1,721,656 research outputs found
Gyrokinetic theory of the nonlinear saturation of a toroidal Alfvén eigenmode
No full textNonlinear saturation of a toroidal Alfvén eigenmode via ion induced scattering is investigated in the short-wavelength gyrokinetic regime. It is found that the nonlinear evolution depends on the thermal ion β value. Here, β is the plasma thermal to magnetic pressure ratio. Both the saturation levels and associated energetic-particle transport coefficients are derived and estimated correspondingly
On nonlinear scattering of drift wave by toroidal Alfvén eigenmode in tokamak plasmas
Full text linkUsing electron drift wave (eDW) as a paradigm model, we have investigated analytically direct wave-wave interactions between a test DW and ambient toroidal Alfvén eigenmodes (TAEs) in toroidal plasmas, and their effects on the stability of the eDW. The nonlinear effects enter via scatterings to short-wavelength electron Landau damped kinetic Alfvén waves (KAWs). Specifically, it is found that scatterings to upper-sideband KAW lead to stimulated absorption of eDW. Scatterings to the lower-sideband KAW, on the contrary, lead to its spontaneous emission. As a consequence, for typical parameters and fluctuation intensity, nonlinear scatterings by TAEs have negligible net effects on the eDW stability; in contrast to the ‘reverse’ process investigated in Chen et al (2022 Nucl. Fusion 62 094001), where it is shown that nonlinear scattering by ambient eDWs may lead to significant damping of TAE
Gyrokinetic theory of toroidal Alfvén eigenmode saturation via nonlinear wave–wave coupling
Full text linkNonlinear wave–wave coupling constitutes an important route for the turbulence spectrum evolution in both space and laboratory plasmas. For example, in a reactor relevant fusion plasma, a rich spectrum of symmetry-breaking shear Alfvén wave (SAW) instabilities is expected to be excited by energetic fusion alpha particles, and self-consistently determines the anomalous alpha particle transport rate by the saturated electromagnetic perturbations. In this work, we will show that the nonlinear gyrokinetic theory is a necessary and powerful tool in qualitatively and quantitatively investigating the nonlinear wave–wave coupling processes. More specifically, one needs to employ the gyrokinetic approach to account for the breaking of the “pure Alfvénic state” in the short-wavelength kinetic regime, due to the short-wavelength structures associated with nonuniformity intrinsic to magnetically confined plasmas. Using well-known toroidal Alfvén eigenmode (TAE) as a paradigm case, three nonlinear wave–wave coupling channels expected to significantly influence the TAE nonlinear dynamics are investigated to demonstrate the strength and necessity of nonlinear gyrokinetic theory in predicting crucial processes in a future reactor burning plasma. These are: 1. the nonlinear excitation of meso-scale zonal field structures via modulational instability and TAE scattering into short-wavelength stable domain; 2. the TAE frequency cascading due to nonlinear ion-induced scattering and the resulting saturated TAE spectrum; and 3. the cross-scale coupling of TAE with micro-scale ambient drift wave turbulence and its effect on TAE regulation and anomalous electron heating
Nonlinear excitation of a geodesic acoustic mode by toroidal Alfvén eigenmodes and the impact on plasma performance
No full textSpontaneous nonlinear excitation of a geodesic acoustic mode (GAM) by a toroidal Alfvén eigenmode (TAE) is investigated using nonlinear gyrokinetic theory. It is found that the nonlinear decay process depends on the thermal ion βi value. Here, β is the plasma thermal to magnetic pressure ratio. In the low-β limit, a TAE decays into a GAM and a lower TAE sideband in the toroidicity induced shear Alfvén wave continuous spectrum gap; while in the high-βi limit, a TAE decays into a GAM and a propagating kinetic TAE in the continuum. Both cases are investigated for the spontaneous decay conditions. The nonlinear saturation levels of both the GAM and daughter wave are derived. The corresponding power balance and wave particle power transfer to thermal plasma are computed. Implications for thermal plasma heating are also discussed
Zero frequency zonal flow excitation by energetic electron driven beta-induced Alfvén eigenmode
No full textZero frequency zonal flow (ZFZF) excitation by trapped energetic electron driven beta-induced Alfvén eigenmode (eBAE) is investigated using non-linear gyrokinetic theory. It is found that, resonant energetic electrons (EEs) not only effectively drive eBAE unstable, but also contribute to the non-linear coupling, leading to ZFZF excitation. The trapped EE contribution to ZFZF generation is dominated by EE responses to eBAE in the ideal region, and is comparable to thermal plasma contribution to Reynolds and Maxwell stresses
Dynamics of reversed shear Alfvén eigenmode and energetic particles during current ramp-up
