Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks

Biancalani, A.; Bottino, A.; Cole, M.; Troia, C. Di; Lauber, P.; Mishchenko, A.; Scott, B.; Zonca, F.

doi:10.1088/1361-6587/aa61e4

Cited by 14 publications

(12 citation statements)

References 35 publications

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“…7). The TAE mode structure distortion due to the non-perturbative effects of the EPs is observed, consistent with previous simulations 3,20 and theoretical studies [22][23][24] .…”

Section: Discussionsupporting

confidence: 91%

“…Two cases of the TAE damping are studied. In the first case, we choose m i /me = 200, since this is the parameter used in the EP driven TAE in the next section and previous ORB5 simulations 20 . In the second case, we choose m i /m e = 1836, in order to compare with the previous results where m i /m e = 1836 is used for the calculation of the TAE damping 19 .…”

Section: Toroidicity Induced Alfvén Eigenmode W/o Epsmentioning

confidence: 99%

“…The broadening of the radial envelope (full width at half maximum ∼ 0.12 from the bottom right frame) is larger by 100% than that of the TAE damping case in the top right frame. This is due to the EPs' non-perturbative effects broadening the mode structure 3,20 . Another feature is the mode structure symmetry breaking, namely, the mode structure distortion, due to the EPs' contribution to the non-Hermitian part of the dispersion relation [22][23][24] .…”

Section: Energetic Particle Driven Toroidicity Induced Alfvén Eigenmodementioning

confidence: 99%

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The development of an implicit full f method for electromagnetic particle simulations of Alfvén waves and energetic particle physics

Meng²,

Hoelzl³

et al. 2020

Preprint

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In this work, an implicit scheme for particle-in-cell/Fourier electromagnetic simulations is developed and applied to studies of Alfvén waves in one dimension and in tokamak plasmas. An analytical treatment is introduced to achieve efficient convergence of the iterative solution of the implicit field-particle system. Its application to the one-dimensional uniform plasma demonstrates its applicability in a broad range of β/m e values. The toroidicity induced Alfvén eigenmode (TAE) is simulated using the widely studied case defined by the ITPA Energetic particle (EP) Topical Group. The real frequency and the growth (or damping) rate of the TAE with (or without) EPs agree with previous results reasonably well. The full f electromagnetic particle scheme established in this work provides a possible natural choice for EP transport studies where large profile variation needs to be captured in kinetic simulations.

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“…7). The TAE mode structure distortion due to the non-perturbative effects of the EPs is observed, consistent with previous simulations 3,20 and theoretical studies [22][23][24] .…”

Section: Discussionsupporting

confidence: 91%

Section: Toroidicity Induced Alfvén Eigenmode W/o Epsmentioning

confidence: 99%

Section: Energetic Particle Driven Toroidicity Induced Alfvén Eigenmodementioning

confidence: 99%

See 1 more Smart Citation

The development of an implicit full f method for electromagnetic particle simulations of Alfvén waves and energetic particle physics

Meng²,

Hoelzl³

et al. 2020

Preprint

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“…The nonlinear MHD effects on the evolution of a TAE was carefully investigated, and it was found that the energy transfer from the TAE to the nonlinearly generated zonal modes with toroidal mode number n = 0 and to the higher harmonics reduces the saturation level of the TAE (Todo et al 2010. The zonal flow generation induced by AEs was first found in a gyrofluid simulation (Spong et al 1994) and was found also in gyrokinetic simulations (Zhang and Lin 2013;Biancalani et al 2016). Theory of the zonal flow generation by TAE has been also developed .…”

Section: Discussion and Summarymentioning

confidence: 99%

Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

Todo

2018

Rev. Mod. Plasma Phys.

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This article is a tutorial review of the interaction between energetic particles and Alfvén eigenmodes (AEs) which is one of the important research issues for fusion burning plasmas. The destabilization mechanism of AEs is a kind of inverse Landau damping through the resonant interaction with energetic particles. The important properties of the AE instability, such as resonance condition, conserved variable during the interaction, and particle trapping by the AE, are explained. The time evolution of AEs is classified into various types, steady state, frequency splitting, frequency chirping, and recurrent bursts. Berk and Breizman presented both a onedimensional weakly nonlinear theory for marginal stability and a reduced simulation model that qualitatively explain the various types of time evolution. Berk-Breizman's theory and reduced simulation model are introduced, and their limitations and the future works are discussed in this article. In addition, energetic particle transport by AEs is illustrated with surface-of-section plots. The particle trapping by the AE creates phase space islands and leads to the local flattening of the energetic particle spatial profile. The resonance overlap of multiple AEs and the overlap of higherorder resonances of a single AE lead to the emergence of stochasticity in phase space and the global transport of energetic particles.

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“…ORB5. ORB5 is a nonlinear gyrokinetic PIC code [8] with extension to electromagnetic physics and multiple species [57][58][59]. The p formulation is used and the adjustable control variate method is implemented in ORB5 [57,60], in order to avoid the 'cancellation problem'.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Verification and validation of integrated simulation of energetic particles in fusion plasmas

et al. 2019

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This paper reports verification and validation of linear simulations of Alfvén eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alfvén eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. The simulated RSAE frequencies agree with experimental measurements if the minimum safety factor q min is adjusted, within experimental errors. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Moreover, using a calculated fast ion profile that takes into account the diffusion by multiple unstable modes, a toroidal Alfvén eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental observations. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Finally, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear Alfvén eigenmodes is the first step to develop an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes. Nuclear Fusion

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Nonlinear interplay of Alfvén instabilities and energetic particles in tokamaks

Cited by 14 publications

References 35 publications

The development of an implicit full f method for electromagnetic particle simulations of Alfvén waves and energetic particle physics

The development of an implicit full f method for electromagnetic particle simulations of Alfvén waves and energetic particle physics

Introduction to the interaction between energetic particles and Alfven eigenmodes in toroidal plasmas

Verification and validation of integrated simulation of energetic particles in fusion plasmas

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