In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The revers...In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The reversed shear Alfvén eigenmode(RSAE)as a unique branch of the shear Alfvén wave in this equilibrium,can exist with a broad spectrum in wavenumber and frequency,and be resonantly driven unstable by energetic particles(EP).After briefly discussing the RSAE linear properties in burning plasma condition,we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels,and illustrate their potentially important role in reactor-scale fusion plasmas.By means of simplified hybrid MHD-kinetic simulations,the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP,as results of weak/vanishing magnetic shear and relatively low frequency.Through the route of wave-EP nonlinearity,the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure,and the resultant EP transport generally has a convective feature.The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations.Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory,and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE.Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode,which may effectively transfer the EP energy to fuel ions via collisionless Landau damping.Moreover,zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope,and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.展开更多
Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these un...Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these unexpanded nonlinear gyrokinetic equations recover the wellknown drift-kinetic equations. At the expanded limit, they recover the usual nonlinear gyrokinetic equations. These equations can therefore be applied to long-term simulations covering from microscopic to macroscopic spatial scales.展开更多
We have developed, based on the oscillating-center transformation, a general theoretical approach for self-consistent plasma dynamics including, explicitly, effects of nonlinear(higherorder) wave-particle resonances. ...We have developed, based on the oscillating-center transformation, a general theoretical approach for self-consistent plasma dynamics including, explicitly, effects of nonlinear(higherorder) wave-particle resonances. A specific example is then given for low-frequency responses of trapped particles in axisymmetric tokamaks. Possible applications to transport as well as nonlinear wave growth/damping are also briefly discussed.展开更多
Geodesic acoustic modes(GAMs)are oscillating zonal mode structures unique to toroidal plasmas and are capable of regulating microscopic turbulence and associated transports.Inthispaper,three important aspects of GAM...Geodesic acoustic modes(GAMs)are oscillating zonal mode structures unique to toroidal plasmas and are capable of regulating microscopic turbulence and associated transports.Inthispaper,three important aspects of GAM dynamics are investigated,namely(1) GAM continuous spectrum and its mode conversion to kinetic GAM (KGAM);(2) 1inear excitation of energetic particle induced GAM (EGAM) and its coupling to the GAM continuum, and (3) nonlinear saturationofEGAMviawaveparticletrapping.TheanalogybetweentheGAM展开更多
Geodesic acoustic modes(GAM) are oscillating zonal structures unique to toroidal plasmas,and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulence...Geodesic acoustic modes(GAM) are oscillating zonal structures unique to toroidal plasmas,and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport.This article reviews linear and nonlinear theories of GAM;with emphases on kinetic treatment,system nonuniformity and realistic magnetic geometry,in order to reflect the realistic experimental conditions.Specifically,in the linear physics,the resonant wave-particle interactions are discussed,with the application to resonant excitation by energetic particles(EPs).The theory of EP-induced GAM(EGAM) is applied to realistic devices for the interpretation of experimental observations,and global effects due to coupling to GAM continuum are also discussed.Meanwhile,in the nonlinear physics,the spontaneous GAM excitation by microscale turbulences is reviewed,including the effects of various system nonuniformities.A unified theoretical framework of GAM/EGAM is then constructed based on our present understandings.The first-principle-based GAM/EGAM theories reviewed here,thus,provide the tools needed for the understanding and interpretation of experimental/numerical results.展开更多
Fishbone instability excited by barely trapped suprathermal electrons (BTSEs) in tokamaks is investigated theoretically. The frequency of the mode is found to close to procession frequency of BTSEs. The growth rate ...Fishbone instability excited by barely trapped suprathermal electrons (BTSEs) in tokamaks is investigated theoretically. The frequency of the mode is found to close to procession frequency of BTSEs. The growth rate of the mode is much smaller than that of the ideal magnetohytrodynamic (MHD) internal kink mode that is in contrast to the case of trapped ion driven fishbone instability. The analyses also show that spatial density gradient reversal is necessary for the instability. The correlation of the results with experiments is discussed.展开更多