No full textHybrid MHD-gyrokinetic code simulations are used to investigate the dynamics of frequency sweeping reversed shear Alfvén eigenmode (RSAE) strongly driven by energetic particles (EPs) during plasma current ramp-up in a conventional tokamak configuration. A series of weakly reversed shear equilibria representing time slices of long timescale MHD equilibrium evolution is considered, where the self-consistent RSAE-EP resonant interactions on the short timescale are analyzed in detail. Both linear and non-linear RSAE dynamics are shown to be subject to the non-perturbative effect of EPs by maximizing wave-EP power transfer. In the linear stage, EPs induce evident mode structure and frequency shifts; meanwhile, RSAE saturates by radial decoupling with resonant EPs due to weak magnetic shear, and gives rise to global EP convective transport and fast frequency chirping in the non-adiabatic regime. The spatiotemporal scales of phase space wave-EP interactions are characterized by the perpendicular wavelength and wave-particle trapping time. The simulations provide insights into general as well as specific features of the RSAE spectra and EP transport in experimental observations, and illustrate the fundamental physics of wave-EP resonant interaction with the interplay of the magnetic geometry, plasma non-uniformity and non-perturbative EPs. Possible application for understanding the non-adiabatic frequency chirping as convective and relaxation branches is also discussed
Nonlinear velocity redistribution caused by energetic-particle-driven geodesic acoustic modes, mapped with the beam-plasma system
Full text linkThe nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) in tokamaks is investigated, and compared with the beam-plasma system (BPS). The EGAM is studied with the global gyrokinetic (GK) particle-in-cell code ORB5, treating the thermal ions and EP (in this case, fast ions) as GK and neglecting the kinetic effects of the electrons. The wave–particle nonlinearity is only considered in the EGAM nonlinear dynamics. The BPS is studied with a one-dimensional code where the thermal plasma is treated as a linear dielectric, and the EP (in this case, fast electrons) with an N-body Hamiltonian formulation. A one-to-one mapping between the EGAM and the BPS is described. The focus is on understanding and predicting the EP redistribution in phase space. We identify here two distinct regimes for the mapping: in the low-drive regime, the BPS mapping with the EGAM is found to be complete, and in the high-drive regime, the EGAM dynamics and the BPS dynamics are found to differ. The transition is described with the presence of a non-negligible frequency chirping, which affects the EGAM but not the BPS, above the identified drive threshold. The difference can be resolved by adding an ad hoc frequency modification to the BPS model. As a main result, the formula for the prediction of the nonlinear width of the velocity redistribution around the resonance velocity is provided. This article is written as the second of a series of articles (the first being Biancalani et al. (J. Plasma Phys., vol. 83 (6), 2017, 725830602)) on the saturation of EGAMs due to wave–particle nonlinearity
Nonlinear radial envelope evolution equations and energetic particle transport in tokamak plasmas
Full text linkThis work provides a general description of the self-consistent energetic particle phase space transport in burning plasmas, based on nonlinear gyrokinetic theory. The self consistency is ensured by the evolution equations of the Alfvénic fluctuations by means of nonlinear radial envelope evolution equations, while energetic particle fluxes in the phase space are explicitly constructed from long-lived phase space zonal structures, which are undamped by collisionless processes. As a result, this work provides a viable route to computing fluctuation induced energetic particle transport on long time scales in realistic tokamak plasmas
Drift wave soliton formation via beat-driven zonal flow and implication on plasma confinement
No full textIn this work, gyrokinetic theory of drift waves (DWs) self-regulation via the beat-driven zonal flow (ZF) is presented, and finite diamagnetic drift frequency due to plasma nonuniformity is shown to play a dominant role in the ZF beat generation. The obtained nonlinear DW equation is a nonlinear Schrödinger equation, in which the linear dispersiveness, linear growth, nonuniformity of diamagnetic drift frequency, and cubic nonlinearity induced by the feedback of beat-driven ZF to DWs are self-consistently included. The nonlinear DW equation is solved numerically in both uniform and nonuniform plasmas. It is shown that the DW envelope soliton may form due to the balance of linear dispersiveness and nonlinearity and lead to turbulence spreading to linearly stable region. It is further found that though the threshold on the DW amplitude for soliton formation is well within the relevant parameter regimes of realistic tokamak experiments, solitons cannot extend beyond the range bounded by the turning points of the wave packet when plasma nonuniformity is self-consistently accounted for
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