Anomalous transport in magnetically confined plasmas is investigated using temporal fractional transport equations.The use of temporal fractional transport equations means that the order of the partial derivative with...Anomalous transport in magnetically confined plasmas is investigated using temporal fractional transport equations.The use of temporal fractional transport equations means that the order of the partial derivative with respect to time is a fraction. In this case, the Caputo fractional derivative relative to time is utilized, because it preserves the form of the initial conditions. A numerical calculation reveals that the fractional order of the temporal derivative α(α ∈(0, 1), sub-diffusive regime) controls the diffusion rate. The temporal fractional derivative is related to the fact that the evolution of a physical quantity is affected by its past history, depending on what are termed memory effects. The magnitude of α is a measure of such memory effects. When α decreases, so does the rate of particle diffusion due to memory effects. As a result,if a system initially has a density profile without a source, then the smaller the α is, the more slowly the density profile approaches zero. When a source is added, due to the balance of the diffusion and fueling processes, the system reaches a steady state and the density profile does not evolve. As α decreases, the time required for the system to reach a steady state increases. In magnetically confined plasmas, the temporal fractional transport model can be applied to off-axis heating processes. Moreover, it is found that the memory effects reduce the rate of energy conduction and hollow temperature profiles can be sustained for a longer time in sub-diffusion processes than in ordinary diffusion processes.展开更多
Numerical research is conducted to investigate the effects of plasma boundary shape on the tearing mode triggering explosive bursts in toroidal tokamak plasmas.In this work,m/n=2/1 mode is responsible for the triggeri...Numerical research is conducted to investigate the effects of plasma boundary shape on the tearing mode triggering explosive bursts in toroidal tokamak plasmas.In this work,m/n=2/1 mode is responsible for the triggering of the explosive burst.Plasma boundary shape can be adjusted via the adjustment of the parameters triangularityδand elongationκ.The investigations are conducted both under lowβ(close to zero)and under finiteβregimes.In the lowβregime,triangularity and elongation both have stabilizing effect on the explosive burst,and the stabilizing effect of elongation is stronger.Under a large elongation(κ=2.0),the elongation effect can evidently enhance the stabilizing effect in a positive triangularity regime,but barely affects the stabilizing effect in a negative triangularity regime.In the finiteβregime,the explosive burst is delayed in comparison with that in the lowβregime.Similar to the lowβcases,the effects of triangularity and elongation both are stabilizing.Under a large elongation(κ=2.0),the elongation effect can evidently enhance the stabilizing effect on the explosive burst in a positive triangularity regime,but impair the stabilizing effect in a negative triangularity regime.The explosive burst disappears in the large triangularity case(δ=0.5),indicating that the explosive burst can be effectively prevented in experiments via carefully adjusting plasma boundary shape.Moreover,strong magnetic stochasticity appears in the negative triangularity case during the nonlinear phase.展开更多
Enhancements of edge zonal flows,radial electric fields,and turbulence are observed in electron cyclotron resonance heating-heated plasmas(Zhao et al 2013 Nucl.Fusion 53083011).In this paper,the effects of sawtooth he...Enhancements of edge zonal flows,radial electric fields,and turbulence are observed in electron cyclotron resonance heating-heated plasmas(Zhao et al 2013 Nucl.Fusion 53083011).In this paper,the effects of sawtooth heat pulses on flows and turbulence are presented.These experiments are performed using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak.The edge zonal flows,radial electric fields,and turbulence are all enhanced by sawteeth.Propagation of the zonal flow and turbulence intensities is also observed.The delay time of the maximal intensity of the electric fields,zonal flows,and turbulence with respect to the sawtooth crashes is estimated as~1 ms and comparable to that of the sawtooth-triggered intermediate phases.Not only the zonal flows but also the radial electric fields lag behind the turbulence.Furthermore,the intensities of both the zonal flows and electric fields nearly linearly increase/decrease with the increase/decrease of the turbulence intensity.A double-source predator-prey model analysis suggests that a relatively strong turbulence source may contribute to the dominant zonal flow formation during sawtooth cycles.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
