Weak effects in proton beam asymmetries at polarised RHIC and beyond

第21卷第2期2021年2月过程工程学报T h e Chinese Journal of Process EngineeringVol.21 No.2 Feb. 2021Particle vibration frequencyDO I : 10.12034/j.issn. 1009-606X.220323Lattice Boltzmann simulation of mass transfer process affected by a moving particleRui HE 1, Chongzhi QIAO 1, Limin WANG 2*, Shuangliang ZH AO 1*1. State K e y Laboratory of Chemical Engineering, School of Chemical Engineering, East China University of Science and Technology,Shanghai 200237, China2. State K e y Laboratory of Multiphase Compl e x Systems, Institute of Process Engineering, Chinese A c a d e m y of Sciences,Beijing 100190, ChinaAbstract : In the catalytic reaction system , the internaland external diflfusion have a great impact on the total reaction rate through the influence on the mass transfer process . The internal diffusion in porous channels has been well investigated by statistical mechanics on the influence o f w ettability , roughness , and electric properties of channel walls . By contrast , the influence of external diffusion needs to be further studied such as , how the active motion o f particles impacts the mass transfer .Herein , by using the lattice Boltzmann method coupled with mass transfer process , the influence of the forced rotation or vibration o f the catalyst particle was studied .A circular particle with constant interfacial boundary concentration was considered , and the immersed moving boundary and non-equilibrium extrapolation methods were chosen to treat the liquid-particle interface . The effects o f rotational speed , vibrational amplitude , and frequency on mass transfer were investigated . The simulations indicated that when only considering diffusion , particle rotation inhibited mass transfer . The higher the rotation speed , the worse the mass transfer , while the overall suppression effect was not significant . The particle streamwise vibration enhanced mass transfer significantly . The lock-on frequency was about 1.9, and the enhancement amplitude reached 10%. Increasing the amplitude and Reynolds number strengthened the mass transfer , and the lock-on frequency moved towards the low frequency direction , while the Schmidt number had little effect on the value of the lock-on frequency . The transverse vibration was also compared with the streamwise one and showed greater enhancement o f Sherwood number at a lower frequency . This numerical results not only demonstrated the feasibility of the lattice Boltzmann method for simulating the forced convection mass transfer process but also provided a route for enhancing mass transfer .Key words : lattice Boltzmann method ; forced convection mass transfer ; active motion ; moving particle收稿：2020-10-09，修回：2020-12-08，网络发表：2020-12-24，Rece 丨ved: 2020-10-09, Revised: 2020-12-08, Pub 丨ished online: 2020-12-24基金项目：国家重点研发计划资助项目(编号：2018Y FB1500902);国家自然科学基金资助项目(编号：51776212):中国科学院前沿科学研宂重点计划资助项目(编号：QYZDB-SSW -SYS029);国家数值风洞工程(编号：NNW2020ZT1-A20);多相复杂系统国家重点实验室幵放基金资助项目 (编号：MPCS-2019-D-13)及自主研宄课题资助项目(编号：MPCS-2019-A-11)作者简介：贺窨(1995-),男，上海市人，硕士研宄生，化学工程与技术专业•，通讯联系人，王利民，E-mails: *************.cn:赵双良，E-mail:***************.cn.引用格式：贺眘，乔崇智，王利民，等.运动颗粒对传质过程影响的格子Boltzmann 模拟.过程工程学报，2021，21(2):丨25-133.He R, Qiao C Z, Wang L M, et al. Lattice Boltzmann simulation o f mass transfer process affected by a moving particle (in Chinese). Chin. J. Process Eng., 2021, 21(2): 125-133, DOI: 10.12034/j.issn. 1009-606X.220323.Bs J 3J C /5U21S S C 3S126过程工程学报第21卷运动颗粒对传质过程影响的格子Boltzmann模拟贺睿、乔崇智、王利民2，赵双良1I.华东理工大学化工学院，化学工程联合国家重点实验室，上海2002372.中国科学院过程工程研究所多相复杂系统国家重点实验室，北京100190摘要：颗粒的主动运动对传质过程有重要影响。

Shock Waves(2008)17:409–419DOI10.1007/s00193-008-0124-3ORIGINAL ARTICLENumerical investigation of ethyleneflame bubble instability induced by shock wavesGang Dong·Baochun Fan·Jingfang YeReceived:3August2006/Revised:28November2007/Accepted:26February2008/Published online:19March2008©Springer-Verlag2008Abstract In this paper,the ethylene/oxygen/nitrogen premixedflame instabilities induced by incident and reflec-ted shock wave were investigated numerically.The effects of grid resolutions and chemical mechanisms on theflame bubble deformation process are evaluated.In the computatio-nal frame,the2D multi-component Navier–Stokes equations with second-orderflux-difference splitting scheme were used;the stiff chemical source term was integrated using an implicit ordinary differential equations(ODEs)solver.The two ethylene/oxygen/nitrogen chemical mechanisms,namely 3-step reduced mechanism and35-step elementary skeletal mechanism,were used to examine the reliability of chemis-try.On the other hand,the different grid sizes, x× y= 0.25×0.5mm and x× y=0.15×0.2mm,were imple-mented to examine the accuracy of the grid resolution.The computational results were qualitatively validated with expe-rimental results of Thomas et al.(Combust Theory Model 5:573–594,2001).Two chemical mechanisms and two grid resolutions used in present study can qualitatively reproduce the ethylene sphericalflame instability process generated by an incident shock wave of Mach number1.7.For the case of interaction between theflame and reflected shock waves, the35-steps mechanism qualitatively predicts the physical process and is somewhat independent on the grid resolutions, while the3-steps mechanism fails to reproduce the instability Communicated by J.F.L.Haas.G.Dong(B)·B.Fan·J.YeState Key Laboratory of Transient Physics,Nanjing University of Science and Technology,Nanjing,Jiangsu210094,People’s Republic of Chinae-mail:dgvehicle@G.DongState Key Laboratory of Explosion Science and Technology,Beijing Institute of Technology,Beijing100081,China of ethyleneflame for the two selected grid resolutions.It is concluded that the detailed chemical mechanism,which includes the chain elementary reactions of fuel combustion, describes theflame instability induced by shock wave,in spite of the fact that theflame thickness(reaction zone)is represented by1–2grids only.Keywords Ethyleneflame·Shock waves·Chemical mechanism·Grid resolutionPACS82.40.Fp·47.40.Nm·47.70.Pq1IntroductionThe interactions between shock wave and curving contact discontinuity(e.g.,cylindrical or spherical gas with different density)can lead to the Richtmyer–Meshkov instability and further enhance the mixing process of gases with the different densities.The phenomenon occurs frequently in many prac-tice processes such as Scramjet[1,2].For example,theflame instability induced by shock wave can lead to the enhance-ment of the fuel/oxidizer mixing and the increase offlame burning rate.Many studies have been focused on the issues. For the inert shock–bubble interaction case,many experi-mental(e.g.,[3,4])and numerical(e.g.,[5–8])studies have been presented within a wide range of shock wave Mach number.In these studies,the fundamental mechanisms asso-ciated with the interface instability,the vortices structure and the mixing were widely investigated.The shock–bubble interaction has been proposed as a benchmark problem for testing the numerical scheme and grid resolution in CFD [9].On the other hand,for the reactive shock–flame inter-action case,Markstein’s classical experiments[10]showed the interactions offlames with a weak shock wave and its410G.Dong et al. reflected wave for butane/air mixture.Theflame instabi-lities were clearly observed.Recently,Thomas et al.