Effects of diamagnetic drift on nonlinear interaction between multi-helicity neoclassical tearing modes

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.

Effects of counter-current driven by electron cyclotron waves on neoclassical tearing mode suppression

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.

Effect of addition of minor amounts of Sb and Gd on hot tearing susceptibility of Mg-5Al-3Ca alloy

The effects of addition of minor amount of(0.5 wt.%) antimony(Sb) or gadolinium(Gd) and combined addition of Sb and Gd(0.5 wt.%,respectively) on the hot tearing susceptibility(HTS) of Mg-5Al-3Ca alloy were investigated experimentally using a “T-shaped” hot tearing measuring system. Various solidification parameters of the alloys were measured and calculated through thermal analysis experiments. The microstructure, grain size, and morphology of the crack zone were characterized by scanning electron microscopy and electron backscatter diffraction, and the crystal phases of the alloys were analyzed by X-ray diffraction and energy-dispersive X-ray spectroscopy. The results showed that the addition of 0.5 wt.% Gd resulted in the increase in the vulnerable temperature range(Tv) and reduced the eutectic structure content that could participate in feeding, thereby improving the HTS of the alloy. However, addition of 0.5 wt.% Sb or combined addition of Gd and Sb(0.5 wt.%, respectively) to the Mg-5Al-3Ca alloy shortened the Tvand improved the skeleton strength of the alloy, thereby reducing HTS. Moreover, significantly refined structure of Mg-5Al-3Ca-0.5Gd-0.5Sb alloy improved the feeding ability of the eutectic structure, thus the alloy exhibited the lowest HTS.

Effects of plasma radiation on the nonlinear evolution of neo-classical tearing modes in tokamak plasmas with reversed magnetic shear

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.

Validation of the current and pressure coupling schemes with nonlinear simulations of TAE and analysis on the linear stability of tearing mode in the presence of energetic particles

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.

A review on hot tearing of magnesium alloys

Hot tearing is often a major casting defect in magnesium alloys and has a significant impact on the quality of their casting products.Hot tearing of magnesium alloys is a complex solidification phenomenon which is still not fully understood,it is of great importance to investigate the hot tearing behaviour of magnesium alloys.This review attempts to summarize the investigations on hot tearing of magnesium alloys over the past decades.The hot tearing criteria including recently developed Kou’s criterion are summarized and compared.The numeric simulation and assessing methods of hot tearing,factors influencing hot tearing,and hot tearing susceptibility(HTS)of magnesium alloys are discussed.

Influence of alloying elements on hot tearing susceptibility of Mg-Zn alloys based on thermodynamic calculation and experimental

Based on the hot tearing index|△T/△(fs)^(0.5)|recently proposed by Kou and the thermodynamic calculations of Pandat software,Al,Cu,and Mn elements were picked up and their influence on hot tearing susceptibility of Mg-x Zn(x=6,8,10,wt%)alloys was studied by experiments.The results indicate that Al addition can significantly reduce the hot tearing susceptibility of Mg-Zn alloys.Either 0.5Cu or 0.3Mn addition individually can reduce the HTS of the Mg-6Zn-(1,4)Al alloys,while adding together increases the susceptibility.The addition of 0.5Cu and 0.3Mn both individually and together increases the HTS of Mg-8/10Zn-1Al alloys.Based on the experimental and calculation results,the index can be modified to|△T/△(fs)^(0.5)|(d)^(2)for more accurate prediction on the hot tearing resistance of Mg-Zn based alloys.Grain refinement significantly improves the hot tearing resistance of Mg-Zn based alloys.

Tensile properties and hot tearing susceptibility of cast Al–Cu alloys containing excess Fe and Si

This study was undertaken to investigate the tensile properties and hot tearing susceptibility of cast Al–Cu alloys containing excess Fe(up to 1.5 wt%)and Si(up to 2.5 wt%).According to the results,the optimum tensile properties and hot tearing resistance were achieved at Fe/Si mass ratio of 1,where theα-Fe phase was the dominant Fe compound.Increasing the Fe/Si mass ratio above unity increased the amounts of detrimentalβ-Cu Fe platelets in the microstructure,deteriorating the tensile properties and hot tearing resistance.Decreasing the mass ratio below unity increased the size and fraction of Si needles and micropores in the microstructure,also impairing the tensile properties and hot tearing resistance.The investigation of hot-torn surfaces revealed that theβ-Cu Fe platelets disrupted the tear healing phenomenon by blocking interdendritic feeding channels,while theα-Fe intermetallics improved the hot tearing resistivity due to their compact morphology and high melting point.