As an obstacle in high-performance discharge in future fusion devices,disruptions may do great damages to the reactors through causing strong electromagnetic forces,heat loads and so on.The drift waves in tokamak are ...As an obstacle in high-performance discharge in future fusion devices,disruptions may do great damages to the reactors through causing strong electromagnetic forces,heat loads and so on.The drift waves in tokamak are illustrated to play essential roles in the confinement performance as well.Depending on the plasma parameters and mode perpendicular wavelength,the mode phase velocity is either in the direction of electron diamagnetic velocity(namely,typical trapped electron mode)or in the direction of ion diamagnetic velocity(namely,the ubiquitous mode).Among them,the ubiquitous mode is directly investigated using gyro-fluid simulation associating with gyro-fluid equations for drift waves in tokamak plasmas.The ubiquitous mode is charactered by the short wavelength and propagates in ion diamagnetic direction.It is suggested that the density gradient is essential for the occurrence of the ubiquitous mode.However,the ubiquitous mode is also influenced by the temperature gradients and other plasma parameters including the magnetic shear and the fraction of trapped electrons.Furthermore,the ubiquitous mode may play essential roles in the turbulent transport.Meanwhile,the relevant parameters are scanned using a great number of electrostatic gyro-fluid simulations.The stability map is taken into consideration with the micro-instabilities contributing to the turbulent transport.The stability valley of the growth rates occurs with the assumption of the normalized temperature gradient equaling to the normalized density gradient.展开更多
Microturbulence excited by ion temperature gradient(ITG)-dominant and trapped electron mode(TEM)-dominant instabilities is investigated by employing an extended fluid code(ExFC)based on the so-called Landau fluid mode...Microturbulence excited by ion temperature gradient(ITG)-dominant and trapped electron mode(TEM)-dominant instabilities is investigated by employing an extended fluid code(ExFC)based on the so-called Landau fluid model,which includes the trapped electron dynamics.Firstly,the global effect is emphasized through direct comparison of ITG and TEM instability domains based on local and global simulations.The global effect makes differences in both linear instability and nonlinear transport,including the fluxes and the structure of zonal flow.The transitions among ITG,TEM,and ITG&TEM(ITG&TEM represents that ITG and TEM coexist with different wavelengths)instabilities/turbulence depend not only on the three key drive forces(R/L_n,R/L_(Te),R/L_(Ti))but also on their global(profile)effects.Secondly,a lot of electrostatic linear gyro-fluid simulations are concluded to obtain a distribution of the instability.展开更多
Machine learning opens up new possibilities for research of plasma confinement. Specifically, models constructed using machine learning algorithms may effectively simplify the simulation process. Previous firstprincip...Machine learning opens up new possibilities for research of plasma confinement. Specifically, models constructed using machine learning algorithms may effectively simplify the simulation process. Previous firstprinciples simulations could provide physics-based transport information, but not fast enough for real-time applications or plasma control. To address this issue, this study proposes SExFC, a surrogate model of the Gyro-Landau Extended Fluid Code(ExFC). As an extended version of our previous model ExFC-NN, SExFC can capture more features of transport driven by the ion temperature gradient mode and trapped electron mode,using an extended database initially generated with ExFC simulations. In addition to predicting the dominant instability, radially averaged fluxes and radial profiles of fluxes, the well-trained SExFC may also be suitable for physics-based rapid predictions that can be considered in real-time plasma control systems in the future.展开更多