[11]performed a series of experiments which showed the signi-ficantflame acceleration induced by stronger shock wavein C2H4/O2/N2mixture.They also showed that detonationcan emerge near the reaction zone for higher incident shockwave intensity.Numerical investigations on the interactionof shock wave withflame bubble have also been reportedwidely.Picone et al.[12],firstly,reported the interaction ofhot bubble with shock wave.However,the contact disconti-nuity in their model is inert.Ton et al.[13]studied the effectof chemical reaction during the interaction between the shockwave andflame.Khokhlov et al.[14]numerically studied asingle interaction of an incident shock wave with a sinusoi-dally perturbedflame.They developed a2D reactive Navier–Stokes equations solver based on the second-order Godunovtype scheme and the adaptive mesh refinement(AMR)tech-nique.Their results revealed that theflame instability and theenhancement of burned/unburned material mixing are due tothe Richtmyer–Meshkov(RM)instability.In their followingpapers[15–17],reflected shock wave effects were furtherconsidered using the same solver.The multiple shock–flameinteractions,through RM instability,result in the highly dis-tortedflame and further lead to the deflagration-to-detonation(DDT)at the specified conditions.Khokhlov et al.’s numeri-cal investigations represent a state of the art computation ontheflame instability perturbed by shock wave.However,as aone-step lumped reaction mechanism based on the Arrheniusform was used in their model,the effect of elementary reac-tion mechanisms for hydrocarbon fuel on the shock–flameinteraction has not been taken into account.In the present paper,a shock–flame interaction processis presented numerically considering the elementary chemi-cal reactions for ethylene fuel.The effects of the differentchemical reaction mechanisms and the grid resolutions onthe shock–flame interaction are evaluated in the numericalsimulations.The experiment of the ethyleneflame bubbleinstability perturbed by shock wave by Thomas et al.[11]has been used to validate and examine the numerical results.2Numerical methods2.1Governing equationsIn the numerical model,it is assumed that the thermally per-fect ideal gas law is used,thus,the2D axisymmetric reactiveNavier–Stokes equations for multi-component system are asfollows∂U ∂t +∂(F−F D)∂x+∂(G−G D)∂y+W=S(1)where,U denotes the solutions of the Eq.(1);F and G denote the convectionfluxes in x and y directions,respectively;F D and G D denote the transportfluxes in x and y directions, respectively;W denotes the axisymmetric correction term;S denotes the chemical source term.These terms can be expres-sed asU=⎛⎜⎜⎜⎜⎜⎜⎜⎝ρ1...ρKρuρvE⎞⎟⎟⎟⎟⎟⎟⎟⎠,F=⎛⎜⎜⎜⎜⎜⎜⎜⎝ρ1u...ρK uρuu+pρv u+pu(p+E)⎞⎟⎟⎟⎟⎟⎟⎟⎠,G=⎛⎜⎜⎜⎜⎜⎜⎜⎝ρ1v...ρK vρu v+pρvv+pv(p+E)⎞⎟⎟⎟⎟⎟⎟⎟⎠,W=vy⎛⎜⎜⎜⎜⎜⎜⎜⎝ρ1...ρKρuρvp+E⎞⎟⎟⎟⎟⎟⎟⎟⎠,F D=⎛⎜⎜⎜⎜⎜⎜⎜⎝ρD1∂(Y1)/∂x...ρD K∂(Y K)/∂xτxxτxyQ x+uτxx+vτxy⎞⎟⎟⎟⎟⎟⎟⎟⎠,G D=⎛⎜⎜⎜⎜⎜⎜⎜⎝ρD1∂(Y1)/∂y...ρD K∂(Y K)/∂yτyxτyyQ y+uτyx+vτyy⎞⎟⎟⎟⎟⎟⎟⎟⎠,S=⎛⎜⎜⎜⎜⎜⎜⎜⎝˙ω1...˙ωK⎞⎟⎟⎟⎟⎟⎟⎟⎠(2) whereρis the density of the mixture,ρ=Kk=1ρk,ρk=ρY k,Y k is the mass fraction for the species k;u and v are theflow velocities in x and y directions,respectively;p is the pressure;E is the total energy per unit volume,E=ρKk=1Y k e k+ρu2+v2/2;e k is the internal energy of the species k.All of thermodynamic properties in Eqs.(2) are deduced from the thermochemical polynomial descri-bed by Gordon and McBride[18].For the transport proper-ties in Eqs.(2),τxx,τyy andτxy are the normal stress and shear stress involved the molecular viscosity coefficient,µ, of the mixture,respectively;Q x= ∂T∂x+ρKk=1h k D k∂Y k∂x, Q y= ∂T∂y+ρKk=1h k D k∂Y k∂y, is the thermal conductivity of the mixture,h k is the enthalpy of the species k,T is the temperature of the mixture;D k is the diffusion coefficients of the species k.All of the transport properties are obtained from the gas-phase transport library of Kee et al.[19].As a chemical kinetic parameter,˙ωk is the net chemical produc-tion rate for species k in the elemental reactions which are interpreted and processed by the CHEMKIN-II package[20].Numerical investigation of ethyleneflame bubble instability induced by shock waves4112.2Numerical approachesA time splitting technique is used to solve the Eq.(1).Thesolutions of U at the n+1-th time step can be expressed asfollowsU n+1=L F L G L F D L G D L S L W U n(3)where,the terms L F and L G denote the operators of convec-tion computations in x and y directions,respectively;theterms L FD and L GDdenote the operators of transport com-putations in x and y directions,respectively;the term L S and L W denote the operators of chemical computation and axisymmetric correction,respectively.To capture the shock and contact discontinuity accura-tely,a second-order wave propagation algorithm based on theflux-difference splitting scheme and the Roe’s approxi-mate Riemann solver for the hyperbolic system of conserva-tion law,proposed by Leveque[21],is improved to meet the convection process(L F and L G in Eq.3)for multi-component system.In addition,a Superbee limiter with the total variation diminishing(TVD)is included to prevent the occurrence of the oscillations of the solutions at thefluid interfaces produced by shock wave and low-densityflame bubble during the shock–flame interaction simulations pre-sented in the next section.Transport process(L FD and L GDin Eq.3)is approximatedin terms of the second-order centered difference scheme.Axi-symmetric correction(L W in Eq.3)is solved using second-order Runge–Kutta methods.The solutions due to chemical reaction source term(L S in Eq.3)at one time step, t,can be expressed as followsU n+1k=U n k+˙ωk t.(4) Due to the different chemical characteristic time scales for the species in the reactiveflow,chemical stiffness arises.Hence, the LSODE solver[22]based on the implicit Gear algorithm is used to integrate the Eq.(4).For the computations of Eqs.(2)at the one time step,atten-tion should be paid to the solution of temperature.During the convection and axisymmetric correction processes,the solution of temperature is obtained using Newton iteration technique,while during the chemical reaction process the solution of temperature is solved coupled with the solutions of species concentrations,that is,the stiff ODE equations involved in temperature and species concentrations are inte-grated.3Chemical kinetic mechanismsIn this study,the two different chemical kinetic mechanisms are used to examine the effect of chemistry on the ethylene flame bubble instability induced by incident and its reflected shock waves.For the ethyleneflame,the large detailed kine-tic mechanism(e.g.,[23–26])can dramatically increase the computational cost for the multi-dimensional reactingflow simulations.As a result,some simplified ethylene mecha-nisms are proposed.For example,Varatharajan and Williams [27]and Varatharajan et al.