Finite element approach to global gyrokinetic Particle-In-Cell simulations using magnetic coordinates

Fivaz, M.; Brunner, S.; Ridder, Geert; Sauter, O.; Tran, T. M.; Václavík, J.; Villard, L.; Appert, K.

doi:10.1016/s0010-4655(98)00023-x

Cited by 76 publications

(76 citation statements)

References 23 publications

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“…The same region can then be investigated with more advanced gyrokinetic codes (such as GYGLES [19][20][21] or EUTERPE) to check whether the prediction from the simplified model holds. Note that these more advanced codes require much more time for their simulations than STAE-K.…”

Section: Benchmarksmentioning

confidence: 99%

Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

2016

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The resonant interaction of shear Alfvén waves with energetic particles is investigated numerically in tokamak and stellarator geometry using a non-perturbative MHD-kinetic hybrid approach. The focus lies on toroidicity-induced Alfvén eigenmodes (TAEs), which are most easily destabilized by a fast-particle population in fusion plasmas.While the background plasma is treated within the framework of ideal-MHD theory, the drive of the fast particles, as well as Landau damping of the background plasma, is modelled using the drift-kinetic Vlasov equation without collisions. A fast numerical tool, STAE-K, has been developed to solve the resulting eigenvalue problem using a Riccati shooting method. The code, which is suitable for parameter scans, is applied to tokamaks and the stellarator Wendelstein 7-X.Energetic particle modes (EPMs) are found when the pressure of the energetic particles becomes comparable to the pressure of the background plasma. To better understand the physics of EPMs, the connections between TAEs and the shear Alfvén wave continuum are examined. It is shown that, when energetic particles are present, the continuum deforms substantially and the TAE frequency can leave the continuum gap. The interaction of the TAE with the continuum leads to singularities in the eigenfunctions. To further advance the physical model and also to eliminate the MHD continuum together with the singularities in the eigenfunctions, a fourthorder term connected to radiative damping has been included. The radiative damping term is connected to non-ideal effects of the bulk plasma and introduces higher-order derivatives to the model. Thus, it has the potential to substantially change the nature of the solution.For the first time, the fast-particle drive, Landau damping, continuum damping, and radiative damping have been modelled together in tokamak-as well as in stellarator geometry.

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Section: Benchmarksmentioning

confidence: 99%

Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

2016

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“…A detailed description of the discretization procedure can be found in Refs. [26][27][28][29][30]. We apply the so-called phase factor transform [26] to all perturbed quantities in the code.…”

Section: Basic Equations and Numerical Approachmentioning

confidence: 99%

Global particle-in-cell simulations of fast-particle effects on shear Alfvén waves

2009

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“…Furthermore, in PIC simulation the gyro-center distribution is represented by a sum over δ functions at the marker positions [15], [16] …”

Section: Galerkin's Methods In Pic Applicationsmentioning

confidence: 99%

“…For the GYGLES code [15] which uses e. g. the gyro-center coordinates (R, p , v ⊥ ) the corresponding evolution equation for δf is given by…”

Section: The Control Variates Methodsmentioning

confidence: 99%

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Electromagnetic gyrokinetic PIC simulation with an adjustable control variates method

Hatzky

Könies

Mishchenko

2007

Journal of Computational Physics

116

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Finite element approach to global gyrokinetic Particle-In-Cell simulations using magnetic coordinates

Cited by 76 publications

References 23 publications

Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

Numerical investigation of non-perturbative kinetic effects of energetic particles on toroidicity-induced Alfvén eigenmodes in tokamaks and stellarators

Global particle-in-cell simulations of fast-particle effects on shear Alfvén waves

Electromagnetic gyrokinetic PIC simulation with an adjustable control variates method

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