Numerical simulation on the resonant magnetic perturbation penetration is carried out by the newly-updated initial value code MDC(MHD@Dalian Code).Based on a set of two-fluid fourfield equations,the bootstrap current,...Numerical simulation on the resonant magnetic perturbation penetration is carried out by the newly-updated initial value code MDC(MHD@Dalian Code).Based on a set of two-fluid fourfield equations,the bootstrap current,parallel,and perpendicular transport effects are included appropriately.Taking into account the bootstrap current,a mode penetration-like phenomenon is found,which is essentially different from the classical tearing mode model.To reveal the influence of the plasma flow on the mode penetration process,E×B drift flow and diamagnetic drift flow are separately applied to compare their effects.Numerical results show that a sufficiently large diamagnetic drift flow can drive a strong stabilizing effect on the neoclassical tearing mode.Furthermore,an oscillation phenomenon of island width is discovered.By analyzing it in depth,it is found that this oscillation phenomenon is due to the negative feedback regulation of pressure on the magnetic island.This physical mechanism is verified again by key parameter scanning.展开更多
We theoretically investigate the dust charging in the sheath of an electronegative plasma, by using a single dust grain model based on a previous sheath structure [Chin. Phys. Lett 20 (2003) 1537] in which cold positi...We theoretically investigate the dust charging in the sheath of an electronegative plasma, by using a single dust grain model based on a previous sheath structure [Chin. Phys. Lett 20 (2003) 1537] in which cold positive ions and hot negative ions have been assumed. It is found that dust grains are first charged negatively at the展开更多
Effects of the m=0 harmonics on the early quasi-linear stage of m=1 doubletearing modes are investigated.The numerical calculation with the harmonics m = 0 includedshows that the effect of the m=0 harmonics on the mod...Effects of the m=0 harmonics on the early quasi-linear stage of m=1 doubletearing modes are investigated.The numerical calculation with the harmonics m = 0 includedshows that the effect of the m=0 harmonics on the mode is negligible in the linear stage.Asthe mode begins to grow nonlinearly,both the current and flow profiles are pinched due to them=0 harmonics.To make a comparison we also carry out the calculation with m=0 harmonicsturned off.The profiles of the total current,poloidal magnetic field,and poloidal shear velocityin the cases with or without the m=0 harmonics are compared and discussed.In addition,theformation of a poloidal velocity shear is found and its mechanism is investigated.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
基金supported by the National Key R&D Program of China (Grant No. 2022YFE03090000)the National Natural Science Foundation of China (Grant No. 11925501)the Fundamental Research Fund for the Central Universities (Grant No. DUT22ZD215)。
文摘Anomalous transport in magnetically confined plasmas is investigated using temporal fractional transport equations.The use of temporal fractional transport equations means that the order of the partial derivative with respect to time is a fraction. In this case, the Caputo fractional derivative relative to time is utilized, because it preserves the form of the initial conditions. A numerical calculation reveals that the fractional order of the temporal derivative α(α ∈(0, 1), sub-diffusive regime) controls the diffusion rate. The temporal fractional derivative is related to the fact that the evolution of a physical quantity is affected by its past history, depending on what are termed memory effects. The magnitude of α is a measure of such memory effects. When α decreases, so does the rate of particle diffusion due to memory effects. As a result,if a system initially has a density profile without a source, then the smaller the α is, the more slowly the density profile approaches zero. When a source is added, due to the balance of the diffusion and fueling processes, the system reaches a steady state and the density profile does not evolve. As α decreases, the time required for the system to reach a steady state increases. In magnetically confined plasmas, the temporal fractional transport model can be applied to off-axis heating processes. Moreover, it is found that the memory effects reduce the rate of energy conduction and hollow temperature profiles can be sustained for a longer time in sub-diffusion processes than in ordinary diffusion processes.