[28]developed a two-step reduced mechanism used to simulate ethylene ignition and detona-tion properties,according to the steady-state and partial-equilibrium approximations.Baurle et al.[29]developed a three-step mechanism and a ten-step mechanism for ethylene combustion for hypersonicflows in a scramjet combustor.In the present study,we used two different ethylene mecha-nisms.One is the three-step short mechanism proposed by Baurel et al.[29].This mechanism includes three elemen-tary reactions with6species,the reactants,C2H4and O2, are transformed into the major products,CO2and H2O,and minor products,CO and H2,through three selected elemen-tary reaction steps.Another is the skeletal mechanism,which proposed by Li et al.[30]and has successfully applied in prediction of ethylene detonation wave structure[31].This mechanism includes36irreversible elementary reactions and describes the chain reaction process such as C2H4consump-tion,O–H radical interactions,peroxides formations and con-sumptions,and other intermediates consumptions.Here we use a reversible reaction,H+C2H4(+M)=C2H5(+M),to replace the two irreversible reactions(R23and R30)of the original Li’s mechanism[30].Thus,the used mechanism, named35-step mechanism,includes34irreversible and1 reversible elementary reactions.Both mechanisms and their parameters are shown in Tables1and2,respectively.The validation of the chemical mechanisms used in present study wasfirstly performed by1D premixed laminarflame calculations.The calculated C2H4/air laminarflame speeds at the atmospheric pressure by the three-step mechanism and the35-step mechanism were compared with the expe-rimental data[33],as shown in Fig.1.It is shown that the premixedflame speeds by the35-step mechanism at the dif-ferent equivalence ratios show a reasonable agreement with the experimental data.While the three-step mechanism very much underpredicts the premixedflame speeds.Further,in order to determine the grid size for describing theflame thickness(reaction zone)in the2D computations for inter-action offlame bubble with shock waves,we also calcula-ted the1D laminar premixed ethyleneflame structure at the Table1Three-step short kinetic mechanism[29]Chemical reactions A(cm3mol−1s−1)b E a(kJ mol−1) R1C2H4+O2=2CO+2H22.10×10140.0149.729R22CO+O2=2CO23.48×10112.084.233R32H2+O2=2H2O3.00×1020−1.00.000412G.Dong et al.Table2Thirty-five-step skeletal kinetic mechanism[30] a,c,d The third body coefficient:CO=1.9,CO2=3.8,H2=2.5,H2O=12.0b The third body coefficient: CO=1.9,CO2=3.8,H2=2.5,H2O=16.3e The third body coefficient: CO=2.5,CO2=2.5,H2=1.9,H2O=12.0f Lindemann fall-off reaction: A0=6.37×1027,b0=−2.8,Ea0=−0.2;the third body coefficient:H2=2.0,CO=2.0,CO2=3.0,H2O=5.0.Data taken from Miller and Bowman[32]Chemical reactions A(cm3mol−1s−1)b E a(kJ mol−1) R1H+O2→OH+O3.52×1016−0.771.4R2OH+O→H+O21.15×1014−0.3−0.7R3OH+H2→H2O+H1.17×1091.315.2R4H2O+H→OH+H26.72×1091.384.5R5O+H2O→2OH7.60×1003.853.4R62OH→O+H2O2.45×10−14.0−19.0R7a H+O2+M→HO2+M6.76×1019−1.40.0R8HO2+H→2OH1.70×10140.03.7R9HO2+H→H2+O24.28×10130.05.9R10HO2+OH→H2O+O22.89×10130.0−2.1R112HO2→H2O2+O23.02×10120.05.8R12b H2O2+M→2OH+M1.20×10170.0190.0R13c H+OH+M→H2O+M2.20×1022−2.00.0R14d H2O+M→H+OH+M2.18×1023−1.9498.4R15CO+OH→CO2+H4.40×1061.5−3.1R16CO2+H→CO+OH4.97×1081.589.6R17C2H4+O2→C2H3+HO24.22×10130.0241.0R18C2H4+OH→C2H3+H2O2.70×1052.312.4R19C2H4+O→CH3+HCO2.25×1062.10.0R20C2H4+O→CH2HCO+H1.21×1062.10.0R21C2H4+HO2→C2H3+H2O22.23×10120.071.9R22C2H4+H→C2H3+H22.25×1072.155.9R23C2H3+H→C2H2+H23.00×10130.00.0R24C2H3+O2→CH2O+HCO1.70×1029−5.327.2R25C2H3+O2→CH2HCO+O7.00×1014−0.622.0R26CH3+O2→CH2O+OH3.30×10110.037.4R27CH3+O→CH2O+H8.43×10130.00.0R28C2H5+O2→C2H4+HO22.00×10120.020.9R29CH2HCO→CH2CO+H1.05×1037−7.2186.0R30CH2CO+H→CH3+CO1.11×1072.08.4R31CH2O+OH→HCO+H2O3.90×10100.91.7R32e HCO+M→CO+H+M1.86×1017−1.071.0R33HCO+O2→CO+HO23.00×10120.00.0R34C2H2+OH→CH2CO+H1.90×1071.74.2R35f H+C2H4(+M)=C2H5(+M)2.21×10130.08.6specified mixture(C2H4+3O2+4N2),initial temperature (550K)and pressure(13,160Pa)which are same as those in the shock–flame interaction experiment[11].As a baseline,a detailed chemical mechanism,the GRI mechanism30.0[26],was implemented to examine the three-step and35-step mechanisms in theflame structure calculations.As seen from Fig.2,the35-step mechanism shows the good agreements with GRI mechanism.The laminarflame thickness,determi-ned by the distance between the Y=0.95Y C2H4,0and Y=0.05Y C2H4,0(Y C2H4,0is the initial mass fraction of C2H4)intheflame[14],is0.787and0.783mm for the GRI mechanism and the35-step mechanism,respectively.Figure2a shows the vertical shadow bar which represents the ethyleneflame thi-ckness for the35-step mechanism.The three-step mechanism shows the widerflame thickness(4.232mm)and predicts the higher temperature and H2concentrations than those by the 35-step mechanism and GRI mechanism.In Fig.2d,the com-parison of heat release rate between the three-step mechanism and other two mechanisms also shows the difference.For the 35-step and GRI-Mech3.0mechanisms,a higher peak within the narrow region can be seen compared with the results of the three-step mechanism.the three-step and other two mechanisms in Fig.2are due to the simplicity of the three-step chemical kinetic mecha-nism.It is believed that the lack of chain branching reactions (R1in Table2)and the reactions of ethylene with highly length230mm in the test section of the shock tube.The initial flame center was located in the center of the window section, 135mm from the end wall.Figure3a gives the part of window section.In the present study,we use a computational domainFig.2One-dimensional laminarflame structure computed by the different chemical kinetic mechanisms for C2H4+3O2+4N2,T0=500K,p0=13,160Pa414G.Dong et al.Fig.3a initial experimental Schlieren image and b Computational domainwith height38mm and length180mm,which describes a2D axisymmetric region,as shown in Fig.3b.The length ofthe computational domain consists of135mm downstreamand45mm upstream offlame center.The half length of win-dow section is115mm,which is somewhat longer than thedownstream length offlame center as shown in Fig.3a.Thisis because thefinal10mm of window section was obscuredby aflangefitting in the experiment[11].The top and rightboundary is no-slip rigid adiabatic wall boundary condition.The left boundary is the inflow boundary conditions whichtheflow and thermodynamic properties before the arrival ofthe reflected shock wave arefixed to be theflow conditionbehind the incident shock wave.The bottom boundary is theaxis of symmetry.We choose thefirst Schlieren images sequence in theirseries of experiments(see[11,Fig.1])for validating thepresent simulations.In this experiment,an incident shockwave with Mach number1.7was produced by the high-pressure