A rotating neoclassical tearing mode(NTM)can increase the trapped ion losses when the frequency of the NTM is close to the precessional frequency of the trapped particles.When an equilibrium electric field,produced by...A rotating neoclassical tearing mode(NTM)can increase the trapped ion losses when the frequency of the NTM is close to the precessional frequency of the trapped particles.When an equilibrium electric field,produced by the rotation of the plasma and the density gradient,is present,the average precessional frequency of the trapped ions changes and so does the mode frequency corresponding to the maximum loss rate.Our results show that when an electric field with a value of 11.2 kV/m at q=2 is included the maximum of the trapped ion losses increases from 27% to 30% based on EAST equilibrium.展开更多
Tearing modes may play an important role in the density limit disruption.The Magnetohydrodynamic(MHD)code CLT with impurity modules is used to study the tearing mode excited and driven by impurity radiation.The impuri...Tearing modes may play an important role in the density limit disruption.The Magnetohydrodynamic(MHD)code CLT with impurity modules is used to study the tearing mode excited and driven by impurity radiation.The impurity radiation can lead to plasma contraction and local enhancement of the current density.When the locally enhanced region of the current density approaches to the resonance surface,the tearing mode can be excited,even if the tearing mode is stable in the initial equilibrium.Through a scan of the initial atomic number(Z)and impurity concentrations,it is found that impurities with different Z values exhibit similar behaviors in the radiation-driven tearing mode.The impurity radiation can drive tearing mode growth through temperature cooling near the resonance surface,and there exists a linear relationship between the temperature perturbation caused by impurity radiation and the linear growth rate of the tearing mode.Additionally,the impurity can promote the growth of magnetic islands through the radiation cooling inside the magnetic island,and there exists a correlation between the initial parameters of impurity and the width of the saturated magnetic island.展开更多
Stabilization of tearing modes and neoclassical tearing modes is of great importance for tokamak operation.Electron cyclotron waves(ECWs)have been extensively used to stabilize the tearing modes with the virtue of hig...Stabilization of tearing modes and neoclassical tearing modes is of great importance for tokamak operation.Electron cyclotron waves(ECWs)have been extensively used to stabilize the tearing modes with the virtue of highly localized power deposition.Complete suppression of the m/n=2/1 tearing mode(TM)by electron cyclotron resonance heating(ECRH)has been achieved successfully on the J-TEXT tokamak.The effects of ECW deposition location and power amplitude on the 2/1 TM suppression have been investigated.It is found that the suppression is more effective when the ECW power is deposited closer to the rational surface.As the ECW power increases to approximately 230 k W,the 2/1 TM can be completely suppressed.The island rotation frequency is increased when the island width is reduced.The experimental results show that the local heating inside the magnetic island and the resulting temperature perturbation increase at the O-point of the island play dominant roles in TM suppression.As the ECW power increases,the 2/1 island is suppressed to smaller island width,and the flow shear also plays a stabilizing effect on small magnetic islands.With the stabilizing contribution of heating and flow shear,the 2/1 TM can be completely suppressed.展开更多
Double tearing modes(DTMs),induced by double current sheet configurations or two neighboring rational surfaces with the same safety factor in tokamaks,are widely observed in solar,space,and fusion plasmas.In this pape...Double tearing modes(DTMs),induced by double current sheet configurations or two neighboring rational surfaces with the same safety factor in tokamaks,are widely observed in solar,space,and fusion plasmas.In this paper,the evolution of DTMs without a guide field is investigated numerically using a hybrid model(electron fluid+ion PIC).The overall evolution processes of DTMs are qualitatively consistent with previous works using other models.The particle dynamics during the evolution of DTMs is analyzed in detail.Behaviors of ions and electrons present different characteristics around the reconnection region which gives rise to Hall effects producing the out-of-plane quadrupole magnetic field.In the explosive reconnection process with interactions between two DTMs islands,the asymmetric drive and the thin current layer feature lead to the emergence of secondary magnetic islands which develop with the late evolution of the DTMs.展开更多
The double tearing mode(DTM)in a highβ_(N)(β_(N)>1.5)discharge with internal transport barrier on EAST was investigated.A 15 kHz tearing mode(TM)(m≥3,n=3)appears at outer q=2 surface at first,which is stable in ...The double tearing mode(DTM)in a highβ_(N)(β_(N)>1.5)discharge with internal transport barrier on EAST was investigated.A 15 kHz tearing mode(TM)(m≥3,n=3)appears at outer q=2 surface at first,which is stable in the highβ_(N)phase.Then a 2 kHz TM(m=2,n=1)occurs at inner q=2 surface.Soon after,highβ_(N)collapsed with the crash of ELM,and DTM formed during the collapse ofβ_(N).The positions of the two islands of the DTM are consistent with the q=2 surface.The temperature fluctuations are the strongest between the two magnetic islands.A statistical analysis of highβ_(N)discharges operating with the reversed magnetic shear configuration in the EAST 2015-2018 campaign revealed the existence of the DTM in many discharges.During the DTM phase,allβ_(N)are reduced by 10%-30%within 0.1 s.However,there are two differentβ_(N)behaviors thereafter-with and withoutβ_(N)recovery.Studying the physical mechanism ofβ_(N)recovery during the DTM phase will benefit steady-state operation with reversed shear configurations in the future.展开更多