基金supported by the National Natural Science Foundation of China(Grant Nos.11925501,12105034,and 12205034)the Fundamental Research Funds for the Central Universities(Grant Nos.DUT22ZD215)。
文摘Numerical research is conducted to investigate the effects of plasma boundary shape on the tearing mode triggering explosive bursts in toroidal tokamak plasmas.In this work,m/n=2/1 mode is responsible for the triggering of the explosive burst.Plasma boundary shape can be adjusted via the adjustment of the parameters triangularityδand elongationκ.The investigations are conducted both under lowβ(close to zero)and under finiteβregimes.In the lowβregime,triangularity and elongation both have stabilizing effect on the explosive burst,and the stabilizing effect of elongation is stronger.Under a large elongation(κ=2.0),the elongation effect can evidently enhance the stabilizing effect in a positive triangularity regime,but barely affects the stabilizing effect in a negative triangularity regime.In the finiteβregime,the explosive burst is delayed in comparison with that in the lowβregime.Similar to the lowβcases,the effects of triangularity and elongation both are stabilizing.Under a large elongation(κ=2.0),the elongation effect can evidently enhance the stabilizing effect on the explosive burst in a positive triangularity regime,but impair the stabilizing effect in a negative triangularity regime.The explosive burst disappears in the large triangularity case(δ=0.5),indicating that the explosive burst can be effectively prevented in experiments via carefully adjusting plasma boundary shape.Moreover,strong magnetic stochasticity appears in the negative triangularity case during the nonlinear phase.
基金National Natural Science Foundation of China(Nos.12075057,11775069,11320101005,and 11875020)National Magnetic Confinement Fusion Science Program of China(No.2017YFE0301201)+3 种基金East China University of Technology,Doctoral Foundation(Nos.DHBK 2017134 and DHBK 2018059)Grant-in-Aid for Scientific Research of the Japan Society for the Promotion of Science(Nos.15H02155,15H02335,21K03513)Landmark Achievements in Nuclear Science and Technology(No.xxkjs2018011)Natural Science Foundation of Jiangxi Province(Nos.20202ACBL201002 and 0192ACB80006)。
文摘Enhancements of edge zonal flows,radial electric fields,and turbulence are observed in electron cyclotron resonance heating-heated plasmas(Zhao et al 2013 Nucl.Fusion 53083011).In this paper,the effects of sawtooth heat pulses on flows and turbulence are presented.These experiments are performed using multiple Langmuir probe arrays in the edge plasmas of the HL-2A tokamak.The edge zonal flows,radial electric fields,and turbulence are all enhanced by sawteeth.Propagation of the zonal flow and turbulence intensities is also observed.The delay time of the maximal intensity of the electric fields,zonal flows,and turbulence with respect to the sawtooth crashes is estimated as~1 ms and comparable to that of the sawtooth-triggered intermediate phases.Not only the zonal flows but also the radial electric fields lag behind the turbulence.Furthermore,the intensities of both the zonal flows and electric fields nearly linearly increase/decrease with the increase/decrease of the turbulence intensity.A double-source predator-prey model analysis suggests that a relatively strong turbulence source may contribute to the dominant zonal flow formation during sawtooth cycles.
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Project partially supported by the National Natural Science Foundation of China(Grant Nos.12205035 and 11925501)also partially by the National Key Research and Development Program of China(Grant Nos.2017YFE0301200 and 2017YFE0301201).
文摘As an obstacle in high-performance discharge in future fusion devices,disruptions may do great damages to the reactors through causing strong electromagnetic forces,heat loads and so on.The drift waves in tokamak are illustrated to play essential roles in the confinement performance as well.Depending on the plasma parameters and mode perpendicular wavelength,the mode phase velocity is either in the direction of electron diamagnetic velocity(namely,typical trapped electron mode)or in the direction of ion diamagnetic velocity(namely,the ubiquitous mode).Among them,the ubiquitous mode is directly investigated using gyro-fluid simulation associating with gyro-fluid equations for drift waves in tokamak plasmas.The ubiquitous mode is charactered by the short wavelength and propagates in ion diamagnetic direction.It is suggested that the density gradient is essential for the occurrence of the ubiquitous mode.However,the ubiquitous mode is also influenced by the temperature gradients and other plasma parameters including the magnetic shear and the fraction of trapped electrons.Furthermore,the ubiquitous mode may play essential roles in the turbulent transport.Meanwhile,the relevant parameters are scanned using a great number of electrostatic gyro-fluid simulations.The stability map is taken into consideration with the micro-instabilities contributing to the turbulent transport.The stability valley of the growth rates occurs with the assumption of the normalized temperature gradient equaling to the normalized density gradient.