driver section of a shock tube.An electric discharge,which was used to ignite theflame bubble,was triggered bya pressure gauge coupled to a level-sensitive detector and adelay unit.When the pressure gauge detected the incidentshock wave,the delay was chosen so that aflame bubblewith desired diameter could be formed before the shockwave arrived at the ignition plane.Before the ignition,thetest section of the shock tube was evacuated and thenfilledto the C2H4+3O2+4N2mixture with the initial pressure of13,160Pa.Initially,the incident shock wave was locatedon the left of the ethyleneflame bubble(Fig.3)and sub-sequently moved to the right and through theflame bubble.When the shock wave reached the end wall and reboundedfrom it,a reflected shock wave formed and interacted withtheflame bubble again.The multiple shock–flame interac-tions can lead to the instability of theflame surface dueto Richtmyer–Meshkov effect.In the computations,the ini-tial time is same as the experimental time shown as Fig.3aand is set to0µs,the C2H4+3O2+4N2mixturefills the Table3Mixture compositionand thermodynamics parameterswithin the initialflame bubblea C p and C v are the specific heatcapacity at constant pressureand constant volume,respectively,for the mixturewithin the initialflame bubbleMixture mass fractionC2H40O20.113CO20.137H2O0.122CO0.150H20.004N20.474Density(kg m−3)0.0148Temperature(K)2,860a C p/C v 1.242Table4Computational runsRun Grid size Mechanism1 x× y=0.15×0.2mm35-step2 x× y=0.25×0.5mm35-step3 x× y=0.15×0.2mm3-step4 x× y=0.25×0.5mm3-stepwhole computational domain except for the initial bubble made of the combustion products.The temperature and pres-sure before the incident shock wave are T0=298K and p0=13,160Pa,respectively,as those in experiment[11]. The mixture composition and thermodynamic parameters within the initialflame bubble correspond to the adiaba-tic burning at constant pressure,as shown in Table3.The velocity of thefluid before the incident shock wave is zero. The mixture thermodynamic properties behind the shock wave can be calculated in terms of the Rankine–Hugoniot relationship with a given incident shock wave Mach num-ber.Four computational runs were performed to study the effects of chemical kinetic mechanism and grid size on the ethyleneflame instability,as shown in Table4.Beside two selected mechanisms(three-step and35-step mechanisms), two different grid resolutions, x× y=0.25×0.5mm and x× y=0.15×0.2mm,are used.For the coarse grid size andfine grid size,theflame thickness(reaction zone) can be represented by1–2grid width and3–4grid width, respectively,based on the premixedflame structure calcu-lations whichflame thickness is about0.787mm,as shown in Fig.2.The time-splitting scheme(also called Godunov-splitting scheme)comes from the computationalfluid dyna-mic(CFD)code by Leveque[35]and its temporal accuracy is proven to be sufficient[36].For all of the computatio-nal runs,the Courant–Friedrichs–Lewy(CFL)number is set to0.7.With the second-order spatial discretization and the reasonable temporal marching,the effect of numerical per-turbations on the bubble distortions produced by the initialNumerical investigation of ethylene flame bubble instability induced by shock waves415Fig.4Comparisons between the experimental Schlieren images [11]and computational Schlieren images for the interaction between the incident shock wave and flame bubble.The frame time is a 50µs,b 100µs,c 150µs and d 200µs.The Runs 1–4correspond to the com-putational images,as shown in Table 4.Incident shock Mach number is 1.7;mixture is C 2H 4+3O 2+4N 2flame interface cannot be obviously observed for all of com-putational runs with CFL =0.7.For the convenience of comparison,the numerical results are converted to the computational Schlieren images accor-ding to the formula [37]I =I 0 0.5+8max min cos θ∂ρ+sin θ∂ρ(5)where,I and I 0are the computational and initial light inten-sity,respectively;the θis the angle of the knife edge (fromthe horizontal);the ρmax and ρmin are the maximum and minimum density in the flow field.Figure 4gives the experi-mental and computational Schlieren images for case of inci-dent shock wave interaction with the flame bubble.In Fig.4,the experimental images are the 2D optical projection of 3D flame bubble,while the computational images are the 2D computational cutaway section of flame bubble.In addition,it should note that the Eq.5is less representative of actual Schlieren image in the present axisymmetric simulations than those in 2D cylinder.Although some differences between the experiments and computations exist due to the above men-tioned reasons,a qualitative similarity between the experi-mental observations and computational Schlieren images is observed.In the Fig.4a,the incident shock wave is halfway crossing the flame bubble,and the upstream interface of the flame bubble deforms.As time goes on,the flame bubble acquires a kidney shape,as shown in Fig.4b.At this time,the arc transmitted shock wave and foot structure due to the Mach reflection of the incident shock wave are also clearly shown in the both experimental and computational images.In the Fig.4c,a jet due to the Richtmyer–Meshkov instability occurs and breaks up the deformed flame bubble.Figure 4d416G.Dong et al.Fig.5Space–time diagrams of a35-step mechanism and b3-step mechanism for the shock–flame interaction.Incident shock Mach num-ber is1.7;mixture is C2H4+3O2+4N2.Grid resolution is x× y= 0.25×0.5mm.Lines are the computational results,symbols are theexperimental resultsshows the growth of the jet and the formation of the vortex structures due to the impingement of the jet on the downs-tream of theflame bubble at the later time.The comparisons between the experiments and compu-tations in Fig.4illustrate that all of the numerical simula-tions for selected chemical mechanisms and grid resolutions in the present study are capable of reproducing the experi-mental observations on the ethyleneflame bubble instability process perturbed by incident shock wave.Figure5gives the space–time diagram of tracing lines of shock front and left and right interfaces offlame for both mechanisms with x× y=0.25×0.5mm.One can see that even the coarseT/TAT/A56789101112130.050.10.1535-step,coarse g rids3-step,coarse g rids35-step,fine g rids3-step,fine g ridsFig.6Area ratio distributions of temperature forflame bubble instabi-lity induced by incident shock wave,the time corresponds to the Fig.4dgrid resolution is used,the interaction offlame with incident shock wave(below the290µs)shows the good agreement with the experimental results.It should be noted that the axi-symmetric boundary of the computational tube is only the approximation of the experimental shock tube with rectan-gular square cross section(76mm×38mm).However,the agreements between the experiments and computations in Fig.5imply that the axisymmetric assumption in the present study is acceptable.Further,in order to examine the effects of grid resolution and chemistry,we