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
A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the genera...A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the generation of high-frequency quasi-mode due to nonlinear coupling of two RSAEs,which is then damped due to coupling with the shear Alfvén continuum,and leads to the nonlinear saturation of the primary RSAEs.An estimation of the nonlinear damping rate is also provided.展开更多
The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require...The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.展开更多
This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardi...This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardin et al 2012 J.Comput.Sci.Discovery 6014002).Using an HL-2A-like equilibrium,we confirm that in the linear phase,the impact of REs on resistive internal kink instabilities is consistent with previous research.In the nonlinear phase,as the runaway current fully replaces the plasmas current,we observe a significant suppression of sawtooth oscillations,with the first sawtooth cycle occurring earlier compared to the case without runaway current.Following the first sawtooth collapse,plasma current density,runaway current density,and safety factor(q)flatten within the q=1 surface,albeit displaying fine structures.Subsequently,the growing high torodial(n)and poloidal(m)mode number modes disrupt the magnetic surfaces,leading to the loss of REs outside the q=1 surface,while minimally affecting the majority of REs well-confined within it.Thus,in the current model,the physical processes associated with the presence of sawtooth oscillations do not effectively dissipate runaway current,as REs are assumed to be collisionless.In addition,the final profile of runaway current density exhibits increased steepening near the q=1 surface in contrast to the initial profile,displaying a distinctive corrugated inhomogeneity influenced by the growing fluctuation of the n=0 component.Finally,detailed convergence tests are conducted to validate the numerical simulations.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 the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDB0790000)the Collaborative Innovation Program of Hefei Science Center,CAS(No.2022HSC-CIP008)National Natural Science Foundation of China(Nos.12275236 and 12261131622)。
文摘A nonlinear saturation mechanism for reversed shear Alfvén eigenmode(RSAE)is proposed and analyzed,and is shown to be of relevance to typical reactor parameter region.The saturation is achieved through the generation of high-frequency quasi-mode due to nonlinear coupling of two RSAEs,which is then damped due to coupling with the shear Alfvén continuum,and leads to the nonlinear saturation of the primary RSAEs.An estimation of the nonlinear damping rate is also provided.
基金supported by the National Key R&D Program of China(No.2017YFE0301900)National Natural Science Foundation of China(No.11875233)Users of Excellence Program of Hefei Science Center CAS(No.2021HSC-UE016)。
文摘The parametric decay process of a reversed shear Alfvén eigenmeode(RSAE)into a geodesic acoustic mode and a kinetic RSAE is investigated using nonlinear gyrokinetic theory.The excitation conditions mainly require the pump RSAE amplitude to exceed a certain threshold,which could be readily satisfied in burning plasmas operated in steady-state advanced scenario.This decay process can contribute to thermal plasma heating and confinement improvement.
基金supported in part by the National Key R&D Program of China (No.2022YFE03040002)the Natural Science Foundation of Sichuan (No.2022NSFSC1814)+3 种基金National Natural Science Foundation of China (Nos.12305246,12175053 and 12261131622)the Italian Ministry of Foreign Affairs (No.CN23GR02)the Fundamental Research Funds for the Central Universitiessupported by US Department of Energy (No.DE-AC0209CH11466)。
文摘This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons(RE)using the 3D magnetohydrodynamic(MHD)code M3D-C^(1)(Jardin et al 2012 J.Comput.Sci.Discovery 6014002).Using an HL-2A-like equilibrium,we confirm that in the linear phase,the impact of REs on resistive internal kink instabilities is consistent with previous research.In the nonlinear phase,as the runaway current fully replaces the plasmas current,we observe a significant suppression of sawtooth oscillations,with the first sawtooth cycle occurring earlier compared to the case without runaway current.Following the first sawtooth collapse,plasma current density,runaway current density,and safety factor(q)flatten within the q=1 surface,albeit displaying fine structures.Subsequently,the growing high torodial(n)and poloidal(m)mode number modes disrupt the magnetic surfaces,leading to the loss of REs outside the q=1 surface,while minimally affecting the majority of REs well-confined within it.Thus,in the current model,the physical processes associated with the presence of sawtooth oscillations do not effectively dissipate runaway current,as REs are assumed to be collisionless.In addition,the final profile of runaway current density exhibits increased steepening near the q=1 surface in contrast to the initial profile,displaying a distinctive corrugated inhomogeneity influenced by the growing fluctuation of the n=0 component.Finally,detailed convergence tests are conducted to validate the numerical simulations.
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.