This paper reviews the effects of resonant magnetic perturbation(RMP)on classical tearing modes(TMs)and neoclassical tearing modes(NTMs)from the theory,experimental discovery and numerical results with a focus on four...This paper reviews the effects of resonant magnetic perturbation(RMP)on classical tearing modes(TMs)and neoclassical tearing modes(NTMs)from the theory,experimental discovery and numerical results with a focus on four major aspects:(i)mode mitigation,where the TM/NTM is totally suppressed or partly mitigated by the use of RMP;(ii)mode penetration,which means a linearly stable TM/NTM triggered by the externally applied RMP;(iii)mode locking,namely an existing rotating magnetic island braked and finally stopped by the RMP;(iv)mode unlocking,as the name suggests,it is the reverse of the mode locking process.The key mechanism and physical picture of above phenomena are revealed and summarized.展开更多
The stabilizing mechanism of toroidal rotation on the tearing mode is studied using the 3 D toroidal resistive magnetohydrodynamic code M3 D.It is found that the dominating mechanism,either the centrifugal effect or t...The stabilizing mechanism of toroidal rotation on the tearing mode is studied using the 3 D toroidal resistive magnetohydrodynamic code M3 D.It is found that the dominating mechanism,either the centrifugal effect or the Coriolis effect, depends on the specific pressure β and rotation frequency Ω.On the premise that Ω is sufficiently large, when β is greater than a critical value,the effect of the centrifugal force is dominant, and the stabilizing effect mainly comes from the modification of equilibrium induced by the centrifugal force;when β is less than a critical value,the stabilizing effect from the Coriolis force overcomes that from the centrifugal force.However,if Ω is small, then the effect of equilibrium modification due to the centrifugal force is not significant even if β is large.Finally, the results showed that toroidal rotation shear enhances the stabilizing effect.展开更多
The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode(DTM)are numerically investigated through the three-dimensional,toroidal,nonlinear resistive-MHD code(CLT).We find that the nonlinear evolut...The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode(DTM)are numerically investigated through the three-dimensional,toroidal,nonlinear resistive-MHD code(CLT).We find that the nonlinear evolution of the m/n=2/1 DTM can lead to sawtooth-like oscillations,which are similar to those driven by the kink mode.The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations.With a high perpendicular thermal conductivity,the system quickly evolves into a steady state with m/n=2/1 magnetic islands and helical flow.However,with a low perpendicular thermal conductivity,the system tends to exhibit sawtooth-like oscillations.With a sufficiently high or low heating rate,the system exhibits sawtooth-like oscillations,while with an intermediate heating rate,the system quickly evolves into a steady state.At the steady state,there exist the non-axisymmetric magnetic field and strong radial flow,and both are with helicity of m/n=2/1.Like the steady state with m/n=1/1 radial flow,which is beneficial for preventing the helium ash accumulation in the core,the steady state with m/n=2/1 radial flow might also be a good candidate for the advanced steady state operations in future fusion reactors.We also find that the behaviors of the sawtooth-like oscillations are almost independent of tokamak geometry,which implies that the steady state with saturated m/n=2/1 islands might exist in different tokamaks.展开更多
Nonlinear interaction between tearing modes(TM) and slab ion-temperature-gradient(ITG) modes is numerically investigated by using a Landau fluid model. It is observed that the energy spectra with respect to wavenumber...Nonlinear interaction between tearing modes(TM) and slab ion-temperature-gradient(ITG) modes is numerically investigated by using a Landau fluid model. It is observed that the energy spectra with respect to wavenumbers become broader during the transition phase from the ITG-dominated stage to TM-dominated stage. Accompanied with the fast growth of the magnetic island, the frequency of TM/ITG with long/short wavelength fluctuations in the electron/ion diamagnetic direction decreases/increases respectively. The decrease of TM frequency is identified to result from the effect of the profile flattening in the vicinity of the magnetic island, while the increase of the frequencies of ITG fluctuations is due to the eigenmode transition of ITG induced by the large scale zonal flow and zonal current related to TM. Roles of zonal current induced by the ITG fluctuations in the instability of TM are also analyzed. Finally, the electromagnetic transport features in the vicinity of the magnetic island are discussed.展开更多
A numerical study of the diamagnetic drift effect on the nonlinear interaction between multi-helicity neoclassical tearing modes(NTMs) is carried out using a set of four-field equations including two-fluid effects.The...A numerical study of the diamagnetic drift effect on the nonlinear interaction between multi-helicity neoclassical tearing modes(NTMs) is carried out using a set of four-field equations including two-fluid effects.The results show that,in contrast to the single-fluid case,5/3 NTM cannot be completely suppressed by 3/2 NTM with diamagnetic drift flow.Both modes exhibit oscillation and coexist in the saturated phase.To better understand the effect of the diamagnetic drift flow on multiple-helicity NTMs,the influence of typical relevant parameters is investigated.It is found that the average saturated magnetic island width increases with increasing bootstrap current fraction f_(b) but decreases with the ion skin depth δ.In addition,as the ratio of parallel to perpendicular transport coefficients χ_(‖)/χ_(⊥) increases,the average saturated magnetic island widths of the 3/2 and 5/3 NTMs increase.The underlying mechanisms behind these observations are discussed in detail.展开更多
