Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas

Zonca, F.; Chen, L.; Briguglio, S.; Fogaccia, G.; Vlad, G.; Wang, X.

doi:10.1088/1367-2630/17/1/013052

Cited by 125 publications

(389 citation statements)

References 132 publications

(558 reference statements)

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“…dominates the principal series of secular terms in the perturbation expansion [7]. δH N L Z is the phase space zonal structure, and reproduces hole-clump pair creation in the adiabatic limit [9,10,34].…”

Section: A Nonlinear Zfzs Equationsmentioning

confidence: 93%

“…Another reason for EP contribution to be favored in the CCT is that CCT is related to the particles pressure instead of density. Noting |ω * ,E | ≫ |ω 0 | for typical EP driven TAEs [16,33], the nonlinear gyrokinetic equation for EP response to TAE can be written as [7] …”

Section: A Nonlinear Zfzs Equationsmentioning

confidence: 99%

“…Equation (11) can be derived from equation (15) of Ref. [7], assuming |ω * ,E | ≫ |ω 0 | ordering and circular cross section. EP response to TAE can be derived as [22,33] …”

Section: A Nonlinear Zfzs Equationsmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear excitation of finite-radial-scale zonal structures by toroidal Alfvén eigenmode

Qiu¹,

Chen²,

Zonca³

2017

Nucl. Fusion

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The set of equations describing nonlinear evolution of a single toroidal Alfvén eigenmode are derived, including both zero frequency zonal structure (ZFZS) generation and wave-particle phase space nonlinearities. The simplified case of neglecting wave-particle phase space nonlinearity is then investigated to focus on different roles of energetic particles and bulk plasmas on ZFZS generation. It is shown that energetic particles and bulk plasma play dominant roles in ZFZS generation in different nonlinear stages, and the corresponding processes are qualitatively different. Several properties of ZFZS generation, e.g., fine-vs. meso-scale, forced driven vs. spontaneous excitation, are clarified by the present analysis.

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Section: A Nonlinear Zfzs Equationsmentioning

confidence: 93%

Section: A Nonlinear Zfzs Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear excitation of finite-radial-scale zonal structures by toroidal Alfvén eigenmode

Qiu¹,

Chen²,

Zonca³

2017

Nucl. Fusion

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“…This chirping was seen in particle simulations to be associated with the dynamics of energetic particles and the formation of coherent structures in the phasespace, moving in the momentum direction 3-5 . Such dynamics in phase space have been studied, not only for the bump-on-tail case, but also for various Energetic Particle Modes (EPMs), be it for specific modes such as the Alfvén waves 6 or in a more general way 7 .…”

Section: Introductionmentioning

confidence: 99%

Linear study of the precessional fishbone instability

et al. 2016

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The precessional fishbone instability is an m = n = 1 internal kink mode destabilized by a population of trapped energetic particles. The linear phase of this instability is studied here, analytically and numerically, with a simplified model. This model uses the reduced magneto-hydrodynamics (MHD) equations for the bulk plasma and the Vlasov equation for a population of energetic particles with a radially decreasing density. A threshold condition for the instability is found, as well as a linear growth rate and frequency. It is shown that the mode frequency is given by the precession frequency of the deeply trapped energetic particles at the position of strongest radial gradient. The growth rate is shown to scale with the energetic particle density and particles energy while it is decreased by continuum damping.

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“…Vice-versa, if the saturation level of TAE due to regulation by the forced driven ZF is below the modulational instability threshold, the spontaneous excitation process can be completely suppressed [26]. To correctly understand the nonlinear dynamics of Alfvén waves, all these mechanisms, including nonlinear wave-particle interactions [1,9,12] and nonlinear mode-mode couplings [1,14], should be taken into account on the same footing. The formulation of such general problem and the derivation of the governing nonlinear equations will be reported in a future publication.…”

mentioning

confidence: 99%

Effects of energetic particles on zonal flow generation by toroidal Alfvén eigenmode

2016

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Generation of zonal flow (ZF) by energetic particle (EP) driven toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that, nonlinear resonant EP contribution dominates over the usual Reynolds and Maxwell stresses due to thermal plasma nonlinear response. ZF can be forced driven in the linear growth stage of TAE, with the growth rate being twice the TAE growth rate. The ZF generation mechanism is shown to be related to polarization induced by resonant EP nonlinearity. The generated ZF has both the usual meso-scale and microscale radial structures. Possible consequences of this forced driven ZF on the nonlinear dynamics of TAE are also discussed.Understanding the nonlinear dynamics of shear Alfvén waves (SAW) is of crucial importance to future burning plasmas with energetic particle (EP) population such as fusion-αs significantly contributing to the overall plasma energy density [1]. With frequency comparable to the characteristic frequencies of EPs, and group velocities mainly along magnetic field lines, SAWs are expected to be driven unstable by resonant EPs [2-5]; leading to EP transport and degradation of overall confinement, as reviewed in Ref. 1. Toroidal Alfvén eigenmode (TAE) [6,7], excited inside the toroidicity-induced SAW continuum gap to minimize continuum damping, is one of most dangerous candidates for effectively scattering EPs.There are two routes for the nonlinear saturation of TAEs, i.e., nonlinear wave-particle and nonlinear wavewave interactions [8]. Wave-particle phase space nonlinearity [9], e.g., wave-particle trapping, describes the nonlinear distortion of the EP distribution function; and leads to SAW saturation as the wave-particle trapping frequency, proportional to square root of the mode amplitude, is comparable with linear growth rate [10][11][12][13]. On the other hand, wave-wave coupling accounts for the transfer of TAE wave energy away from the most unstable modes. Among various wave-wave nonlinearities, generation of zonal structures (ZS) is of particular importance. Chen et al [14] investigated the nonlinear excitation of zero frequency zonal structure (ZFZS) by TAE with a prescribed amplitude, and found that finite amplitude TAE can excite ZFZS via modulational instability at a rate proportional to the amplitude of the pump TAE. Meanwhile, zonal current with lower excitation threshold could be preferentially excited in specific plasma equilibria, which, however, do not reflect typical experimental tokamak plasmas [14]. Numerical simulations of nonlinear dynamics of EP driven TAE are carried out by both hybrid code [15] and PIC code [16], and found that zonal flow (ZF) is excited by forced driven process, with the ZF growth rate being twice of TAE growth rate. In this paper, we will clarify the "discrepancies" between analytical theory and simulation, with emphasis on the important role played by EPs [1,17]. Our results indicate that there is no conflict between analytical theory [14] and numerical simulations [15,16]; in fact, they desc...

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Nonlinear dynamics of phase space zonal structures and energetic particle physics in fusion plasmas

Cited by 125 publications

References 132 publications

Nonlinear excitation of finite-radial-scale zonal structures by toroidal Alfvén eigenmode

Nonlinear excitation of finite-radial-scale zonal structures by toroidal Alfvén eigenmode

Linear study of the precessional fishbone instability

Effects of energetic particles on zonal flow generation by toroidal Alfvén eigenmode

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