Three-Dimensional Multiferroic Structures under Time-Harmonic Loading

Magneto-electro-elastic(MEE)materials are a specific class of advanced smart materials that simultaneouslymanifest the coupling behavior under electric,magnetic,and mechanical loads.This unique combination ofproperties allows MEE materials to respond to mechanical,electric,and magnetic stimuli,making them versatile forvarious applications.This paper investigates the static and time-harmonic field solutions induced by the surface loadin a three-dimensional(3D)multilayered transversally isotropic(TI)linear MEE layered solid.Green’s functionscorresponding to the applied uniform load(in both horizontal and vertical directions)are derived using the FourierBessel series(FBS)system of vector functions.By virtue of this FBS method,two sets of first-order ordinarydifferential equations(i.e.,N-type and LM-type)are obtained,with the expansion coefficients being Love numbers.It is noted that the LM-type system corresponds to the MEE-coupled P-,SV-,and Rayleigh waves,while the N-typecorresponds to the purely elastic SH-and Love waves.By applying the continuity conditions across interfaces,the solutions for each layer of the structure(from the bottom to the top)are derived using the dual-variable andposition(DVP)method.This method(i.e.,DVP)is unconditionally stable when propagating solutions throughdifferent layers.Numerical examples illustrate the impact of load types,layering,and frequency on the response ofthe structure,as well as the accuracy and convergence of the proposed approach.The numerical results are usefulin designing smart devices made of MEE solids,which are applicable to engineering fields like renewable energy.

Drilling-based measuring method for the c-φ parameter of rock and its field application

The technology of drilling tests makes it possible to obtain the strength parameter of rock accurately in situ. In this paper, a new rock cutting analysis model that considers the influence of the rock crushing zone(RCZ) is built. The formula for an ultimate cutting force is established based on the limit equilibrium principle. The relationship between digital drilling parameters(DDP) and the c-φ parameter(DDP-cφ formula, where c refers to the cohesion and φ refers to the internal friction angle) is derived, and the response of drilling parameters and cutting ratio to the strength parameters is analyzed. The drillingbased measuring method for the c-φ parameter of rock is constructed. The laboratory verification test is then completed, and the difference in results between the drilling test and the compression test is less than 6%. On this basis, in-situ rock drilling tests in a traffic tunnel and a coal mine roadway are carried out, and the strength parameters of the surrounding rock are effectively tested. The average difference ratio of the results is less than 11%, which verifies the effectiveness of the proposed method for obtaining the strength parameters based on digital drilling. This study provides methodological support for field testing of rock strength parameters.

Strong coupling and catenary field enhancement in the hybrid plasmonic metamaterial cavity and TMDC monolayers

Strong coupling between resonantly matched surface plasmons of metals and excitons of quantum emitters results in the formation of new plasmon-exciton hybridized energy states.In plasmon-exciton strong coupling,plasmonic nanocavities play a significant role due to their ability to confine light in an ultrasmall volume.Additionally,two-dimensional transition metal dichalcogenides(TMDCs) have a significant exciton binding energy and remain stable at ambient conditions,making them an excellent alternative for investigating light-matter interactions.As a result,strong plasmon-exciton coupling has been reported by introducing a single metallic cavity.However,single nanoparticles have lower spatial confinement of electromagnetic fields and limited tunability to match the excitonic resonance.Here,we introduce the concept of catenary-shaped optical fields induced by plasmonic metamaterial cavities to scale the strength of plasmon-exciton coupling.The demonstrated plasmon modes of metallic metamaterial cavities offer high confinement and tunability and can match with the excitons of TMDCs to exhibit a strong coupling regime by tuning either the size of the cavity gap or thickness.The calculated Rabi splitting of Au-MoSe_2 and Au-WSe_2 heterostructures strongly depends on the catenary-like field enhancement induced by the Au cavity,resulting in room-temperature Rabi splitting ranging between 77.86 and 320 me V.These plasmonic metamaterial cavities can pave the way for manipulating excitons in TMDCs and operating active nanophotonic devices at ambient temperature.