The influence of m/n=2/1(m and n are poloidal and toroidal mode numbers)tearing modes on plasma perpendicular flows and micro-fluctuations has been investigated in HL-2A neutral beam injection heated L-mode plasmas.It...The influence of m/n=2/1(m and n are poloidal and toroidal mode numbers)tearing modes on plasma perpendicular flows and micro-fluctuations has been investigated in HL-2A neutral beam injection heated L-mode plasmas.It is found that the local perpendicular rotation velocity and turbulence energy are modulated by the alternation between the island X-point and O-point of the naturally rotating tearing modes.Cross-correlation analysis indicates that the modulation of density fluctuations by the tearing mode is not only limited to the island region,but also occurs in the edge region near the last closed flux surface.The turbulence exhibits distinct spectral characteristics inside and outside the island region.In addition,it is observed that the particle flux near the strike point is also significantly impacted by the tearing modes.The experimental evidence reveals that there are strong core-edge interactions between the core tearing modes and the edge transport.展开更多
Magnetic reconnection and tearing mode instability play a critical role in many physical processes.The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated i...Magnetic reconnection and tearing mode instability play a critical role in many physical processes.The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated in this paper.A resistive magnetohydrodynamic code is developed,by the Galerkin spectral method both in the periodic and aperiodic directions.Spectral schemes are provided for global modes and local modes.Mode structures,resistivity scaling,convergence and stability of tearing modes are discussed.The effectiveness of the code is demonstrated,and the computational results are compared with the results using Galerkin spectral method only in the periodic direction.The numerical results show that the code using Galerkin spectral method individually allows larger time step in global and local modes simulations,and has better convergence in global modes simulations.展开更多
Non-shear flow can change the O-point position of a magnetic island, and thus it may play an important role in the effects of resonant magnetic perturbation(RMP) on the single tearing mode. We employ the nonlinear mag...Non-shear flow can change the O-point position of a magnetic island, and thus it may play an important role in the effects of resonant magnetic perturbation(RMP) on the single tearing mode. We employ the nonlinear magnetohydrodynamics model in a slab geometry to investigate how RMP affects the single tearing mode instability with non-shear flow. It is found that the driving and suppressing effects of RMP on single tearing mode instability will appear alternately. When the flow velocity is small, the suppressing effect plays a major role through the development of the mode, and the tearing mode instability will be suppressed. With the flow velocity increasing, the driving effect will increase, while the suppressing effect will decrease. When the two effects reach equilibrium, the tearing mode will become stable.展开更多
Investigation of neoclassical tearing mode and its suppression by electron cyclotron current drive(ECCD)has been carried out in HL-2 M tokamak.The current driving capability of the electron cyclotron wave is evaluated...Investigation of neoclassical tearing mode and its suppression by electron cyclotron current drive(ECCD)has been carried out in HL-2 M tokamak.The current driving capability of the electron cyclotron wave is evaluated.It is found that the deposition location can be effectively controlled by changing the poloidal angle.The validation of electron cyclotron wave heating and current driving has been demonstrated for the upper launcher port.We show that 3.0 MW and2.5 MW modulated ECCD can completely stabilize(2,1)and(3,2)NTMs,respectively.The non-modulated ECCD,radial misalignment as well as current profile broadening have deleterious effect on the NTM stabilization.The time required for suppression of(3,2)mode is shorter than that required for the suppression of(2,1)mode.Moreover,the time needed for complete stabilization at different initial island width has been quantitatively presented and analyzed.展开更多
Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is ...Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is used with this model to obtain the modified Rutherford equation with co-current and counter-current contributions.Consistent with the reported experimental results,numerical simulations have shown that the localized counter external current can only partially suppress NTM when it is far from the resonant magnetic surface.Under some circumstances,the Ohkawa mechanism dominated current drive(OKCD)by electron cyclotron waves can concurrently create both co-current and counter-current.In this instance,the minimal electron cyclotron wave power that suppresses a particular NTM was calculated by the Rutherford equation.The result is marginally less than when taking co-current alone into consideration.As a result,to suppress NTM using OKCD,one only needs to align the co-current with a greater OKCD peak well with the resonant magnetic surface.The effect of its lower counter-current does not need to be considered because the location of the counter-current deviates greatly from the resonant magnetic surface.展开更多
The general dispersion of tearing modes due to the effects of electron inertia and resistivity in pair plasmas is derived analytically,and is discussed in two cases：Δ＇〉〉 1 andΔ＇〈〈 1,where Δ’ is the instabil...The general dispersion of tearing modes due to the effects of electron inertia and resistivity in pair plasmas is derived analytically,and is discussed in two cases：Δ＇〉〉 1 andΔ＇〈〈 1,where Δ’ is the instability criterion of the tearing mode.It is found that the conditions under which either resistivity or electron inertia dominates depend strongly on the limit of Δ＇considered.展开更多
Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes(NDTMs)in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodyn...Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes(NDTMs)in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics(MHD)equations.Cases with different separations △_(rs)=|r_(s2)-r_(s1)|between the two same rational surfaces are considered.In the small △_(rs)cases,the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear phase.Moreover,the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation,forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD turbulence.As a result,the profiles of safety factors also enter a nonlinear oscillation phase.In the intermediate △_(rs)case,the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces,because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational surfaces.In the large △_(rs)case,through destabilizing the outer islands significantly,the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.展开更多
Effects of tearing modes are inves shows that the effect of the m = 0 harmonics on the early quasi-linear stage of m = 1 double tigated. The numerical calculation with the harmonics m = 0 included the m = 0 harmonics ...Effects of tearing modes are inves shows that the effect of the m = 0 harmonics on the early quasi-linear stage of m = 1 double tigated. The numerical calculation with the harmonics m = 0 included the m = 0 harmonics on the mode is negligible in the linear stage. As the mode begins to grow nonlinearly, both the current and flow profiles are pinched due to the m = 0 harmonics. To make a comparison we also carry out the calculation with m = 0 harmonics turned off. The profiles of the total current, poloidal magnetic field, and poloidal shear velocity in the cases with or without the m = 0 harmonics are compared and discussed. In addition, the formation of a poloidal velocity shear is found and its mechanism is investigated.展开更多
The effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes are investigated based on a set of reduced magnetohydrodynamic equations.It is found that the radiation can reduce the pressure...The effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes are investigated based on a set of reduced magnetohydrodynamic equations.It is found that the radiation can reduce the pressure near the rational surface.During the nonlinear evolution,the magnitude of perturbed bootstrap current is drastically enhanced in the presence of the radiation.Besides,the radiation can increase the growth rate of the magnetic islands by diminishing the pressure,such that the magnetic islands do not saturate compared with that without radiation.On the other hand,with the increase of the ratio of parallel to perpendicular transport coefficientχ‖/χ⊥,the reduction of pressure can further increase the growth rate of magnetic islands in the presence of plasma radiation.Finally,the mechanisms of the destabilizing effects driven by the radiation are discussed in detail as well.展开更多
Both current and pressure coupling schemes have been adopted in the hybrid kinetic–magnetohydrodynamic code CLT-K recently.Numerical equivalences between these two coupling schemes are strictly verified under differe...Both current and pressure coupling schemes have been adopted in the hybrid kinetic–magnetohydrodynamic code CLT-K recently.Numerical equivalences between these two coupling schemes are strictly verified under different approximations.First,when considering only the perturbed distribution function of energetic particles(EPs),the equivalence can be proved analytically.Second,when both the variations of the magnetic field and the EP distribution function are included,the current and pressure coupling schemes numerically produce the same result in the nonlinear simulations.On this basis,the influences of co-/counter-passing and trapped EPs on the linear stabilities of the m/n=2/1 tearing mode(TM)have been investigated(where m and n represent the poloidal and toroidal mode numbers,respectively).The results of scanningβh of EPs show that the co-passing and trapped EPs are found to stabilize the TM,while the counter-passing EPs tend to destabilize the TM.The behind(de)stabilization mechanisms of the TM by EPs are carefully analyzed.Furthermore,after exceeding critical EP betas,the same branch of the high-frequency mode is excited by co-/counterpassing and trapped EPs,which is identified as the m/n=2/1 energetic particle mode.展开更多
基金partially supported by the Comisión Nacional de Energía Atómica,CNEA(Controlled Nuclear Fusion Program),CONICET(No.11220200101929CO)Universidad Nacional de Cuyo(No.06-C565).
文摘A rotating neoclassical tearing mode(NTM)can increase the trapped ion losses when the frequency of the NTM is close to the precessional frequency of the trapped particles.When an equilibrium electric field,produced by the rotation of the plasma and the density gradient,is present,the average precessional frequency of the trapped ions changes and so does the mode frequency corresponding to the maximum loss rate.Our results show that when an electric field with a value of 11.2 kV/m at q=2 is included the maximum of the trapped ion losses increases from 27% to 30% based on EAST equilibrium.
基金supported by the National Magnetic Confinement Fusion Energy R&D Program of China (Nos.2019YFE03030004 and 2022YFE03100001)。
文摘Tearing modes may play an important role in the density limit disruption.The Magnetohydrodynamic(MHD)code CLT with impurity modules is used to study the tearing mode excited and driven by impurity radiation.The impurity radiation can lead to plasma contraction and local enhancement of the current density.When the locally enhanced region of the current density approaches to the resonance surface,the tearing mode can be excited,even if the tearing mode is stable in the initial equilibrium.Through a scan of the initial atomic number(Z)and impurity concentrations,it is found that impurities with different Z values exhibit similar behaviors in the radiation-driven tearing mode.The impurity radiation can drive tearing mode growth through temperature cooling near the resonance surface,and there exists a linear relationship between the temperature perturbation caused by impurity radiation and the linear growth rate of the tearing mode.Additionally,the impurity can promote the growth of magnetic islands through the radiation cooling inside the magnetic island,and there exists a correlation between the initial parameters of impurity and the width of the saturated magnetic island.