give the distributions of the2Dflame bubble area ratio of the different computational temperatures,as shown in Fig.6.In thisfigure,A T denotes the2Dflame bubble area of the temperature T,A denotes the total2Dflame bubble area which is defined by region of temperature between T/T0=5and13.The computational results show that the area ratio peak appears within tempera-ture range T/T0=10.5±0.5for all of four computational runs.The distributions imply that the major part offlame area concentrates in the narrow high-temperature range.The fur-ther observation shows that for both chemical mechanisms, computations using coarse grids give a more high tempera-ture area than those byfine grids.On the other hand,the three-step mechanism predicts the higher temperature than that by the35-step mechanism when grid resolution isfixed. In spite of the differences shown above,the all grid reso-lutions and chemical mechanisms in the present study can predict the similar interaction process between the incident shock wave andflame bubble.The similarity implies that the hydrodynamic process instead of the chemical process plays an important role in this case.The computations of interaction offlame bubble with the reflected shock wave show the distinguishing images forNumerical investigation of ethylene flame bubble instability induced by shock waves417Fig.7Comparisons between the experimental Schlieren images [11]and computational Schlieren images for the interaction between the reflected shock wave and flame bubble.The frame time is a 400µs,b 450µs and c 500µs.The Runs 1–4correspond to the computatio-nal images,as shown in Table 4.Incident shock Mach number is 1.7;mixture is C 2H 4+3O 2+4N 2different computational runs.Figure 7gives the sequential frames of reflected shock wave from end wall.In this case,the stagnant state of the fluid behind the reflected shock wave is formed so that the chemical reactions play an impor-tant role in the flame instability.As seen from experimental images of Fig.7,the deformed flame expands and develops towards left.The 35-step mechanism qualitatively predictsthe interaction process for both of grid resolutions (Runs 1and 2).Note that the minor discrepancies of flame shape between the experimental and computational images can be observed,since the computational flame shape based on the axisymmetric assumption is different from the actual one in which the expanded flame has partly touched to the optical window section of the shock tube after the reflected shock wave.Even through the minor discrepancies exist,the Run 1of fine grids shows the wrinkly flame interface and the qua-litative agreement with the experimental Schlieren image,Run 2of coarse grids also qualitatively describes the shape of deformed flame although it misses the subtle structure of flame interface.On the other hand,computational results by the three-step mechanism (Runs 3and 4)for both coarse and fine grids give the wrong images which seem that flame develops as the inert pocket without chemical activity.As can been seen from Fig.1and 2d,the three-step mechanism gives the lower flame speed and the lower heat release rate and thus slows the flame expansion process in the interaction process of Fig.7.In addition,Fig.5also shows the tracing lines of left and right interfaces of developing flame for both mecha-nisms after the shock wave reflects (beyond the 290µs).Note that there are no experimental data of right interface of flame owing to the optical obstruction by a flange fitting.However,it is believed that the right interface of the flame stays at the end wall of the test section after the shock wave reflection,as shown by the computational results.For 35-step mecha-nism as shown in Fig.5a,the computational tracing lines of reflected shock front and left interface of flame reasonably agree with the experiments.The computational distance bet-ween the left and right interfaces of flame increases when the time goes on,this also indicates that the flame expands after the reflected shock wave.For the three-step mechanism as shown in Fig.5b,flame expansion has not been occurred owing to the lower flame speed as illustrated by Fig.1.Also,the three-step mechanism underpredicts the reflected shock velocity and flame speed compared with the experiments.Figure 8shows the 2D flame area ratio distributions along with the flame temperature after the reflected shock wave.The results further illustrate that the different chemical mech-anisms show the remarkably difference in predicting the flame temperature.The 35-step mechanism for both coarse and fine grid resolutions gives the similar area ratio distribu-tion which the high temperature area (wide area ratio peak)concentrates in the temperature range of T /T 0=8−10.Generally,the computational results by 35-step mechanism are independent of the grid resolution.Whereas the three-step mechanism gives the different computational results for the different grid resolutions,which also implies that the three-step mechanism is sensitive to the grid resolutions.Figure 9gives the area ratio distributions of mass fractions of CO 2for both 35-step and three-step mechanism in the flame inter-acted by the reflected shock.For the 35-step mechanism,。

第19卷 第3期太赫兹科学与电子信息学报Vo1.19，No.3 2021年6月 Journal of Terahertz Science and Electronic Information Technology Jun.，2021 文章编号：2095-4980(2021)03-0380-06低磁场S波段相对论返波振荡器模拟与实验严余军1,2，吴洋2，周自刚*，李正红2(1.西南科技大学理学院，四川绵阳 621010；2.中国工程物理研究院高功率微波技术重点实验室，四川绵阳 621999)摘要：为实现高功率微波(HPM)系统的小型化，设计一个S波段较低磁场相对论返波管(RBWO)振荡器。

针对低磁场特点，分析慢波结构、引导磁场、束压、束流等对输出微波的影响，通过模拟软件(PIC)优化结构。

以此设计引导磁场为0.24 T，电子束束压为725 kV，束流为6 kA，频率为3.53 GHz，输出微波功率为1.22 GW，束波转换效率为27%的低磁场S波段相对论返波管。

仿真实验结果表明：在强流电子束加速器平台上外加磁场为0.24T时，得到平均功率1GW、频率3.58 GHz、脉宽90 ns的微波输出，与理论值一致。

进行了重频为1Hz，20s的稳定性实验，该实验结果为实现相对论返波管的永磁包装奠定了良好的基础。

关键词：相对论返波管；S波段；高功率微波；低磁场中图分类号：TN125 文献标志码：A doi：10.11805/TKYDA2020441Simulation and experiment of S-band relativistic backwardwave oscillator with low magnetic fieldYAN Yujun1,2，WU Yang2，ZHOU Zigang*，LI Zhenghong2(1.College of Science, Southwest University of Science and Technology, Mianyang Sichuan 621010, China; 2.National Key Laboratory ofScience and Technology on HPM Technology, China Academy of Engineering Physics, Mianyang Sichuan 621999, China)Abstract：An S-band Relativistic Backward Wave Oscillator(RBWO) with lower magnetic field is designed in order to achieve the miniaturization of High-Power Microwave(HPM) systems. According to thecharacteristics of low magnetic field, the effects of slow wave structure, guided magnetic field, beampressure, beam current, etc. on the output microwave are analyzed. The structure is optimized by usingparticle simulation software. On this basis, a low magnetic field S-band relativistic backward wave tube isdesigned, which has a guided magnetic field of 0.24 T, an electron beam voltage of 725 kV, a beam currentof 6 kA, a frequency of 3.53 GHz, an output microwave power of 1.22 GW and a beam conversion efficiencyof 27%. The preliminary experiment is performed on the accelerator platform with high current electronbeam when the external magnetic field is 0.24 T. The microwave is output with average power of 1 GW,3.58 GHz frequency and 90 ns pulse width. And a stability test at 1Hz repetition frequency in 20s isperformed. The experimental results have laid a good foundation for realizing the relativistic backwardwave tube of the permanent magnet packaging.Keywords：relativistic backward wave oscillator；S-band；High Power Microwave；low guiding magnetic field相对论返波管振荡器[1–2](RBWO)是最具潜力的高功率微波器件，其具有结构简单[3]、适合重复频率、高功率和高效率等优点被广泛研究，其要求的磁场也超过1 T。

