Structure of wave-particle resonances and Alfvén mode saturation

Wang, X.; Briguglio, S.; Lauber, P.; Fusco, V.; Zonca, F.

doi:10.1063/1.4940785

Cited by 21 publications

(47 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 94%

See 1 more Smart Citation

Saturation of single toroidal number Alfvén modes

Wang

Briguglio

2016

New J. Phys.

View full text Add to dashboard Cite

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...

show abstract

Section: Resonance Detuning and Radial Decouplingmentioning

confidence: 94%

“…The simulation parameters are the same as those used in [47]. A tokamak equilibrium is considered, characterised by aspect ratio = R a 10 0 and safety factor = + -( )( ) q q q q r a a 0 0 2 , with q 0 =1.9 and q a =2.3.…”

Section: Simulation Parametersmentioning

confidence: 99%

Saturation of single toroidal number Alfvén modes

Wang

Briguglio

2016

New J. Phys.

View full text Add to dashboard Cite

show abstract

“…The code has been used to investigate fast-ion driven modes (such as TAEs, BAEs and EPMs [15,24,32,33]), as well as to analyse modes observed in existing devices (JT-60U [34], DIII-D [35]) or expected in forthcoming burning plasmas (ITER [36,37]) and proposed experiments (FAST [38][39][40]). The fluid response of the thermal background plasma is described by a set of O(ǫ 3 )-reduced MHD equations [41] (with ǫ being the inverse aspect ratio) for a low-β plasma, and the fast-ion and thermal-ion kinetic dynamics enter via the respective pressure tensors, which are computed by solving the Vlasov equation for each species in the driftkinetic limit by PIC techniques.…”

Section: A Xhmgcmentioning

confidence: 99%

“…Second, the nonlinear modification of mode frequency (so-called frequency chirping) and structure has been observed even for very weak (slightly above threshold) EPMs [23]. Finally, the relevance of finite mode structure in determining the saturation process of gap modes has been pointed out [21], and the transition from the quadratic scaling to a weaker one, for the saturation mode amplitude, as the growth rate increases above a certain level has been demonstrated [24].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2017

Self Cite

View full text Add to dashboard Cite

Nonlinear dynamics of single toroidal number gap Alfvén modes destabilised by the the resonant interaction with fast ions is investigated, in Tokamak equilibria, by means of Hamiltonian mapping techniques. The results obtained by two different simulation codes, XHMGC and HAGIS, are considered with reference to n = 2 Beta induced Alfvén Eigenmodes and, respectively n = 6 Toroidal Alfvén Eigenmodes; simulations of the bump-on-tail instability performed by a 1-dimensional code, PIC1DP, are also analysed. A general feature emerges from these results: modes saturate as the resonant-particle distribution function is flattened, because of the fluxes associated to the motion of particles captured in the potential well of the wave, over the whole region where mode-particle power transfer can take place in the linear phase. Such region can be limited by the narrowest of the resonance width and the mode width. In the former case, mode amplitude at saturation exhibits a quadratic scaling with the linear growth rate; in the latter case, a linear growth rate.These findings are explained in terms of the approximate analytic solution of a nonlinear pendulum model. They are also used to prove that the radial width of the single poloidal harmonic sets an upper limit to the radial displacement of passing fast ions produced by a single-toroidal-number gap mode in the large n limit, irrespectively of the possible existence of a large global mode structure formed by many harmonics.

show abstract

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

et al. 2020

View full text Add to dashboard Cite

Numerical simulations of Alfvén modes driven by energetic particles are performed with the gyrokinetic (GK) global particle-in-cell code ORB5. A reversed shear equilibrium magnetic field is adopted. A simplified configuration with circular flux surfaces and large aspect ratio is considered. The nonlinear saturation of beta-induced Alfvén eigenmodes (BAE) is investigated. The roles of the wave–particle nonlinearity of the different species, i.e. thermal ions, electrons and energetic ions are described, in particular for their role in the saturation of the BAE and the generation of zonal flows. The nonlinear redistribution of the electron population is found to be important in increasing the BAE saturation level and the zonal flow amplitude.

show abstract

Structure of wave-particle resonances and Alfvén mode saturation

Cited by 21 publications

References 46 publications

Saturation of single toroidal number Alfvén modes

Saturation of single toroidal number Alfvén modes

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

Effect of the electron redistribution on the nonlinear saturation of Alfvén eigenmodes and the excitation of zonal flows

Contact Info

Product

Resources

About