基金supported by the National Magnetic Confinement Fusion Energy R&D Program of China(No.2019YFE03010004)the Hubei Provincial Natural Science Foundation of China(No.2022CFA072)National Natural Science Foundation of China(No.51821005)。
文摘Stabilization of tearing modes and neoclassical tearing modes is of great importance for tokamak operation.Electron cyclotron waves(ECWs)have been extensively used to stabilize the tearing modes with the virtue of highly localized power deposition.Complete suppression of the m/n=2/1 tearing mode(TM)by electron cyclotron resonance heating(ECRH)has been achieved successfully on the J-TEXT tokamak.The effects of ECW deposition location and power amplitude on the 2/1 TM suppression have been investigated.It is found that the suppression is more effective when the ECW power is deposited closer to the rational surface.As the ECW power increases to approximately 230 k W,the 2/1 TM can be completely suppressed.The island rotation frequency is increased when the island width is reduced.The experimental results show that the local heating inside the magnetic island and the resulting temperature perturbation increase at the O-point of the island play dominant roles in TM suppression.As the ECW power increases,the 2/1 island is suppressed to smaller island width,and the flow shear also plays a stabilizing effect on small magnetic islands.With the stabilizing contribution of heating and flow shear,the 2/1 TM can be completely suppressed.
基金supported by National Natural Science Foundation of China(Nos.11705039,11975087,and 42011530086)the China Postdoctoral Science Foundation(No.2018M631918)the Heilongjiang Postdoctoral Foundation(No.184744)。
文摘Double tearing modes(DTMs),induced by double current sheet configurations or two neighboring rational surfaces with the same safety factor in tokamaks,are widely observed in solar,space,and fusion plasmas.In this paper,the evolution of DTMs without a guide field is investigated numerically using a hybrid model(electron fluid+ion PIC).The overall evolution processes of DTMs are qualitatively consistent with previous works using other models.The particle dynamics during the evolution of DTMs is analyzed in detail.Behaviors of ions and electrons present different characteristics around the reconnection region which gives rise to Hall effects producing the out-of-plane quadrupole magnetic field.In the explosive reconnection process with interactions between two DTMs islands,the asymmetric drive and the thin current layer feature lead to the emergence of secondary magnetic islands which develop with the late evolution of the DTMs.
基金the National Key R&D Program of China(Nos.2015GB110001,2017 YFE0300501 and 2017YFE0301205)National Natural Science Foundation of China(Nos.11505221,11675211,11805136,11875289,11975230).
文摘The double tearing mode(DTM)in a highβ_(N)(β_(N)>1.5)discharge with internal transport barrier on EAST was investigated.A 15 kHz tearing mode(TM)(m≥3,n=3)appears at outer q=2 surface at first,which is stable in the highβ_(N)phase.Then a 2 kHz TM(m=2,n=1)occurs at inner q=2 surface.Soon after,highβ_(N)collapsed with the crash of ELM,and DTM formed during the collapse ofβ_(N).The positions of the two islands of the DTM are consistent with the q=2 surface.The temperature fluctuations are the strongest between the two magnetic islands.A statistical analysis of highβ_(N)discharges operating with the reversed magnetic shear configuration in the EAST 2015-2018 campaign revealed the existence of the DTM in many discharges.During the DTM phase,allβ_(N)are reduced by 10%-30%within 0.1 s.However,there are two differentβ_(N)behaviors thereafter-with and withoutβ_(N)recovery.Studying the physical mechanism ofβ_(N)recovery during the DTM phase will benefit steady-state operation with reversed shear configurations in the future.
基金supported by National Natural Science Foundation of China(No.11925501)the Fundamental Research Funds for the Central Universities(Nos.DUT21GJ204 and DUT21LK28)。
文摘This paper reviews the effects of resonant magnetic perturbation(RMP)on classical tearing modes(TMs)and neoclassical tearing modes(NTMs)from the theory,experimental discovery and numerical results with a focus on four major aspects:(i)mode mitigation,where the TM/NTM is totally suppressed or partly mitigated by the use of RMP;(ii)mode penetration,which means a linearly stable TM/NTM triggered by the externally applied RMP;(iii)mode locking,namely an existing rotating magnetic island braked and finally stopped by the RMP;(iv)mode unlocking,as the name suggests,it is the reverse of the mode locking process.The key mechanism and physical picture of above phenomena are revealed and summarized.