Displacement field reconstruction in landslide physical modeling by using a terrain laser scanner e Part 2:Application and large strain/displacement and water effect analysis

Deformation analysis is fundamental in geotechnical modeling.Nevertheless,there is still a lack of an effective method to obtain the deformation field under various experimental conditions.In this study,we introduce a processebased physical modeling of a pileereinforced reservoir landslide and present an improved deformation analysis involving large strains and water effects.We collect multieperiod point clouds using a terrain laser scanner and reconstruct its deformation field through a point cloud processing workflow.The results show that this method can accurately describe the landslide surface deformation at any time and area by both scalar and vector fields.The deformation fields in different profiles of the physical model and different stages of the evolutionary process provide adequate and detailed landslide information.We analyze the large strain upstream of the pile caused by the pile installation and the consequent violent deformation during the evolutionary process.Furthermore,our method effectively overcomes the challenges of identifying targets commonly encountered in geotechnical modeling where water effects are considered and targets are polluted,which facilitates the deformation analysis at the wading area in a reservoir landslide.Eventually,combining subsurface deformation as well as numerical modeling,we comprehensively analyze the kinematics and failure mechanisms of this complicated object involving landslides and pile foundations as well as water effects.This method is of great significance for any geotechnical modeling concerning large-strain analysis and water effects.

ST-LSTM-SA:A New Ocean Sound Velocity Field Prediction Model Based on Deep Learning

The scarcity of in-situ ocean observations poses a challenge for real-time information acquisition in the ocean.Among the crucial hydroacoustic environmental parameters,ocean sound velocity exhibits significant spatial and temporal variability and it is highly relevant to oceanic research.In this study,we propose a new data-driven approach,leveraging deep learning techniques,for the prediction of sound velocity fields(SVFs).Our novel spatiotemporal prediction model,STLSTM-SA,combines Spatiotemporal Long Short-Term Memory(ST-LSTM) with a self-attention mechanism to enable accurate and real-time prediction of SVFs.To circumvent the limited amount of observational data,we employ transfer learning by first training the model using reanalysis datasets,followed by fine-tuning it using in-situ analysis data to obtain the final prediction model.By utilizing the historical 12-month SVFs as input,our model predicts the SVFs for the subsequent three months.We compare the performance of five models:Artificial Neural Networks(ANN),Long ShortTerm Memory(LSTM),Convolutional LSTM(ConvLSTM),ST-LSTM,and our proposed ST-LSTM-SA model in a test experiment spanning 2019 to 2022.Our results demonstrate that the ST-LSTM-SA model significantly improves the prediction accuracy and stability of sound velocity in both temporal and spatial dimensions.The ST-LSTM-SA model not only accurately predicts the ocean sound velocity field(SVF),but also provides valuable insights for spatiotemporal prediction of other oceanic environmental variables.

Field test of high-power microwave-assisted mechanical excavation for deep hard iron ore

Microwave-assisted mechanical excavation has great application prospects in mines and tunnels,but there are few field experiments on microwave-assisted rock breaking.This paper takes the Sishanling iron mine as the research object and adopts the self-developed high-power microwave-induced fracturing test system for hard rock to conduct field experiments of microwave-induced fracturing of iron ore.The heating and reflection evolution characteristics of ore under different microwave parameters(antenna type,power,and working distance)were studied,and the optimal microwave parameters were obtained.Subsequently,the ore was irradiated with the optimal microwave parameters,and the cracking effect of the ore under the action of the high-power open microwave was analyzed.The results show that the reflection coefficient(standing wave ratio)can be rapidly(<5 s)and automatically adjusted below the preset threshold value(1.6)as microwave irradiation is performed.When using a right-angle horn antenna with a working distance of 5 cm,the effect of automatic reflection adjustment reaches the best among other antenna types and working distances.When the working distance is the same,the average temperature of the irradiation surface and the area of the high-temperature area under the action of the two antennas(right-angled and equal-angled horn antenna)are basically the same and decrease with the increase of working distance.The optimal microwave parameters are:a right-angle horn antenna with a working distance of 5 cm.Subsequently,in further experiments,the optimal parameters were used to irradiate for 20 s and 40 s at a microwave power of 60 kW,respectively.The surface damage extended 38 cm×30 cm and 53 cm×30 cm,respectively,and the damage extended to a depth of about 50 cm.The drilling speed was increased by 56.2%and 66.5%,respectively,compared to the case when microwaves were not used.

Reactor field reconstruction from sparse and movable sensors using Voronoi tessellation-assisted convolutional neural networks

The aging of operational reactors leads to increased mechanical vibrations in the reactor interior.The vibration of the incore sensors near their nominal locations is a new problem for neutronic field reconstruction.Current field-reconstruction methods fail to handle spatially moving sensors.In this study,we propose a Voronoi tessellation technique in combination with convolutional neural networks to handle this challenge.Observations from movable in-core sensors were projected onto the same global field structure using Voronoi tessellation,holding the magnitude and location information of the sensors.General convolutional neural networks were used to learn maps from observations to the global field.The proposed method reconstructed multi-physics fields(including fast flux,thermal flux,and power rate)using observations from a single field(such as thermal flux).Numerical tests based on the IAEA benchmark demonstrated the potential of the proposed method in practical engineering applications,particularly within an amplitude of 5 cm around the nominal locations,which led to average relative errors below 5% and 10% in the L_(2) and L_(∞)norms,respectively.