Soil-Structure InteractionECIV 724A Fall 2004Earthquake AnalysisStructures supported by rigid foundations Earthquakes=>Specified motion of base Rigid Base AnalysisTall Buildings Acceptable•Light & Flexible•Firm Foundations •Methods focus on modeling of structure •Displacements wrt fixed base•Finite Element Methods Nuclear Power Plants Wrong Assumption •Massive & Stiff•Soft Soils•Interaction with supporting soils becomes importantMachine FoundationParameters•Local Soil Conditions•Peak Acceleration•Frequency Content ofMotion•Proximity to Fault•Travel Path etcInertial Interaction Inertial forces in structure are transmitted to flexible soil Kinematic Interaction Stiffer foundation cannot conform to the distortions of soilTOTAL=INERTIAL + KINEMATICSeismic Excitation0.00E+002.50E-055.00E-057.50E-051.00E-041.25E-041.50E-040.250.50.751 1.251.51.752ω/ωνA m p l i t u d e i n f t .SSI - Proposed BE-FE SSI - Spring Dashpot ModelProposed BE-FE, Stiff SoilFixed Base AnalysisPosin(ωt)Half Space2bH-1.0E-05-5.0E-060.0E+005.0E-061.0E-051.5E-052.0E-052.5E-05255075100125150175200225250Time x 1.08x10-4 (sec)H o r i z o n t a l A m p l i t u d eU1 SSI - RelativeU1 Fixed Base U2 SSI - Relative U2 Fixed BaseP(t)Half Spacem mCross Interaction Effects1. Moment is applied2. Waves Propagate…3. …Reach Receiver…4. …and life goes on…SSI EffectsAlter the Natural Frequency of the StructureAdd DampingThrough the Soil Interaction Effects Traveling Wave EffectsObjective:Given the earthquake ground motions that would occur on the surface of the ground in the absence of the structure (control or design motions), find the dynamic response of the structure.MethodsCompleteIdealizedDirect MultiStepComplete Interaction AnalysisHigh Degree of Complexity •Account for the variation of soil properties with depth.•Consider the material nonlinear behavior of the soil •Consider the 3-D nature of the problem•Consider the nature of the wave propagation which produced the ground motion•Consider possible interaction with adjacent structures.IdealizationHorizontal Layers Simplified Wave Mechanisms etcPreliminary description of free field motion before any structure has been builtThe definition of the motion itselfthe control motion in terms of response spectra, acceleration records etcThe location of the control motionfree surface, soil-rock interfaceThe generation mechanism at the control point vertically or obliquely incident SH or SV waves, Rayleigh waves, etc.Idealized AnalysisIdealized Interaction AnalysisTools: FEM, BEM, FDE, Analytical solutionsDirect Methods Evaluation of Dynamic Response in a Single Step MultiStep Methods Evaluation of Dynamic Response in Several Steps SUPERPOSITION•Two-StepKinematic+Inertia Interaction•Three-StepRigid FoundationsLumped Parameter Models•SubstructureDivision to SubsystemsEquilibrium & CompatibilityTrue Nonlinear SolutionsFinite Element Method (FEM)()()()()t t t t f Ku u C uM =++&&&Governing Equation•Modal Analysis •Direct Integration •Fourier Analysis -Complex ResponseSolution TechniquesFEM Solution TechniquesSelection Criteria Cost and Feasibility Paramount Consideration AccuracyDifferences-Handling of Damping-Ability to Handle High FrequencyComponents of MotionFEM -Modal AnalysisDamping is neglected during early stagesActual displacements are dampedDamping is considered in arbitrary mannerStructural Dynamics: First few modes need to be evaluated (<20)SSI: Acceleration response spectra over a large frequency range and large number of modes need to be considered (>150)Not recommended for Direct SSI -Stiff Massive Structure Soft SoilOK for SubstructureFEM -Direct IntegrationTime Marching SchemesNewmark’s Methods, WilsonϑMethods, Bathe and WilsonCubic Inertia MethodSmall Time Step for AccuracyStability and ConvergenceChoice of Damping MatrixFrequency Dependent Damping Ratio -filters out high frequency componentsProportional DampingGood Choice if True Dynamic Nonlinear Analysis is feasibleFEM-Complex ResponseFourier Transformation -Transfer FunctionsTransfer Functions Independent of External ExcitationControl of AccuracyEfficientOnly Linear or Pseudo non-linear analysisFEM -Geometric ModelingFEM Modeling⎪⎪⎪⎩⎪⎪⎪⎨⎧≤ Matrix Mass Mixed 51 Matrix Mass Consistent 81 Matrix Mass Lumped 81max s s s h λλλMax Element Size Governed by Highest frequency which must be transmitted correctly within theelementFEM Modeling of Infinite SpaceFEM Modeling of Infinite SpaceModeling Introduces Artificial Boundaries that Reflect WavesFEM Modeling of Infinite Soil„Absorbing Boundaries„ „ „Viscous Boundary Variable Depth Method Damping proportional to Wave Velocities„Radiating Boundaries (Hyperelements)„ „ „Satisfy Boundary Conditions at Infinity Eigenvalue Analysis Frequency Domain AnalysisSSI – FEM MethodsFEMAdvantages • Non-Linear Analysis • Well Established Shortcomings • Finite Domains • Volume DiscretizationsBoundary Element MethodsGoverning Equation„„ „ „Small Displacement Field Homogeneous Isotropic Elastic(c2 1&& j − c u i ,ij + c u j ,ii + f j = u2 2 2 2)Boundary Element MethodGOVERNING EQUATION Dynamic Reciprocal Theorem BOUNDARY INTEGRAL EQUATIONDIRECT Transform Domain TIME DOMAINIndirectDirac-δStep ImpulseB-SPLINESystem of Algebraic Equations Time Marching SchemeBoundary Element MethodBOUNDARY INTEGRAL EQUAT ION B-SPLINE FUNDAMENTAL SOLUT IONSSPAT IAL DISCRETIZAT ION TEMPORAL DISCRET IZATIONBOUNDARY INTEGRAL EQUAT ION IN A DISCRET E FORMT IME M ARCHING SCHEME & B-SPLINE IMPULSE RESPONSERESPONSE TO ARBIT RARY EXCITATIONu = ∑B fN n =1N +1n N −n + 2=Ff + HNNBEM – MethodsBEMAdvantages • Infinite Media • Surface Discretization Shortcomings • Non-symmetric matrices • Not Efficient for NonlinearSSI Methods Combined BEM-FEMeliminate disadvantages of each method and retain advantagesApproach • FEM Approach • BEM Approach • Staggered SolutionsGoverning Equations&& (t ) + C u & (t ) + Mu Ku (t ) = f (t )(c2 12 &&j )ui ,ij + c22u j ,ii + f j = u − c2FEM Method Time Marching SchemeGoverning Equation&&(t ) + Cu & (t ) + Ku (t ) = f (t ) MuDiscrete Form in TimeDu = fNNFEM-BEM Coupling Staggered SolutionsFEMDuN FEM=fN FEMBEMuN BEM= FfN BEM+HNCan be Solved in a Staggered Approach...FEM-BEM Coupling Staggered SolutionsAt Every Time Step...Equilibrium of Forces at Interfaceint f BEMint f FEMExternal ExcitationBEMSolverFEMSolverint BEMExternal Excitationuuint FEMCompatibility of Displacements at InterfaceFEM-BEM Coupling Advantages„ „ „ „ „Independent Solutions for BEM and FEM Independent Time Step Selection Smaller Systems of Equations BEM System of Reduced Size In the Absence of Incidence Displacement Field in Soil, BEM does not require Solution.Lumped Parameter Models for SSIP(t)mP (t)mHalf SpaceStick ModelSpring-Dashpot ModelLumped Parameter Foundation ModelsReissner (1936) Analytic Solutions to Vertical Vibration of Circular Footing Due to Harmonic Excitation Assumptions: Elastic ½-space Material G,v,ρ Uniform Vertical Pressure Formed Basis of Almost All Analytical StudiesLumped Parameter Foundation ModelsQuinlan and Sung Assumed Different Pressure Distributions Richart & Whitman Effects of Poisson’ Bycroft (1956) Displacement Functions Hsieh K and C in terms of Soil and Foundation ParametersLumped Parameter Foundation ModelsLysmer Analog Constant Lumped Parameters Richart Hall & Wood(1970) Gazetas (1983) Wolf (1988)Lumped Parameter Foundation ModelsRepresentative Lumped Parameter Values - SquareLumped Parameter Foundation ModelsRepresentative Lumped Parameter Values CircularMode Vertical (z) Sliding (x) Rocking (ψ) Torsional (θ)K 4Gro (1 −ν ) 8Gro (2 −ν ) 8Gro3 3(1 −ν ) 6Gro3 3C 3.4 2 ro ρG 1 −ν 4.6 2 ro ρG 2 −ν 0.8ro4 ρG (1 −ν )(1 − Bψ ) 4 BθρG (1 + 2Bθ )B 1 −ν m 4 ρro3 2 −ν m 8 ρro3 3(1 −ν ) Iψ 8 ρro5 Iθ ρro5D 0.425 Bz 0.288 Bx 0.15 (1 + Bψ ) Bψ 0.5 (1 + 2Bθ )Stehmeyer and Rizos (2003)Properties k, and c are known to be frequency (ω) dependentThe Real SystemEquivalent SDOF Systemnn m c M K ωξω2==3.003.253.503.754.00yB (t )0.00E+002.50E-055.00E-057.50E-051.00E-041.25E-041.50E-040.250.50.751 1.251.51.752ω/ωνA m p l i t u d e i n f t .SSI - Proposed BE-FE SSI - Spring Dashpot ModelProposed BE-FE, Stiff SoilFixed Base AnalysisPosin(ωt)Half Space2bH-1.0E-05-5.0E-060.0E+005.0E-061.0E-051.5E-052.0E-052.5E-05255075100125150175200225250Time x 1.08x10-4 (sec)H o r i z o n t a l A m p l i t u d eU1 SSI - RelativeU1 Fixed Base U2 SSI - Relative U2 Fixed BaseP(t)Half Spacem mBased on the Simplified Lumped Parameter Models it can be shown thatθk k k k TT hh 21~++=P(t)mLonger Period of Foundation-Structure SystemSSI Effects –Cross InteractionSource FoundationReceiver FoundationSSI Effects –Cross Interaction0.0E+005.0E-111.0E-101.5E-102.0E-102.5E-100.511.522.533.54Dimensionless Frequency a oH o r i z o n t a l A m p l i t u d e Δ1Source M=10Receiver M=10Source M=5Receiver M=5Source M=1Receiver M=1Receiver FoundationSource FoundationSSI Effects –Cross Interaction0.0E+005.0E-111.0E-101.5E-102.0E-102.5E-100.250.50.7511.251.51.7522.252.52.753Dimensionless Frequency a oH o r i z o n t a l A m p l i t u d ed/a=0.25Source Foundationd/a=1.00d/a=2.00d/a=3.00d/a=0.25Receiver Foundationd/a=1.00d/a=2.00d/a=3.00Receiver FoundationSource FoundationAfter Betti et al.After Betti et al.。

a r X i v :a s t r o -p h /0504557v 2 25 J u l 2005D RAFT VERSION F EBRUARY 2,2008Preprint typeset using L A T E X style emulateapj v.6/22/04IMPACT OF DARK MATTER SUBSTRUCTURE ON THE MATTER AND WEAK LENSING POWER SPECTRAB RADLEY H AGAN 1,C HUNG -P EI M A 2,A NDREY V.K RAVTSOV 3Draft version February 2,2008ABSTRACTWe explore the effect of substructure in dark matter halos on the power spectrum and bispectrum of matter fluctuations and weak lensing shear.By experimenting with substructure in a cosmological N =5123simu-lation,we find that when a larger fraction of the host halo mass is in subhalos,the resulting power spectrum has less power at 1 k 100h Mpc −1and more power at k 100h Mpc −1.We explain this effect using an analytic halo model including subhalos,which shows that the 1 k 100h Mpc −1regime depends sensitively on the radial distribution of subhalo centers while the interior structure of subhalos is important at k 100h Mpc −1.The corresponding effect due to substructures on the weak lensing power spectrum is up to ∼11%at angular scale l 104.Predicting the nonlinear power spectrum to a few percent accuracy for future surveys would therefore require large cosmological simulations that also have exquisite numerical resolution to model accurately the survivals of dark matter subhalos in the tidal fields of their hosts.Subject headings:cosmology:theory —dark matter —large-scale structure of the universe1.INTRODUCTIONOne phenomenon to emerge from N -body simulations of increasingly higher resolution is the existence of substructure (or subhalos)in dark matter halos (e.g.,Tormen et al.1998;Klypin et al.1999b;Moore et al.1999;Ghigna et al.2000).These small subhalos,relics of hierarchical structure forma-tion,have accreted onto larger host halos and survived tidal forces.Depending on their mass,density structure,orbit,and accretion time,the subhalos with high central densities can avoid complete tidal destruction although many lose a large fraction of their initial mass.These small and dense dark matter substructures,however,are prone to numerical arti-facts and can be disrupted due to insufficient force and mass resolution.Disentangling these numerical effects from the actual subhalo dynamics is an essential step towards under-standing the composition and formation of structure.Quan-tifying the effects due to dark matter substructure is also im-portant for interpreting weak lensing surveys,which are sen-sitive to the clustering statistics of the overall density field.The level of precision for which surveys such as SNAP are striving (Massey et al.2004)suggests that theoretical predic-tions for the weak lensing convergence power spectrum need to be accurate to within a few percent over a wide of range of scales (e.g.Huterer &Takada 2005).At this level,subhalos may contribute significantly to the nonlinear power spectrum because they typically constitute about 10%of the host mass.In the sections to follow,we examine the effects of sub-structure on the matter and weak lensing power spectra with two methods.In §2we use the result of a high resolution N -body simulation and quantify the changes in the power spec-tra when we smooth out increasing amounts of substructures.Our other approach,detailed in §3,is to incorporate substruc-ture into the analytic halo model.The results are dependent on the parameters used in the model,but they provide useful physical insight into the results from N -body simulations.We summarize and discuss the results in §4.1Department of Physics,University of California,Berkeley,CA 947202Department of Astronomy,University of California,Berkeley,CA 947203Dept.of Astronomy and Astrophysics,Enrico Fermi Institute,Kavli Institute for Cosmological Physics,The University of Chicago,Chicago,IL 606372.SUBSTRUCTURE IN SIMULATIONSWe use the outputs of a cosmological dark-matter-only simulation that contains a significant amount of substruc-ture.This simulation is a concordance,flat ΛCDM model:Ωm =1−ΩΛ=0.3,h =0.7and σ8=0.9.The box size is 120h −1Mpc,the number of particles is 5123,and the particle mass is 1.07×109h −1M ⊙.The simulation uses the Adaptive Refinement Tree N -body code (ART;Kravtsov et al.1997;Kravtsov 1999)to achieve high force resolution in dense re-gions.In this particular run the volume is initially resolved with a 10243grid,and the smallest grid cell found at the end of the simulation is 1.8h −1kpc.The actual resolution is about twice this value (Kravtsov et al.1997).More details about the simulation can be found in Tasitsiomi et al.