基金supported by National Natural Science Foundation of China(Grant Nos.11975068 and 11605021)the National Key R&D Program of China(Grant No.2017YFE0301900)+2 种基金the Key Research Program of Frontier Science of Chinese Academy of Sciences(Grant No.QYZDJSSW-SYS016)the Youth Innovation Promotion Association of CASthe Fundamental Research Funds for the Central Universities(Grant No.DUT18ZD101)。
文摘The stabilizing mechanism of toroidal rotation on the tearing mode is studied using the 3 D toroidal resistive magnetohydrodynamic code M3 D.It is found that the dominating mechanism,either the centrifugal effect or the Coriolis effect, depends on the specific pressure β and rotation frequency Ω.On the premise that Ω is sufficiently large, when β is greater than a critical value,the effect of the centrifugal force is dominant, and the stabilizing effect mainly comes from the modification of equilibrium induced by the centrifugal force;when β is less than a critical value,the stabilizing effect from the Coriolis force overcomes that from the centrifugal force.However,if Ω is small, then the effect of equilibrium modification due to the centrifugal force is not significant even if β is large.Finally, the results showed that toroidal rotation shear enhances the stabilizing effect.
基金supported by National MCF Energy R&D Program of China(Nos.2019YFE03090500 and 2019YFE03030004)National Natural Science Foundation of China(Nos.12005185,11775188 and 11835010)Fundamental Research Fund for Chinese Central Universities(No.2021FZZX003-03-02)。
文摘The sawtooth-like oscillations resulting from the m/n=2/1 double tearing mode(DTM)are numerically investigated through the three-dimensional,toroidal,nonlinear resistive-MHD code(CLT).We find that the nonlinear evolution of the m/n=2/1 DTM can lead to sawtooth-like oscillations,which are similar to those driven by the kink mode.The perpendicular thermal conductivity and the external heating rate can significantly alter the behaviors of the DTM driven sawtooth-like oscillations.With a high perpendicular thermal conductivity,the system quickly evolves into a steady state with m/n=2/1 magnetic islands and helical flow.However,with a low perpendicular thermal conductivity,the system tends to exhibit sawtooth-like oscillations.With a sufficiently high or low heating rate,the system exhibits sawtooth-like oscillations,while with an intermediate heating rate,the system quickly evolves into a steady state.At the steady state,there exist the non-axisymmetric magnetic field and strong radial flow,and both are with helicity of m/n=2/1.Like the steady state with m/n=1/1 radial flow,which is beneficial for preventing the helium ash accumulation in the core,the steady state with m/n=2/1 radial flow might also be a good candidate for the advanced steady state operations in future fusion reactors.We also find that the behaviors of the sawtooth-like oscillations are almost independent of tokamak geometry,which implies that the steady state with saturated m/n=2/1 islands might exist in different tokamaks.
基金Project supported by the National Key R&D Program of China(Grant Nos.2017YFE0301100 and 2017YFE0300500)the National Natural Science Foundation of China(Grant Nos.11675038,11775069,and 11305027)the Fundamental Research Funds for the Central Universities of China(Grant No.DUT17RC(4)54)
文摘Nonlinear interaction between tearing modes(TM) and slab ion-temperature-gradient(ITG) modes is numerically investigated by using a Landau fluid model. It is observed that the energy spectra with respect to wavenumbers become broader during the transition phase from the ITG-dominated stage to TM-dominated stage. Accompanied with the fast growth of the magnetic island, the frequency of TM/ITG with long/short wavelength fluctuations in the electron/ion diamagnetic direction decreases/increases respectively. The decrease of TM frequency is identified to result from the effect of the profile flattening in the vicinity of the magnetic island, while the increase of the frequencies of ITG fluctuations is due to the eigenmode transition of ITG induced by the large scale zonal flow and zonal current related to TM. Roles of zonal current induced by the ITG fluctuations in the instability of TM are also analyzed. Finally, the electromagnetic transport features in the vicinity of the magnetic island are discussed.
基金Project supported by the National Key R&D Program of China (Grant No. 2022YFE03090000)the National Natural Science Foundation of China (Grant Nos. 11925501 and 12075048)the Fundament Research Funds for the Central Universities (Grant No. DUT22ZD215)。
文摘A numerical study of the diamagnetic drift effect on the nonlinear interaction between multi-helicity neoclassical tearing modes(NTMs) is carried out using a set of four-field equations including two-fluid effects.The results show that,in contrast to the single-fluid case,5/3 NTM cannot be completely suppressed by 3/2 NTM with diamagnetic drift flow.Both modes exhibit oscillation and coexist in the saturated phase.To better understand the effect of the diamagnetic drift flow on multiple-helicity NTMs,the influence of typical relevant parameters is investigated.It is found that the average saturated magnetic island width increases with increasing bootstrap current fraction f_(b) but decreases with the ion skin depth δ.In addition,as the ratio of parallel to perpendicular transport coefficients χ_(‖)/χ_(⊥) increases,the average saturated magnetic island widths of the 3/2 and 5/3 NTMs increase.The underlying mechanisms behind these observations are discussed in detail.
基金the National Key R&D Program of China(Nos.2017YFE0301201 and 2017YFE0301106)National Natural Science Foundation of China(Nos.11705051,11820101004,11875021 and 11775069)the Young Elite Scientists Sponsorship Program by CAST(No.2018QNRC001).
