Nonlinear physics of shear Alfvén waves

Zonca, F.; Chen, Liu

doi:10.1063/1.4864496

Cited by 7 publications

(30 citation statements)

References 21 publications

(33 reference statements)

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“…2,6,7,54 As discussed in Secs. II and III, nonlinear wave-wave interactions and spectral transfers are accounted for by K NL , since they are enhanced by the radial singular structures of the SAW continuous spectrum.…”

Section: The General Fishbone-like Dispersion Relationmentioning

confidence: 98%

“…More precisely, we can introduce the vector A ¼ (…, A n ,…) of complex amplitudes of relevant toroidal mode numbers at the reference inertial layer; and cast Eq. (42) as 2,6,7,54 …”

Section: The General Fishbone-like Dispersion Relationmentioning

confidence: 99%

“…2,54,60,61 Phase-locking and self-consistent interplay of EP transports and nonlinear EPM mode structures have also been demonstrated to be the essential and crucial ingredients for explaining onset and evolution of EPM avalanches, obtained as convectively amplified selfsimilar solutions of the GFLDR cast as initial value problem for the EPM wave packets. 2,6,7,47,54,60,61 Detailed discussions and applications of the GFLDR framework to nonlinear DAW dynamics excited by EPs are given in Ref. 2 and are beyond the scope of the present work and its companion, Ref.…”

mentioning

confidence: 99%

“…For nonlinear applications, as mentioned above, the GFLDR framework can address nonlinear dynamics and saturation of EP driven DAW by both wave-wave and wave-particle nonlinear interactions. 2,53,54 Within the first route, 1 the GFLDR has been recently adopted to discuss the spontaneous generation of zonal flows and fields by Toroidal AEs (TAE), 55 showing that the same approach may be used to discuss TAE saturation by parametric decay into an ion sound wave and a daughter TAE. 56 The GFLDR framework has also been adopted to analyze TAE saturation by parametric decay into a lower sideband TAE and a geodesic acoustic mode.…”

mentioning

confidence: 99%

“…56 The GFLDR framework has also been adopted to analyze TAE saturation by parametric decay into a lower sideband TAE and a geodesic acoustic mode. 57 Within the second route, 1 the GFLDR has been used for explaining the nonlinear dynamics of fishbone oscillations 2,36,53,54,58,59 and their nonadiabatic frequency chirping by phase-locking. 2,54,60,61 Phase-locking and self-consistent interplay of EP transports and nonlinear EPM mode structures have also been demonstrated to be the essential and crucial ingredients for explaining onset and evolution of EPM avalanches, obtained as convectively amplified selfsimilar solutions of the GFLDR cast as initial value problem for the EPM wave packets.…”

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confidence: 99%

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Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

2014

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A unified theoretical framework is presented for analyzing various branches of drift Alfvén waves and describing their linear and nonlinear behaviors, covering a wide range of spatial and temporal scales. Nonlinear gyrokinetic quasineutrality condition and vorticity equation, derived for drift Alfvén waves excited by energetic particles in fusion plasmas, are cast in integral form, which is generally variational in the linear limit; and the corresponding gyrokinetic energy principle is obtained. Well known forms of the kinetic energy principle are readily recovered from this general formulation. Furthermore, it is possible to demonstrate that the general fishbone like dispersion relation, obtained within the present theoretical framework, provides a unified description of drift Alfvén waves excited by energetic particles as either Alfvén eigenmodes or energetic particle modes. The advantage of the present approach stands in its capability of extracting underlying linear and nonlinear physics as well as spatial and temporal scales of the considered fluctuation spectrum. For these reasons, this unified theoretical framework can help understanding experimental observations as well as numerical simulation and analytic results with different levels of approximation. Examples and applications are given in Paper II [F. Zonca and L. Chen, “Theory on excitations of drift Alfvén waves by energetic particles. II. The general fishbone-like dispersion relation,” Phys. Plasmas 21, 072121 (2014)].

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Section: The General Fishbone-like Dispersion Relationmentioning

confidence: 98%

“…More precisely, we can introduce the vector A ¼ (…, A n ,…) of complex amplitudes of relevant toroidal mode numbers at the reference inertial layer; and cast Eq. (42) as 2,6,7,54 …”

Section: The General Fishbone-like Dispersion Relationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

2014

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Analysis of the nonlinear behavior of shear-Alfvén modes in tokamaks based on Hamiltonian mapping techniques

Briguglio¹,

et al. 2014

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We present a series of numerical simulation experiments set up to illustrate the fundamental physics processes underlying the nonlinear dynamics of Alfv enic modes resonantly excited by energetic particles in tokamak plasmas and of the ensuing energetic particle transports. These phenomena are investigated by following the evolution of a test particle population in the electromagnetic fields computed in self-consistent MHD-particle simulation performed by the HMGC code. Hamiltonian mapping techniques are used to extract and illustrate several features of wave-particle dynamics. The universal structure of resonant particle phase space near an isolated resonance is recovered and analyzed, showing that bounded orbits and untrapped trajectories, divided by the instantaneous separatrix, form phase space zonal structures, whose characteristic non-adiabatic evolution time is the same as the nonlinear time of the underlying fluctuations. Bounded orbits correspond to a net outward resonant particle flux, which produces a flattening and/or gradient inversion of the fast ion density profile around the peak of the linear wave-particle resonance. The connection of this phenomenon to the mode saturation is analyzed with reference to two different cases: a Toroidal Alfv en eigenmode in a low shear magnetic equilibrium and a weakly unstable energetic particle mode for stronger magnetic shear. It is shown that, in the former case, saturation is reached because of radial decoupling (resonant particle redistribution matching the mode radial width) and is characterized by a weak dependence of the mode amplitude on the growth rate. In the latter case, saturation is due to resonance detuning (resonant particle redistribution matching the resonance width) with a stronger dependence of the mode amplitude on the growth rate. [

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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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Nonlinear physics of shear Alfvén waves

Cited by 7 publications

References 21 publications

Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

Theory on excitations of drift Alfvén waves by energetic particles. I. Variational formulation

Analysis of the nonlinear behavior of shear-Alfvén modes in tokamaks based on Hamiltonian mapping techniques

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

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