Electromagnetic fields in ultra-peripheral relativistic heavy-ion collisions

Ultra-peripheral heavy-ion collisions(UPCs)offer unique opportunities to study processes under strong electromagnetic fields.In these collisions,highly charged fast-moving ions carry strong electromagnetic fields that can be effectively treated as photon fluxes.The exchange of photons can induce photonuclear and two-photon interactions and excite ions.This excitation of the ions results in Coulomb dissociation with the emission of photons,neutrons,and other particles.Additionally,the electromagnetic fields generated by the ions can be sufficiently strong to enforce mutual interactions between the two colliding ions.Consequently,the two colliding ions experience an electromagnetic force that pushes them in opposite directions,causing a back-to-back correlation in the emitted neutrons.Using a Monte Carlo simulation,we qualitatively demonstrate that the above electromagnetic effect is large enough to be observed in UPCs,which would provide a clear means to study strong electromagnetic fields and their effects.

Constructing Built-In Electric Fields with Semiconductor Junctions and Schottky Junctions Based on Mo-MXene/Mo-Metal Sulfides for Electromagnetic Response

The exploration of novel multivariate heterostructures has emerged as a pivotal strategy for developing high-performance electromagnetic wave(EMW)absorption materials.However,the loss mechanism in traditional heterostructures is relatively simple,guided by empirical observations,and is not monotonous.In this work,we presented a novel semiconductor-semiconductor-metal heterostructure sys-tem,Mo-MXene/Mo-metal sulfides(metal=Sn,Fe,Mn,Co,Ni,Zn,and Cu),including semiconductor junctions and Mott-Schottky junctions.By skillfully combining these distinct functional components(Mo-MXene,MoS_(2),metal sulfides),we can engineer a multiple heterogeneous interface with superior absorption capabilities,broad effective absorption bandwidths,and ultrathin matching thickness.The successful establishment of semiconductor-semiconductor-metal heterostructures gives rise to a built-in electric field that intensifies electron transfer,as confirmed by density functional theory,which collaborates with multiple dielectric polarization mechanisms to substantially amplify EMW absorption.We detailed a successful synthesis of a series of Mo-MXene/Mo-metal sulfides featuring both semiconductor-semiconductor and semiconductor-metal interfaces.The achievements were most pronounced in Mo-MXene/Mo-Sn sulfide,which achieved remarkable reflection loss values of-70.6 dB at a matching thickness of only 1.885 mm.Radar cross-section calculations indicate that these MXene/Mo-metal sulfides have tremendous potential in practical military stealth technology.This work marks a departure from conventional component design limitations and presents a novel pathway for the creation of advanced MXene-based composites with potent EMW absorption capabilities.

Enhancing the resolution of sparse rock property measurements using machine learning and random field theory

The travel time of rock compressional waves is an essential parameter used for estimating important rock properties,such as porosity,permeability,and lithology.Current methods,like wireline logging tests,provide broad measurements but lack finer resolution.Laboratory-based rock core measurements offer higher resolution but are resource-intensive.Conventionally,wireline logging and rock core measurements have been used independently.This study introduces a novel approach that integrates both data sources.The method leverages the detailed features from limited core data to enhance the resolution of wireline logging data.By combining machine learning with random field theory,the method allows for probabilistic predictions in regions with sparse data sampling.In this framework,12 parameters from wireline tests are used to predict trends in rock core data.The residuals are modeled using random field theory.The outcomes are high-resolution predictions that combine both the predicted trend and the probabilistic realizations of the residual.By utilizing unconditional and conditional random field theories,this method enables unconditional and conditional simulations of the underlying high-resolution rock compressional wave travel time profile and provides uncertainty estimates.This integrated approach optimizes the use of existing core and logging data.Its applicability is confirmed in an oil project in West China.