文摘The influence of m/n=2/1(m and n are poloidal and toroidal mode numbers)tearing modes on plasma perpendicular flows and micro-fluctuations has been investigated in HL-2A neutral beam injection heated L-mode plasmas.It is found that the local perpendicular rotation velocity and turbulence energy are modulated by the alternation between the island X-point and O-point of the naturally rotating tearing modes.Cross-correlation analysis indicates that the modulation of density fluctuations by the tearing mode is not only limited to the island region,but also occurs in the edge region near the last closed flux surface.The turbulence exhibits distinct spectral characteristics inside and outside the island region.In addition,it is observed that the particle flux near the strike point is also significantly impacted by the tearing modes.The experimental evidence reveals that there are strong core-edge interactions between the core tearing modes and the edge transport.
基金Project supported by the Sichuan Science and Technology Program(Grant No.22YYJC1286)the China National Magnetic Confinement Fusion Science Program(Grant No.2013GB112005)the National Natural Science Foundation of China(Grant Nos.12075048 and 11925501)。
文摘Magnetic reconnection and tearing mode instability play a critical role in many physical processes.The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated in this paper.A resistive magnetohydrodynamic code is developed,by the Galerkin spectral method both in the periodic and aperiodic directions.Spectral schemes are provided for global modes and local modes.Mode structures,resistivity scaling,convergence and stability of tearing modes are discussed.The effectiveness of the code is demonstrated,and the computational results are compared with the results using Galerkin spectral method only in the periodic direction.The numerical results show that the code using Galerkin spectral method individually allows larger time step in global and local modes simulations,and has better convergence in global modes simulations.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11647314 and 11747311)
文摘Non-shear flow can change the O-point position of a magnetic island, and thus it may play an important role in the effects of resonant magnetic perturbation(RMP) on the single tearing mode. We employ the nonlinear magnetohydrodynamics model in a slab geometry to investigate how RMP affects the single tearing mode instability with non-shear flow. It is found that the driving and suppressing effects of RMP on single tearing mode instability will appear alternately. When the flow velocity is small, the suppressing effect plays a major role through the development of the mode, and the tearing mode instability will be suppressed. With the flow velocity increasing, the driving effect will increase, while the suppressing effect will decrease. When the two effects reach equilibrium, the tearing mode will become stable.
基金the National Key Research and Development Program of China(Grant Nos.2018YFE0303102,2018YFE0301100,and2017YFE0301702)the National Natural Science Foundation of China(Grant Nos.11905109 and 11947238)+1 种基金U.S.DOE Sci DAC ISEP,users with Excellence Program(on EAST tokamak)of Hefei Science Center CAS under(Grant No.2021HSC-UE017)the Center for Computational Science and Engineering of Southern University of Science and Technology。
文摘Investigation of neoclassical tearing mode and its suppression by electron cyclotron current drive(ECCD)has been carried out in HL-2 M tokamak.The current driving capability of the electron cyclotron wave is evaluated.It is found that the deposition location can be effectively controlled by changing the poloidal angle.The validation of electron cyclotron wave heating and current driving has been demonstrated for the upper launcher port.We show that 3.0 MW and2.5 MW modulated ECCD can completely stabilize(2,1)and(3,2)NTMs,respectively.The non-modulated ECCD,radial misalignment as well as current profile broadening have deleterious effect on the NTM stabilization.The time required for suppression of(3,2)mode is shorter than that required for the suppression of(2,1)mode.Moreover,the time needed for complete stabilization at different initial island width has been quantitatively presented and analyzed.
基金Project supported by the National Key R&D Program of China(Grant Nos.2022YFE03070000 and 2022YFE03070003)the National Natural Science Foundation of China(Grant Nos.12375220 and 12075114)+3 种基金the Hunan Provincial Natural Science Foundation(Grant No.2021JJ30569)the Doctoral Initiation Fund Project of University of South China(Grant No.190XQD114)the Hunan Nuclear Fusion International Science and Technology Innovation Cooperation Base(Grant No.2018WK4009)the Hengyang Key Laboratory of Magnetic Confinement Nuclear Fusion Research(Grant No.2018KJ108)。
文摘Through theoretical analysis,we construct a physical model that includes the influence of counter-external driven current opposite to the plasma current direction in the neoclassical tearing mode(NTM).The equation is used with this model to obtain the modified Rutherford equation with co-current and counter-current contributions.Consistent with the reported experimental results,numerical simulations have shown that the localized counter external current can only partially suppress NTM when it is far from the resonant magnetic surface.Under some circumstances,the Ohkawa mechanism dominated current drive(OKCD)by electron cyclotron waves can concurrently create both co-current and counter-current.In this instance,the minimal electron cyclotron wave power that suppresses a particular NTM was calculated by the Rutherford equation.The result is marginally less than when taking co-current alone into consideration.As a result,to suppress NTM using OKCD,one only needs to align the co-current with a greater OKCD peak well with the resonant magnetic surface.The effect of its lower counter-current does not need to be considered because the location of the counter-current deviates greatly from the resonant magnetic surface.
