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
Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and scrape-off layer are developed for the'divertor-type'and'limiter-type'free boundaries in the tokamak cylindrical coordinate.With a...Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and scrape-off layer are developed for the'divertor-type'and'limiter-type'free boundaries in the tokamak cylindrical coordinate.With a toroidal plasma flow,the flux functions are considerably different under the isentropic and isothermal assumptions.The effects of the toroidal flow on the magnetic axis shift are investigated.In a high beta plasma,the magnetic shifts due to the toroidal flow are almost the same for both the isentropic and isothermal cases and are about 0.04a_(0)(a_(0)is the minor radius)for M_(0)=0.2(the toroidal Alfvén Mach number on the magnetic axis).In addition,the X-point is slightly shifted upward by 0.0125a_(0).But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M_(0) is usually less than 0.05 in a real tokamak.The effects of the toroidal flow on the plasma parameters are also investigated.The high toroidal flow shifts the plasma outward due to the centrifugal effect.Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.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
A Hall magnetohydrodynamics （MHD） simulation is carried out to study the dynamic process of double tearing mode. The results indicated that the growth rates in the earlier nonlinear and transition phases agree with ...A Hall magnetohydrodynamics （MHD） simulation is carried out to study the dynamic process of double tearing mode. The results indicated that the growth rates in the earlier nonlinear and transition phases agree with the previous results. With further development of reconnection, the current sheet thickness is much smaller than the ion inertia length, which leads to a strong influence of the Hall effects. As a result, the reconnection in the late nonlinear phase exhibits an explosive nature with a time scale nearly independent of resistivity. A localized and severely intensified current density is observed and the maximum kinetic energy is over one order of magnitude higher in Hall MHD than that in resistive MHD.展开更多
The effect of the reconnection rate on the generation of Alfvén wave energy is systematically investigated using Hall magnetohydrodynamics（MHD）. It is well known that a decrease in magnetic energy is proportion...The effect of the reconnection rate on the generation of Alfvén wave energy is systematically investigated using Hall magnetohydrodynamics（MHD）. It is well known that a decrease in magnetic energy is proportional to the reconnection rate. It is found that an instantaneous increase in Alfvén wave energy in unit Alfvén time is the square dependence on the reconnection rate. The converted Alfvén wave energy is strongly enhanced due to the large increase in the reconnection rate in Hall MHD. For solar-terrestrial plasmas, the maximum converted Alfvén wave energy in unit Alfvén time with the Hall effect can be over 50 times higher than that without the Hall effect during magnetic reconnection.展开更多
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.
基金supported by National Key Research and Development Program of China(Nos.2019YFE03030004 and 2019YFE03020003)National Natural Science Foundation of China(NSFC)(Nos.11775188 and 11835010)。
文摘Magnetohydrodynamic equilibrium schemes with toroidal plasma flows and scrape-off layer are developed for the'divertor-type'and'limiter-type'free boundaries in the tokamak cylindrical coordinate.With a toroidal plasma flow,the flux functions are considerably different under the isentropic and isothermal assumptions.The effects of the toroidal flow on the magnetic axis shift are investigated.In a high beta plasma,the magnetic shifts due to the toroidal flow are almost the same for both the isentropic and isothermal cases and are about 0.04a_(0)(a_(0)is the minor radius)for M_(0)=0.2(the toroidal Alfvén Mach number on the magnetic axis).In addition,the X-point is slightly shifted upward by 0.0125a_(0).But the magnetic axis and the X-point shift due to the toroidal flow may be neglected because M_(0) is usually less than 0.05 in a real tokamak.The effects of the toroidal flow on the plasma parameters are also investigated.The high toroidal flow shifts the plasma outward due to the centrifugal effect.Temperature profiles are noticeable different because the plasma temperature is a flux function in the isothermal case.
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National Science Foundation of China(Nos.40474058,40536030 and 10575031)
文摘A Hall magnetohydrodynamics （MHD） simulation is carried out to study the dynamic process of double tearing mode. The results indicated that the growth rates in the earlier nonlinear and transition phases agree with the previous results. With further development of reconnection, the current sheet thickness is much smaller than the ion inertia length, which leads to a strong influence of the Hall effects. As a result, the reconnection in the late nonlinear phase exhibits an explosive nature with a time scale nearly independent of resistivity. A localized and severely intensified current density is observed and the maximum kinetic energy is over one order of magnitude higher in Hall MHD than that in resistive MHD.
基金supported by the Fundamental Research Fund for Chinese Central UniversitiesNational Natural Science Foundation of China under Grant No. 41474123the ITER-CN under Grant Nos. 2013GB104004 and 2013GB111004
文摘The effect of the reconnection rate on the generation of Alfvén wave energy is systematically investigated using Hall magnetohydrodynamics（MHD）. It is well known that a decrease in magnetic energy is proportional to the reconnection rate. It is found that an instantaneous increase in Alfvén wave energy in unit Alfvén time is the square dependence on the reconnection rate. The converted Alfvén wave energy is strongly enhanced due to the large increase in the reconnection rate in Hall MHD. For solar-terrestrial plasmas, the maximum converted Alfvén wave energy in unit Alfvén time with the Hall effect can be over 50 times higher than that without the Hall effect during magnetic reconnection.