Flow field, sedimentation, and erosion characteristics around folded linear HDPE sheet sand fence: Numerical simulation study

Wind and sand hazards are serious in the Milan Gobi area of the Xinjiang section of the Korla Railway. In order to ensure the safe operation of railroads, there is a need for wind and sand protection in heavily sandy areas. The wind and sand flow in the region is notably bi-directional. To shield railroads from sand, a unique sand fence made of folded linear high-density polyethylene(HDPE) is used, aligning with the principle that the dominant wind direction is perpendicular to the fence. This study employed field observations and numerical simulations to investigate the effectiveness of these HDPE sand fences in altering flow field distribution and offering protection. It also explored how these fences affect the deposition and erosion of sand particles. Findings revealed a significant reduction in wind speed near the fence corner;the minimum horizontal wind speed on the leeward side of the first sand fence(LSF) decreased dramatically from 3 m/s to 0.64 m/s. The vortex area on the LSF markedly impacted horizontal wind speeds. Within the LSF, sand deposition was a primary occurrence. As wind speeds increased, the deposition zone shrank, whereas the positive erosion zone expanded. Close to the folded corners of the HDPE sand fence, there was a notable shift from the positive erosion zone to a deposition zone. Field tests and numerical simulations confirmed the high windproof efficiency(WE) and sand resistance efficiency(SE) in the HDPE sand fence. Folded linear HDPE sheet sand fence can effectively slow down the incoming flow and reduce the sand content, thus achieving good wind and sand protection. This study provides essential theoretical guidance for the design and improvement of wind and sand protection systems in railroad engineering.

Subsoil tillage enhances wheat productivity,soil organic carbon and available nutrient status in dryland fields

Tillage practices during the fallow period benefit water storage and yield in dryland wheat crops.However,there is currently no clarity on the responses of soil organic carbon(SOC),total nitrogen(TN),and available nutrients to tillage practices within the growing season.This study evaluated the effects of three tillage practices(NT,no tillage;SS,subsoil tillage;DT,deep tillage)over five years on soil physicochemical properties.Soil samples at harvest stage from the fifth year were analyzed to determine the soil aggregate and aggregate-associated C and N fractions.The results indicated that SS and DT improved grain yield,straw biomass and straw carbon return of wheat compared with NT.In contrast to DT and NT,SS favored SOC and TN concentrations and stocks by increasing the soil organic carbon sequestration rate(SOCSR)and soil nitrogen sequestration rate(TNSR)in the 0-40 cm layer.Higher SOC levels under SS and NT were associated with greater aggregate-associated C fractions,while TN was positively associated with soluble organic nitrogen(SON).Compared with DT,the NT and SS treatments improved soil available nutrients in the 0-20 cm layer.These findings suggest that SS is an excellent practice for increasing soil carbon,nitrogen and nutrient availability in dryland wheat fields in North China.

Effects of vacancy and external electric field on the electronic properties of the MoSi_(2)N_(4)/graphene heterostructure

Recently,the newly synthesized septuple-atomic layer two-dimensional(2D)material MoSi_(2)N_(4)(MSN)has attracted attention worldwide.Our work delves into the effect of vacancies and external electric fields on the electronic properties of the MSN/graphene(Gr)heterostructure using first-principles calculation.We find that four types of defective structures,N-in,N-out,Si and Mo vacancy defects of monolayer MSN and MSN/Gr heterostructure are stable in air.Moreover,vacancy defects can effectively modulate the charge transfer at the interface of the MSN/Gr heterostructure as well as the work function of the pristine monolayer MSN and MSN/Gr heterostructure.Finally,the application of an external electric field enables the dynamic switching between n-type and p-type Schottky contacts.Our work may offer the possibility of exceeding the capabilities of conventional Schottky diodes based on MSN/Gr heterostructures.

Semi-analytical investigation of heat transfer in a porous convective radiative moving longitudinal fin exposed to magnetic field in the presence of a shape-dependent trihybrid nanofluid

The thermal examination of a non-integer-ordered mobile fin with a magnetism in the presence of a trihybrid nanofluid(Fe_3O_4-Au-Zn-blood) is carried out. Three types of nanoparticles, each having a different shape, are considered. These shapes include spherical(Fe_3O_4), cylindrical(Au), and platelet(Zn) configurations. The combination approach is utilized to evaluate the physical and thermal characteristics of the trihybrid and hybrid nanofluids, excluding the thermal conductivity and dynamic viscosity. These two properties are inferred by means of the interpolation method based on the volume fraction of nanoparticles. The governing equation is transformed into a dimensionless form, and the Adomian decomposition Sumudu transform method(ADSTM) is adopted to solve the conundrum of a moving fin immersed in a trihybrid nanofluid. The obtained results agree well with those numerical simulation results, indicating that this research is reliable. The influence of diverse factors on the thermal overview for varying noninteger values of γ is analyzed and presented in graphical representations. Furthermore, the fluctuations in the heat transfer concerning the pertinent parameters are studied. The results show that the heat flux in the presence of the combination of spherical, cylindrical, and platelet nanoparticles is higher than that in the presence of the combination of only spherical and cylindrical nanoparticles. The temperature at the fin tip increases by 0.705 759% when the value of the Peclet number increases by 400%, while decreases by 11.825 13% when the value of the Hartman number increases by 400%.