基金supported by the National Magnetic Confinement Fusion Science ProgramNational Natural Science Foundation of China under Grant Nos.2014GB106004, 2013GB111000,11375189,11075161 and 11275260the Youth Innovation Promotion Association CAS
文摘The general dispersion of tearing modes due to the effects of electron inertia and resistivity in pair plasmas is derived analytically,and is discussed in two cases：Δ＇〉〉 1 andΔ＇〈〈 1,where Δ’ is the instability criterion of the tearing mode.It is found that the conditions under which either resistivity or electron inertia dominates depend strongly on the limit of Δ＇considered.
基金Project supported by the National Key R&D Program of China(Grant No.2022YFE03090000)the National Natural Science Foundation of China(Grant No.11925501)the Fundament Research Funds for the Central Universities(Grant No.DUT22ZD215)。
文摘Effects of plasma radiation on the nonlinear evolution of neo-classical double tearing modes(NDTMs)in tokamak plasmas with reversed magnetic shear are numerically investigated based on a set of reduced magnetohydrodynamics(MHD)equations.Cases with different separations △_(rs)=|r_(s2)-r_(s1)|between the two same rational surfaces are considered.In the small △_(rs)cases,the plasma radiation destabilizes the NDTMs and makes the kinetic energy still grow gradually in the late nonlinear phase.Moreover,the NDTM harmonics with high mode numbers reach a high level in the presence of plasma radiation,forming a broad spectrum of MHD perturbations that induces a radially broadened region of MHD turbulence.As a result,the profiles of safety factors also enter a nonlinear oscillation phase.In the intermediate △_(rs)case,the plasma radiation can advance the explosive burst of kinetic energy that results from the fast driven reconnection between the two rational surfaces,because it can further promote the destabilizing effects of bootstrap current perturbation on the magnetic island near the outer rational surfaces.In the large △_(rs)case,through destabilizing the outer islands significantly,the plasma radiation can even induce the explosive burst in the reversed magnetic shear configuration where the burst cannot be induced in the absence of plasma radiation.
基金supported by the National Natural Science Function of China(Nos.40390150,40390155,10575018)
文摘Effects of tearing modes are inves shows that the effect of the m = 0 harmonics on the early quasi-linear stage of m = 1 double tigated. The numerical calculation with the harmonics m = 0 included the m = 0 harmonics on the mode is negligible in the linear stage. As the mode begins to grow nonlinearly, both the current and flow profiles are pinched due to the m = 0 harmonics. To make a comparison we also carry out the calculation with m = 0 harmonics turned off. The profiles of the total current, poloidal magnetic field, and poloidal shear velocity in the cases with or without the m = 0 harmonics are compared and discussed. In addition, the formation of a poloidal velocity shear is found and its mechanism is investigated.
基金supported by the National Magnetic Confinement Fusion Energy R&D Program of China(Nos.2019YFE03090300 and 2017YFE0301100)National Natural Science Foundation of China(Nos.11925501 and 12075048)the Fundamental Research Funds for the Central Universities(Nos.DUT21GJ204 and DUT21LK28)。
文摘The effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes are investigated based on a set of reduced magnetohydrodynamic equations.It is found that the radiation can reduce the pressure near the rational surface.During the nonlinear evolution,the magnitude of perturbed bootstrap current is drastically enhanced in the presence of the radiation.Besides,the radiation can increase the growth rate of the magnetic islands by diminishing the pressure,such that the magnetic islands do not saturate compared with that without radiation.On the other hand,with the increase of the ratio of parallel to perpendicular transport coefficientχ‖/χ⊥,the reduction of pressure can further increase the growth rate of magnetic islands in the presence of plasma radiation.Finally,the mechanisms of the destabilizing effects driven by the radiation are discussed in detail as well.
基金supported by National Natural Science Foundation of China(No.11835010)by the National Key Research and Development Program of China(Nos.2019YFE03030004 and 2022YFE031000001)。
文摘Both current and pressure coupling schemes have been adopted in the hybrid kinetic–magnetohydrodynamic code CLT-K recently.Numerical equivalences between these two coupling schemes are strictly verified under different approximations.First,when considering only the perturbed distribution function of energetic particles(EPs),the equivalence can be proved analytically.Second,when both the variations of the magnetic field and the EP distribution function are included,the current and pressure coupling schemes numerically produce the same result in the nonlinear simulations.On this basis,the influences of co-/counter-passing and trapped EPs on the linear stabilities of the m/n=2/1 tearing mode(TM)have been investigated(where m and n represent the poloidal and toroidal mode numbers,respectively).The results of scanningβh of EPs show that the co-passing and trapped EPs are found to stabilize the TM,while the counter-passing EPs tend to destabilize the TM.The behind(de)stabilization mechanisms of the TM by EPs are carefully analyzed.Furthermore,after exceeding critical EP betas,the same branch of the high-frequency mode is excited by co-/counterpassing and trapped EPs,which is identified as the m/n=2/1 energetic particle mode.
