz for the so-called ‘Hamiltonian formulation’ using $p_{\Vert }$ as a dynamic variable. As a result, the density and current moment of the distribution function develop large statistical errors. To overcome this obstacle we propose to solve the potential equations in the symplectic formulation using $v_{\Vert }$ as a dynamic variable. The distribution function itself is still evolved in the Hamiltonian formulation which is better suited for the numerical integration of the parallel dynamics. The contributions from the full Jacobian of phase space, a finite velocity sphere of the simulation domain and a shifted Maxwellian as a background are considered. Special care has been taken at the discretisation level to make damped magnetohydrodynamics (MHD) mode simulations within a realistic gyrokinetic model feasible. This includes devices like e.g. large tokamaks with a small aspect ratio.

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“…In order to control the noise inherent to PIC simulations, ORB5 includes a Krook operator, a coarse graining technique, and quadtree smoothing. The electromagnetic cancellation problem in Ampère's law can be cured using an enhanced control variate scheme [23] or the pullback scheme [24]. The gyro-averaging operations make use of numerical markers along the Larmor rings of each guiding center, as shown in Figure 1.…”

Section: Algorithms and Mpi Implementationmentioning

confidence: 99%

Gyrokinetic simulations on many- and multi-core architectures with the global electromagnetic Particle-In-Cell Code ORB5

Ohana

Gheller

Lanti

et al. 2021

Computer Physics Communications

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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 parallelism through MPI-based on 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 can still be 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.

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Mitigation of the cancellation problem in the gyrokinetic particle-in-cell simulations of global electromagnetic modes

Abstract: Electromagnetic gyrokinetic particle-in-cell simulations have been inhibited for long time by numerical problems. This paper discusses the origin of these problems. It also gives an overview and summary of the mitigation techniques. a alexey.mishchenko@ipp.mpg.de

Cited by 22 publications

References 27 publications

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

Reduction of the statistical error in electromagnetic gyrokinetic particle-in-cell simulations

Gyrokinetic simulations on many- and multi-core architectures with the global electromagnetic Particle-In-Cell Code ORB5

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