Saturation of Alfvén modes in tokamak plasmas investigated by Hamiltonian mapping techniques

Briguglio, S.; Schneller, M.; Wang, X.; Troia, C. Di; Hayward-Schneider, T.; Fusco, V.; Vlad, G.; Fogaccia, G.

doi:10.1088/1741-4326/aa515b

Cited by 24 publications

(43 citation statements)

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“…The saturation due to the particle trapping was demonstrated by the earlier works on nonlinear simulation of Alfvén eigenmode (Wu and White 1994;Fu and Park 1995;Todo et al 1995;Briguglio et al 1995). The quadratic scaling of the Alfvén eigenmode saturation level on the linear growth rate is also investigated in detail (Briguglio et al 2017;Slaby et al 2018). The quadratic scaling means that larger phase space islands are created for larger growth rate.…”

Section: Saturation Of the Energetic Particle Driven Instabilitiesmentioning

confidence: 90%

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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Section: Saturation Of the Energetic Particle Driven Instabilitiesmentioning

confidence: 90%

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

Todo

2018

Rev. Mod. Plasma Phys.

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“…In the next section, we will show that each of the two regimes corresponds to a specific scaling of the saturation amplitude with the linear growth rate. This correspondence has been explained in [47] and [48] on the basis of a simple nonlinear pendulum model. An approximate analytical solution of that model connects the radial width of the resonant particle density flattening with the instantaneous mode amplitude and the linear growth rate.…”

Section: Resonance Detuning and Radial Decouplingmentioning

confidence: 91%

Saturation of single toroidal number Alfvén modes

Wang

Briguglio

2016

New J. Phys.

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The results of numerical simulations are presented to illustrate the saturation mechanism of a single toroidal number Alfvén mode, driven unstable, in a tokamak plasma, by the resonant interaction with energetic ions. The effects of equilibrium geometry non-uniformities and finite mode radial width on the wave-particle nonlinear dynamics are discussed. Saturation occurs as the fast-ion density flattening produced by the radial flux associated to the resonant particles captured in the potential well of the Alfvén wave extends over the whole region where mode-particle power exchange can take place. The occurrence of two different saturation regimes is shown. In the first regime, dubbed resonance detuning, that region is limited by the resonance radial width (that is, the width of the region where the fast-ion resonance frequency matches the mode frequency). In the second regime, called radial decoupling, the power exchange region is limited by the mode radial width. In the former regime, the mode saturation amplitude scales quadratically with the growth rate; in the latter, it scales linearly. The occurrence of one or the other regime can be predicted on the basis of linear dynamics: in particular, the radial profile of the fast-ion resonance frequency and the mode structure. Here, we discuss how such properties can depend on the considered toroidal number and compare simulation results with the predictions obtained from a simplified nonlinear pendulum model.Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. © EUROfusionunstable. As the EP pressure gradient exceeds a certain threshold, even strongly damped continuum oscillations, besides these normal modes of the background plasma, can be driven unstable; they are called energetic particle modes (EPM) [3]. Alvénic fluctuations of various types, excited by EPs, have been identified in several tokamak experiments [4][5][6][7][8][9].Linear properties of Alfvénic fluctuations driven by EPs can be investigated within the theoretical framework of the generalised fishbone-like dispersion relation [3,10,11]. On this basis, several successful comparison between theoretical predictions and experimental observations, as well as numerical simulation results, have been reported [12][13][14][15][16][17][18][19][20].Concerning the nonlinear dynamics of Alfvén modes (and its consequences on the overall performances of tokamak plasmas), it is determined by two main factors: the nonlinear wave-wave coupling and nonlinear waveparticle interactions. With reference to the former factor, various wave-wave interactions leading to the breaking of the Alfvénic state have been analyzed in [21,22]. Although these effects play a crucial role in multi-scale dynamics in burning plasmas, we will focus, in our current work, on the nonlinear wave-particle interactions. This issue has been first addressed withi...

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“…Simulation results suggest that fluctuations are further enhanced in this self-consistent non-perturbative process, and saturate at a higher amplitude than the predicted linear scaling, which assumes constant mode frequency and frequencyindependent mode structure. 28,29,31 From Fig. 10, it is also interesting to note that, on longer time scale of the strongly unstable case with clear non-perturbative wave-EP interactions, the frequency chirping shows non-adiabatic features, as the mode structure is strongly modified.…”

Section: Nonlinear Dynamicsmentioning

confidence: 92%

“…As shown theoretically 5,24 and by recent numerical simulations, 23,25-31 the saturation mechanism is determined by the relative ordering of nonlinear EP orbit excursion to the perpendicular (with respect to equilibrium magnetic field) fluctuation wavelength and/or equilibrium nonuniformity; and it can be reflected by the relative scale lengths of wave-EP power transfer, mode structure and effective resonance condition. 23, 28,29,31 For two paradigmatic cases, typically in the marginally unstable limit, nonlinear EP orbit excursion is restricted by the effective resonance condition, and is much smaller than the perpendicular fluctuation wavelength; that is, the resonant EP response is similar to that of a uniform plasma. Hence, in this regime, resonance detuning outweighs radial decoupling and, when only resonance detuning is considered, the saturated fluctuation amplitude scales quadratically with respect to the linear growth rate of the mode, 32,33 consistent with that predicted by wave-particle trapping mechanism typical of a 1-D beam-plasma system.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamics of shear Alfvén fluctuations in divertor tokamak test facility plasmas

Wang

Briguglio

et al. 2019

Physics of Plasmas

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Following the analysis on linear spectra of shear Alfvén fluctuations excited by energetic particles (EPs) in the Divertor Tokamak Test (DTT) facility plasmas [T. Wang et al., Phys. Plasmas 25, 062509 (2018)], in this work, nonlinear dynamics of the corresponding mode saturation and the fluctuation induced EP transport is studied by hybrid magnetohydrodynamic-gyrokinetic simulations. For the reversed shear Alfvén eigenmode driven by magnetically trapped EP precession resonance in the central core region of DTT plasmas, the saturation is mainly due to radial decoupling of resonant trapped EPs. Consistent with the wave-EP resonance structure, EP transport occurs in a similar scale to the mode width. On the other hand, passingEP transport is analyzed in detail for toroidal Alfvén eigenmode in the outer core region, with mode drive from both passing and trapped EPs. It is shown that passing EPs experience only weak redistributions in the weakly unstable case; and the transport extends to meso-scale diffusion in the strongly unstable case, due to orbit stochasticity induced by resonance overlap. Here, weakly/strongly unstable regime is determined by Chirikov condition for resonance overlap. This work then further illuminates rich and diverse nonlinear EP dynamics related to burning plasma studies, and the capability of DTT to address these key physics.

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Saturation of Alfvén modes in tokamak plasmas investigated by Hamiltonian mapping techniques

Cited by 24 publications

References 50 publications

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

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

Saturation of single toroidal number Alfvén modes

Nonlinear dynamics of shear Alfvén fluctuations in divertor tokamak test facility plasmas

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