Theoretical and numerical models of chorus waves are reviewed in this paper. Specifically, we focus on the nonlinear wave particle interactions and the current understanding of the frequency chirping of rising tone ch...Theoretical and numerical models of chorus waves are reviewed in this paper. Specifically, we focus on the nonlinear wave particle interactions and the current understanding of the frequency chirping of rising tone chorus waves. Various other related topics, such as the optimal excitation condition of chorus, the formation of subpackets, and the non-adiabaticity of the nonlinear interaction are also discussed. We end this review paper with a short list of questions of chorus waves that are still under research and debate.展开更多
We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations.This novel model(termed as GK-...We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations.This novel model(termed as GK-E&B)employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields.It,thus,not only includes kinetic effects,such as wave-particle interaction and microscopic(ion Larmor radius scale)physics;but also is computationally more efficient than the conventional formulation described in terms of potentials.As a benchmark,we perform linear as well as nonlinear simulations of the kinetic Alfvén wave;demonstrating physics in agreement with the analytical theories.展开更多
基金supported by National Natural Science Foundation of China (Nos. 12205251, 12275236 and 12261131622)Italian Ministry for Foreign Affairs and International Cooperation Project (No. CN23GR02)+2 种基金the National Key Research and Development Program of China (Nos. 2019YFE03020003 and 2017YFE0301900)Users of Excellence program of Hefei Science Center CAS (No. 2021HSC-UE016)funded by the European Union via the Euratom Research and Training Programme (No. 101052200–EUROfusion)
文摘In a tokamak fusion reactor operated at steady state,the equilibrium magnetic field is likely to have reversed shear in the core region,as the noninductive bootstrap current profile generally peaks off-axis.The reversed shear Alfvén eigenmode(RSAE)as a unique branch of the shear Alfvén wave in this equilibrium,can exist with a broad spectrum in wavenumber and frequency,and be resonantly driven unstable by energetic particles(EP).After briefly discussing the RSAE linear properties in burning plasma condition,we review several key topics of the nonlinear dynamics for the RSAE through both wave-EP resonance and wave-wave coupling channels,and illustrate their potentially important role in reactor-scale fusion plasmas.By means of simplified hybrid MHD-kinetic simulations,the RSAEs are shown to have typically broad phase space resonance structure with both circulating and trapped EP,as results of weak/vanishing magnetic shear and relatively low frequency.Through the route of wave-EP nonlinearity,the dominant saturation mechanism is mainly due to the transported resonant EP radially decoupling with the localized RSAE mode structure,and the resultant EP transport generally has a convective feature.The saturated RSAEs also undergo various nonlinear couplings with other collective oscillations.Two typical routes as parametric decay and modulational instability are studied using nonlinear gyrokinetic theory,and applied to the scenario of spontaneous excitation by a finite amplitude pump RSAE.Multiple RSAEs could naturally couple and induce the spectral energy cascade into a low frequency Alfvénic mode,which may effectively transfer the EP energy to fuel ions via collisionless Landau damping.Moreover,zero frequency zonal field structure could be spontaneously excited by modulation of the pump RSAE envelope,and may also lead to saturation of the pump RSAE by both scattering into stable domain and local distortion of the continuum structure.
基金supported by National Natural Science Fundation of China (Nos. 11235009 and 11905097)Fundamental Research Fund for Chinese Central Universities (No. 2019FZA3003)carried out within the framework of the EUROfusion Consortium and received funding from Euratom research and training programme 2014–2018 and 2019–2020 under Grant Agreement No. 633053 (Project No. WP19-ER/ENEA-05)。
文摘Nonlinear electromagnetic gyrokinetic equations have been constructed without expanding the field variables into background and finite but small-amplitude fluctuating components. At the long-wavelength limit, these unexpanded nonlinear gyrokinetic equations recover the wellknown drift-kinetic equations. At the expanded limit, they recover the usual nonlinear gyrokinetic equations. These equations can therefore be applied to long-term simulations covering from microscopic to macroscopic spatial scales.
基金supported by the ITER-CN under Grant No. 2017YFE0301900carried out within the framework of the EUROfusion Consortium and received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under Grant Agreement No. 633053 (Project No. WP19-ER/ENEA-05)
文摘We have developed, based on the oscillating-center transformation, a general theoretical approach for self-consistent plasma dynamics including, explicitly, effects of nonlinear(higherorder) wave-particle resonances. A specific example is then given for low-frequency responses of trapped particles in axisymmetric tokamaks. Possible applications to transport as well as nonlinear wave growth/damping are also briefly discussed.