Discovery and inspiration of large-and medium-sized glutenite-rich oil and gas fields in the eastern South China Sea:An example from Paleogene Enping Formation in Huizhou 26 subsag,Pearl River Mouth Basin

Based on the practice of oil and gas exploration in the Huizhou Sag of the Pearl River Mouth Basin,the geochemical indexes of source rocks were measured,the reservoir development morphology was restored,the rocks and minerals were characterized microscopically,the measured trap sealing indexes were compared,the biomarker compounds of crude oil were extracted,the genesis of condensate gas was identified,and the reservoir-forming conditions were examined.On this basis,the Paleogene Enping Formation in the Huizhou 26 subsag was systematically analyzed for the potential of oil and gas resources,the development characteristics of large-scale high-quality conglomerate reservoirs,the trapping effectiveness of faults,the hydrocarbon migration and accumulation model,and the formation conditions and exploration targets of large-and medium-sized glutenite-rich oil and gas fields.The research results were obtained in four aspects.First,the Paleogene Wenchang Formation in the Huizhou 26 subsag develops extensive and thick high-quality source rocks of semi-deep to deep lacustrine subfacies,which have typical hydrocarbon expulsion characteristics of"great oil generation in the early stage and huge gas expulsion in the late stage",providing a sufficient material basis for hydrocarbon accumulation in the Enping Formation.Second,under the joint control of the steep slope zone and transition zone of the fault within the sag,the large-scale near-source glutenite reservoirs are highly heterogeneous,with the development scale dominated hierarchically by three factors(favorable facies zone,particle component,and microfracture).The(subaqueous)distributary channels near the fault system,with equal grains,a low mud content(<5%),and a high content of feldspar composition,are conducive to the development of sweet spot reservoirs.Third,the strike-slip pressurization trap covered by stable lake flooding mudstone is a necessary condition for oil and gas preservation,and the NE and nearly EW faults obliquely to the principal stress have the best control on traps.Fourth,the spatiotemporal configuration of high-quality source rocks,fault transport/sealing,and glutenite reservoirs controls the degree of hydrocarbon enrichment.From top to bottom,three hydrocarbon accumulation units,i.e.low-fill zone,transition zone,and high-fill zone,are recognized.The main area of the channel in the nearly pressurized source-connecting fault zone is favorable for large-scale hydrocarbon enrichment.The research results suggest a new direction for the exploration of large-scale glutenite-rich reservoirs in the Enping Formation of the Pearl River Mouth Basin,and present a major breakthrough in oil and gas exploration.

A new electric field mill array with each of the mill’s rotor controlled precisely by a GPS module:Equipment and initial results

We have newly designed an electrostatic sensor,called an electric field mill(EFM),to simplify the estimation of the charge position and charge amount transferred by lightning discharges.It is necessary for this remote estimation of the transferred charge to measure electric field changes caused by charge loss at the time of a lightning strike at multiple locations.For multiple-station measurement of electric field changes,not only speed but also phase for exposure and shielding of the sensing plates inside each EFM of the array should be synchronized to maintain the sensitivities of the deployed instruments.Currently,there is no such EFM with specified speed and phase control performance of the rotary part.Thus,we developed a new EFM in which the rotary mechanism was controlled consistently to within 3%error by a GPS module.Five EFMs had been distributed in the Hokuriku area of Japan during the winter season of 2022-2023 for a test observation.Here we describe the design and a simple calibration method for our new EFM array.Data analysis method based on the assumption of a simple monopole charge structure is also summarized.For validation,locations of assumed point charges were compared with three-dimensional lightning mapping data estimated by radio observations in the MF-HF bands.Initial results indicated the validity to estimate transferred charge amounts and positions of winter cloud-to-ground lightning discharges with our new EFM array.