Hot tearing susceptibility of MgZn_(4.5)Y_xZr_(0.5) alloys and mechanism

The hot tearing susceptibility of MgZn_(4.5)Y_xZr_(0.5)(x = 0.5, 1, 2, 4, 6) alloys was evaluated using ClyneDavies' theoretical model and a constrained rod casting(CRC) apparatus equipped with a load cell and data acquisition system. The results obtained from these two approaches were in good agreement, illustrating that the hot tearing susceptibility of the investigated alloys is in the order of MgZn_(4.5)Y_xZr_(0.5) > MgZn_(4.5)Y_xZr_(0.5) > MgZn_(4.5)Y_xZr_(0.5) > MgZn_(4.5)Y_xZr_(0.5)> MgZn_(4.5)Y_xZr_(0.5). The microstructure and morphology of hot tearing regions were observed by means of X-ray diffraction and scanning electron microscopy. The function curves on variation of contraction force and temperature versus time were recorded by a computer during solidification of the MgZn_(4.5)Y_xZr_(0.5) alloys in a "T" type mold after A/D(Analog to digital) conversion. Results show that both the amount and morphology of the second phases have a great relationship with the hot tearing susceptibility. But the former plays a more important role on that of MgZn_(4.5)Y_xZr_(0.5) alloys. The role of low-melting point eutectic phases on the hot tearing susceptibility of MgZn_(4.5)Y_xZr_(0.5) alloys changes gradually with different Y contents. When Y ≤ 1wt.%, it is mainly a damaging effect on intergranular bonding force; when Y > 1wt.%, it is mainly an intergranular feeding effect on formed separated dendrites.

A STUDY OF TEARING PROPERTIES OF MEMBRANE COATED FABRICS

In this paper,an equation expressing relationship between trapezoid tear strength and fabrictensile properties,weave texture and geomitry of specimen was studied.It could be used to predicttrapezoid tear strength for uncoated fabrics well,and also for coated fabrics if multipling a stressconcentration coefficient.The four tear test standard methods(single-rip,double-rip,wing-ripand trapezoid tear)have been adopted to measure the tear strength of fifteen coated fabrics whichwere used for architecture and gencral industrial purposes and the nine corresponding uncoatedfabrics respectively.Analysis and comparison of experimental results showed that there are an ex-cellent correlation between each two methods with the four tear parameters respectively and a goodconsistency of the order of the tear strength for different samples.In addition,the experimental results showed that a good correlation exists between the tenslieproperties and tear strength of coated and uncoated fabrics.

Influence of Al addition on solidification path and hot tearing susceptibility of Mg-2Zn-(3+0.5 x)Y-x Al alloys

Hot tearing susceptibility(HTS)of Mg-2Zn-(3+0.5 x)Y-x Al(x=0,2 and 3 at%)alloys is predicted by using modified Clyne-Davies’model(CSC^(∗)).The solidification path,solidification characteristic temperatures and dendritic coherency solid fraction have been studied by double-thermocouple thermal analysis.The solidification contraction stress vs.temperature(and time)curves are measured by using a“T”type hot tearing permanent-mold.The results reveal that the CSC^(∗)prediction values are in good agreement with the experimental results.Moreover,Al_(2)Y phase acts as the heterogeneous nucleation core ofα-Mg and significantly influences the grain size.It has been observed that minimum grain size,optimal dendritic coherency and minimum HTS are exhibited by Mg-2Zn-(3+0.5 x)Y-x Al alloy(x=2).Furthermore,when Al content was increased to 3 at%,Al_(2)Y phase exhibited a peritectic reaction and transformed into a mixed structure of Al_(2)Y and Al+Al_(3)Y phases,which increased the HTS of the alloy due to reduced fine-grained Al_(2)Y content.