文摘Geodesic acoustic modes(GAMs)are oscillating zonal mode structures unique to toroidal plasmas and are capable of regulating microscopic turbulence and associated transports.Inthispaper,three important aspects of GAM dynamics are investigated,namely(1) GAM continuous spectrum and its mode conversion to kinetic GAM (KGAM);(2) 1inear excitation of energetic particle induced GAM (EGAM) and its coupling to the GAM continuum, and (3) nonlinear saturationofEGAMviawaveparticletrapping.TheanalogybetweentheGAM
基金supported by National Natural Science Foundation of China under grant Nos.11575157 and 11235009the National Magnetic Confinement Fusion Research Program under Grants Nos.2013GB104004 and 2013GB111004+2 种基金Fundamental Research Fund for Chinese Central Universities under Grant No.2017FZA3004EUROfusion Consortium under grant agreement No.633053US DoE Grants
文摘Geodesic acoustic modes(GAM) are oscillating zonal structures unique to toroidal plasmas,and have been extensively studied in the past decades due to their potential capabilities of regulating microscopic turbulences and associated anomalous transport.This article reviews linear and nonlinear theories of GAM;with emphases on kinetic treatment,system nonuniformity and realistic magnetic geometry,in order to reflect the realistic experimental conditions.Specifically,in the linear physics,the resonant wave-particle interactions are discussed,with the application to resonant excitation by energetic particles(EPs).The theory of EP-induced GAM(EGAM) is applied to realistic devices for the interpretation of experimental observations,and global effects due to coupling to GAM continuum are also discussed.Meanwhile,in the nonlinear physics,the spontaneous GAM excitation by microscale turbulences is reviewed,including the effects of various system nonuniformities.A unified theoretical framework of GAM/EGAM is then constructed based on our present understandings.The first-principle-based GAM/EGAM theories reviewed here,thus,provide the tools needed for the understanding and interpretation of experimental/numerical results.
基金Supported by National Natural Science Foundations of China under Grant Nos. 19885006, 10175020 and 10135020.
文摘Fishbone instability excited by barely trapped suprathermal electrons (BTSEs) in tokamaks is investigated theoretically. The frequency of the mode is found to close to procession frequency of BTSEs. The growth rate of the mode is much smaller than that of the ideal magnetohytrodynamic (MHD) internal kink mode that is in contrast to the case of trapped ion driven fishbone instability. The analyses also show that spatial density gradient reversal is necessary for the instability. The correlation of the results with experiments is discussed.
基金supported by the National Natural Science Foundation of China (Grant Nos. 41631071, 41674174, and 41474142)the Fundamental Research Funds for the Central Universities
文摘Theoretical and numerical models of chorus waves are reviewed in this paper. Specifically, we focus on the nonlinear wave particle interactions and the current understanding of the frequency chirping of rising tone chorus waves. Various other related topics, such as the optimal excitation condition of chorus, the formation of subpackets, and the non-adiabaticity of the nonlinear interaction are also discussed. We end this review paper with a short list of questions of chorus waves that are still under research and debate.
基金supported by the National Science Foundation of China(Grant Nos.11235009,and 11905097)funding from the Euratom Research And Training Programme 2014-2018 and 2019-2020(Grant Agreement No.633053,Project No.WP19-ER/ENEA-05)。
文摘We present a new model for simulating the electromagnetic fluctuations with frequencies much lower than the ion cyclotron frequency in plasmas confined in general magnetic configurations.This novel model(termed as GK-E&B)employs nonlinear gyrokinetic equations formulated in terms of electromagnetic fields along with momentum balance equations for solving fields.It,thus,not only includes kinetic effects,such as wave-particle interaction and microscopic(ion Larmor radius scale)physics;but also is computationally more efficient than the conventional formulation described in terms of potentials.As a benchmark,we perform linear as well as nonlinear simulations of the kinetic Alfvén wave;demonstrating physics in agreement with the analytical theories.