Numerical simulation of melt flow and temperature field during DC casting 2024 aluminium alloy under different casting conditions

Casting speed,casting temperature and secondary cooling water flow rate are the main process parameters affecting the DC casting process.These parameters significantly influence the flow and temperature fields during casting,which are crucial for the quality of the ingot and can determine the success or failure of the casting operation.Numerical simulation,with the advantages of low cost,rapid execution,and visualized results,is an important method to study and optimize the DC casting process.In the present work,a simulation model of DC casting 2024 aluminum alloy was established,and the reliability of the model was verified.Then,the influence of casting parameters on flow field and temperature field was studied in detail by numerical simulation method.Results show that with the increase of casting speed,the melt flow becomes faster,the depths of slurry zone and mushy zone increase,and the variation of slurry zone depth is greater than that of mushy zone.With an increase in casting temperature,the melt flow rate increases,the depth of the slurry zone becomes shallower,and the depth of the mushy zone experiences only minor changes.The simulation results further indicate that the increase of the flow rate of the secondary cooling water slightly reduces the depths of both slurry and mushy zone.

Strong field ionization of molecules on the surface of nanosystems

Besides the diverse investigations on the interactions between intense laser fields and molecular systems,extensive research has been recently dedicated to exploring the response of nanosystems excited by well-tailored femtosecond laser fields.Due to the fact that nanostructures hold peculiar effects when illuminated by laser pulses,the underlying mechanisms and the corresponding potential applications can make significant improvements in both fundamental research and development of novel techniques.In this review,we provide a summarization of the strong field ionization occurring on the surface of nanosystems.The molecules attached to the nanoparticle surface perform as the precursor in the ionization and excitation of the whole nanosystem,the fundamental processes of which are yet to be discovered.We discuss the influence on nanoparticle constituents,geometric shapes and sizes,as well as the specific waveforms of the excitation laser fields.The intriguing characteristics observed in surface ion emission reflect how enhanced near field affects the localized ionizations and nanoplasma expansions,thereby paving the way for further precision controls on the light-and-matter interactions in the extreme spatial temporal levels.

Research progress on semi-continuous casting of magnesium alloys under external field

High-performance magnesium alloys are moving towards a trend of being produced on a large scale and in an integrated manner.The foundational key to their successful production is the high-quality cast ingots.Magnesium alloys produced through the conventional semi-continuous casting process inevitably contain casting defects,which makes it challenging to manufacture high-quality ingots.The integration of external field assisted controlled solidification technology,which combines physical fields such as electromagnetic and ultrasonic fields with traditional semi-continuous casting processes,enables the production of high-quality magnesium alloy ingots characterized by a homogeneous microstructure and absence of cracks.This article mainly summarizes the technical principles of those external field assisted casting process.The focus is on elaborating the refinement mechanism of different types of electromagnetic fields,ultrasonic fields,and combined physical fields during the solidification of magnesium alloys.Finally,the development prospects of producing highquality magnesium alloy ingots through semi-continuous casting under the external field were discussed.

The Effect of External Magnetic Field on Electron Scale Kelvin–Helmholtz Instability

We use particle-in-cell,fully electromagnetic,plasma kinetic simulation to study the effect of external magnetic field on electron scale Kelvin–Helmholtz instability(ESKHI).The results are applicable to collisionless plasmas when,e.g.,solar wind interacts with planetary magnetospheres or a magnetic field is generated in AGN jets.We find that as in the case of magnetohydrodynamic(MHD)KHI,in the kinetic regime,the presence of an external magnetic field reduces the growth rate of the instability.In the MHD case,there is a known threshold magnetic field for KHI stabilization,while for ESKHI this is to be analytically determined.Without a kinetic analytical expression,we use several numerical simulation runs to establish an empirical dependence of ESKHI growth rate,Γ(B_(0))ω_(pe),on the strength of the applied external magnetic field.We find the best fit is hyperbolic,Γ(B_(0))ω_(pe)=Γ_(0)ω_(pe)/(A+BB_(0)),where Γ_(0) is the ESKHI growth rate without an external magnetic field and B_(0)=B_(0)/B_(MHD)is the ratio of external and two-fluid MHD stability threshold magnetic field,derived here.An analytical theory to back up this growth rate dependence on the external magnetic field is needed.The results suggest that in astrophysical settings where a strong magnetic field pre-exists,the generation of an additional magnetic field by the ESKHI is suppressed,which implies that nature provides a“safety valve”—natural protection not to“over-generate”magnetic field by the ESKHI mechanism.Remarkably,we find that our two-fluid MHD threshold magnetic field is the same(up to a factor √γ_(0))as the DC saturation magnetic field,previously predicted by fully kinetic theory.