Influence of a low-frequency alternating magnetic field on hot tearing susceptibility of EV31 magnesium alloy

The effect of a low-frequency alternating magnetic field (AMF,0 A 0 Hz,5 A 10 Hz,10 A 10 Hz,15 A 10 Hz) on the hot tearing susceptibility (HTS) of a magnesium alloy (EV31) was systematically studied using a combination of experiment and numerical simulation.By observing the macroscopic hot cracks in hot joints of the "T" samples,the hot tearing tendency of the samples was analyzed.The HTS of the alloy can be predicted via numerical simulation and the crack susceptibility coefficient (CSC).The microstructure and morphology of the hot tearing zone of EV31 were investigated using scanning electron microscopy (SEM).Results show that increasing the magnetic field strength reduces both the alloy solidification temperature range and the dendrite coherency temperature,which increases the feeding time during solidification and decreases the HTS of the alloy.When the magnetic field parameters are 10 Hz 15 A,the EV31 alloy shows the lowest HTS.The main component of the second phase in the microstructure is Mg12Nd.This study also found that the electromagnetic field can effectively refine the grains,purify the melt,and reduce the oxide content in the melt.The obtained simulation results are consistent with the experimental results.

Solidification pathways and hot tearing susceptibility of MgZn_xY_4Zr_(0.5) alloys

Hot tearing is known as one of the most serious solidification defects commonly encountered during solidification. It is very important to study the solidification path of alloys. In the work, thermal analysis with cooling curve was used for the investigation of microstructure evolution with different Zn contents during solidification process of MgZn_xY_4Zr_(0.5) alloys. Thermal analysis results of MgY_4Zr_(0.5) alloys revealed one distinct phase precipitation: α-Mg. Three different phase peaks were detected in the Zn-containing alloys: α-Mg, Z-phase(Mg_(12)YZn) and W-phase(Mg_3 Y_2Zn_3). In addition, for the present MgZn_xY_4Zr_(0.5) alloys, the freezing ranges of these alloys from large to small were: MgZn_(1.5)Y_4Zr_(0.5)>MgZn)(3.0) Y)4Zr_(0.5)>MgZn0.5 Y4 Zr0.5>MgY_4Zr_(0.5). The effect of different contents of Zn(0, 0.5, 1.5, 3.0 wt.%) on hot tearing behavior of MgY_4Zr_(0.5) alloy was investigated using a constrained rod casting(CRC) apparatus equipped with a load cell and data acquisition system. The experimental results show that the addition of Zn element significantly increases hot tearing susceptibility(HTS) of the MgY_4Zr_(0.5) alloy due to its extended freezing range. Some free dendrite-like bumps and ruptured liquid films on the fracture surfaces were observed in all the fracture surfaces. These phenomena proved the fact that the hot tearing formation was caused by interdendritic separation due to lack of feeding at the end of solidification.

Effects of resonant magnetic perturbation on the instability of single tearing mode with non-shear flow

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.

Effects of resonant magnetic perturbation on locked mode of neoclassical tearing modes

The effects of externally applied resonant magnetic perturbation (RMP) on the locked mode of the neoclassical tearing mode (NTM) are numerically investigated by means of a set of reduced magnetohydrodynamic equations.It is found that,for a small bootstrap current fraction,three regimes,namely the slight suppression regime,the small locked island (SLI) regime and the big locked island (BLI) regime,are discovered with the increase of RMP strength.For a much higher bootstrap current fraction,however,a new oscillation regime appears instead of the SLI regime,although the other regimes still remain.The physical process in each regime is analyzed in detail based on the phase difference between the NTM and the RMP.Moreover,the critical values of the RMP in both SLI and BLI regimes are obtained,and their dependence on key plasma parameters is discussed as well.

Influence of stationary driven helical current on the m=2/n=1 resistive tearing mode

The influence of stationary driven helical current on tearing mode instability in the m=2/n=1 rational surface is explored numerically using resistive magnetohydrodynamic simulation in cylindrical geometry.The results indicate that the flip instabilities result from the sustained injection of the sufficiently strong helical current driven in the island O-point.The driven helical current induces high order harmonics of instabilities due to the delay of suppressing timing and the increase of its current intensity.With the appropriate current density values,the development of the perturbed kinetic energy can be limited and the occurrence of the flip instabilities can be delayed for a long time.The radial deviation of the current deposition can lead to poor inhibition effect,and the effect of current bias on the boundary is greater than that on the axis.

Basic features of the multiscale interaction between tearing modes and slab ion-temperature-gradient modes

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.

Sawtooth-like oscillations and steady states caused by the m/n=2/1 double tearing mode

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.

Multi-scale interaction between tearing modes and micro-turbulence in the HL-2A plasmas

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.

Application of Galerkin spectral method for tearing mode instability

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.