基金supported by the National Natural Science Foundation of China(Grant Nos.12205035,11925501,12275071,and U1967206)。
文摘Microturbulence excited by ion temperature gradient(ITG)-dominant and trapped electron mode(TEM)-dominant instabilities is investigated by employing an extended fluid code(ExFC)based on the so-called Landau fluid model,which includes the trapped electron dynamics.Firstly,the global effect is emphasized through direct comparison of ITG and TEM instability domains based on local and global simulations.The global effect makes differences in both linear instability and nonlinear transport,including the fluxes and the structure of zonal flow.The transitions among ITG,TEM,and ITG&TEM(ITG&TEM represents that ITG and TEM coexist with different wavelengths)instabilities/turbulence depend not only on the three key drive forces(R/L_n,R/L_(Te),R/L_(Ti))but also on their global(profile)effects.Secondly,a lot of electrostatic linear gyro-fluid simulations are concluded to obtain a distribution of the instability.
基金supported by the National Natural Science Foundation of China(Grant Nos.12205035, 11925501, 12275071, and U1967206)。
文摘Machine learning opens up new possibilities for research of plasma confinement. Specifically, models constructed using machine learning algorithms may effectively simplify the simulation process. Previous firstprinciples simulations could provide physics-based transport information, but not fast enough for real-time applications or plasma control. To address this issue, this study proposes SExFC, a surrogate model of the Gyro-Landau Extended Fluid Code(ExFC). As an extended version of our previous model ExFC-NN, SExFC can capture more features of transport driven by the ion temperature gradient mode and trapped electron mode,using an extended database initially generated with ExFC simulations. In addition to predicting the dominant instability, radially averaged fluxes and radial profiles of fluxes, the well-trained SExFC may also be suitable for physics-based rapid predictions that can be considered in real-time plasma control systems in the future.
基金supported by the National Key R&D Program of China(No.2022YFE03040001)National Natural Science Foundation of China(Nos.11925501 and 12075048)+1 种基金Chinese Academy of Sciences,Key Laboratory of Geospace Environment,University of Science&Technology of China(No.GE2019-01)Fundamental Research Funds for the Central Universities(No.DUT21GJ204)。
文摘Numerical simulation on the resonant magnetic perturbation penetration is carried out by the newly-updated initial value code MDC(MHD@Dalian Code).Based on a set of two-fluid fourfield equations,the bootstrap current,parallel,and perpendicular transport effects are included appropriately.Taking into account the bootstrap current,a mode penetration-like phenomenon is found,which is essentially different from the classical tearing mode model.To reveal the influence of the plasma flow on the mode penetration process,E×B drift flow and diamagnetic drift flow are separately applied to compare their effects.Numerical results show that a sufficiently large diamagnetic drift flow can drive a strong stabilizing effect on the neoclassical tearing mode.Furthermore,an oscillation phenomenon of island width is discovered.By analyzing it in depth,it is found that this oscillation phenomenon is due to the negative feedback regulation of pressure on the magnetic island.This physical mechanism is verified again by key parameter scanning.
文摘We theoretically investigate the dust charging in the sheath of an electronegative plasma, by using a single dust grain model based on a previous sheath structure [Chin. Phys. Lett 20 (2003) 1537] in which cold positive ions and hot negative ions have been assumed. It is found that dust grains are first charged negatively at the
基金supported by the National Natural Science Function of China(Nos.40390150,40390155,10575018)
文摘Effects of the m=0 harmonics on the early quasi-linear stage of m=1 doubletearing modes are investigated.The numerical calculation with the harmonics m = 0 includedshows that the effect of the m=0 harmonics on the mode is negligible in the linear stage.Asthe mode begins to grow nonlinearly,both the current and flow profiles are pinched due to them=0 harmonics.To make a comparison we also carry out the calculation with m=0 harmonicsturned off.The profiles of the total current,poloidal magnetic field,and poloidal shear velocityin the cases with or without the m=0 harmonics are compared and discussed.In addition,theformation of a poloidal velocity shear is found and its mechanism is investigated.
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.