(2004).To quantify the effects of subhalos on the matter and weak lensing power spectra,we first identify the simulation parti-cles that comprise subhalos within each halo.This is achieved using a version of the Bound Density Maxima algorithm (Klypin et al.1999a),which identifies all local density peaks and therefore finds both halos and subhalos.It identifies the particles that make up each of the peaks and removes those not bound to the corresponding halo.As a controlled exper-iment,we then smooth out the subhalos within the virial ra-dius of each host halo by redistributing these subhalo parti-cles back in the smooth component of the host halo according to a spherically-symmetric NFW profile (Navarro,Frenk,&White 1996).For the concentration parameter c of the profile,we do not use the fitting formulae (e.g.,Bullock et al.2001;Dolag et al.2004)but instead fit each host halo individually to take into account the significant halo-to-halo scatter in c .We therefore smooth over the subhalos and increase the normal-ization but not the shape of the spherically averaged profile of the smooth component to accommodate the mass from the subhalo component.This smoothing procedure also serves as a simple model for the effects of resolution on the abundance of subhalos in sim-ulations,in which the lack of sufficient resolution will cause an incoming small halo to be disrupted quickly and lose most of its particles over its short-lived orbit.We quantify this ef-fect by experimenting with different cut-offs on the subhalo mass:subhalos with masses below the cut-off are removed2F IG . 1.—Effects of dark matter substructure on the matter fluctuationpower spectrum (top)and the equilateral bispectrum (bottom)of a N =5123cosmological simulation.Plotted is the ratio of the original spectrum to that with a subset of the substructures smoothed out.The curves (from top down)correspond to increasing subhalo mass cut-offs,below which the mass in the subhalos is redistributed smoothly back into the host halo.The bottom panel is plotted to a lower k because B (k )becomes too noisy.The effects due to substructures are up to ∼12%in ∆2and 24%in B .and have their particles spread over the host halo;subhalos with masses above the cut-off are left alone.Increasing mass cut-offs should roughly mimic increasingly lower resolution simulations because only higher mass subhalos will stay in-tact in the halo environment.We then calculate the matter fluctuation power spectrum P (k ),the Fourier transform of the 2-point correlation function,and the matter bispectrum B (k 1,k 2,k 3),the Fourier transform of the 3-point correlation function.In order to compute P and B at large k without using an enormous amount of mem-ory,we subdivide the simulation cube into smaller cubes and stack these on top of each other (called "chaining the power"in Smith et al.2003).A typical stacking level used is 8,mean-ing that we subdivide the box into 83cubes and stack these.We use stacked spectra for the high-k regime and unstacked spectra for low-k .Finally,we subtract shot noise (∝1/N )from the outputted spectra to eliminate discreteness effects.Fig.1shows the effects of substructure on the dimension-less power spectrum ∆2(k )≡k 3P (k )/(2π2)and the equilat-eral bispectrum B (k 1)(k 1=k 2=k 3).Plotted is the ratio of the spectrum from the raw ART output divided by the spec-trum from the altered data.The altered data have no subha-los with masses below the labeled mass cutoff.The mass in the removed subhalos has been redistributed smoothly into thehost halo as described above.The deviation from the original spectrum becomes larger as the cutoff is increased because more subhalos have been smoothed out.For a given cutoff,the figure shows that a simulation with dark matter substruc-tures (such as the raw ART output)has more power at k >100h Mpc −1and less power at 1 k 100h Mpc −1than a simu-lation with smoother halos.We believe these opposite behav-iors reflect the two competing factors present in our numeri-cal experiments:removal of mass within subhalos,which af-fects scales comparable to or below subhalo radii (and hence k 100h Mpc −1),and addition of this mass back into the smooth component of the halo,which affects the larger scales of 1 k 100h Mpc −1.The ratio approaches unity for k 1h Mpc −1simply because the mass distribution on scales above individual host halos is unaltered.We will examine these ef-fects further in the context of the halo model in §3.For a given curve in Fig.1,we have also calculated the contributions from subhalos in host halos of varying masses to quantify the relative importance of cluster versus galactic host halos.For the 1012.5h −1M ⊙curve,e.g.,we find that smooth-ing over the subhalos in host halos above 1014and 1013M ⊙account for 5%and 10%in the total 12%dip seen in Fig.1,respectively.For the 1011.5h −1M ⊙cutoff,the numbers are 2%and 5%of the total 6%dip.The halos found in N -body simulations are generally triax-ial.When we redistribute the subhalo particles,however,we assume for simplicity a spherical distribution.This assump-tion makes the altered halos slightly rounder.One can esti-mate how this effect changes the power spectrum by using the halo model without substructure.Smith &Watts (2005)in-corporated a distribution of halo shapes found by Jing &Suto (2002)from cosmological simulations into the halo model (ig-noring the substructure contribution).Compared with the case where all the halos are spherical,they observed a peak decre-ment in the power spectrum of about 4%for k ≈1Mpc −1.The corresponding effect in our calculations would be much smaller since we redistribute only the subset of particles that belong to subhalos into the rounder shape (e.g.,about 10%of all particles in the case where the cutoff was 1012.5h −1M ⊙).Thus,by extending the results of Smith &Watts,we expect the spurious rounder halos in our study to account for less than 0.5%of the total 12%drop.Fig.2shows the weak lensing convergence power spectrum ∆2κ(l )corresponding to the matter power spectrum ∆2(k )in Fig.1.It is calculated from ∆2(k )using Limber’s approxima-tion and assumption of a flat universe:∆2κ(ℓ)=9πc 4 χmaxχ3d χW 2(χ)3F IG.2.—Effects of substructure on the weak lensing convergence powerspectrum for the same subhalo mass cutoffs as in Fig.1.The sources areassumed to be at redshift1.The gray band is the1-σstatistical error assumingGaussianfields.We take f sky=0.25,γrms=0.2,¯n=100/arcmin2,and a bandof widthℓ/10.surements assuming Gaussian densityfields(Kaiser1998):σ(∆2κ)22π¯n∆2κ ,(2)where f sky is the fraction of the sky surveyed,γrms is the rmsellipticity of galaxies,and¯n is the number density of galaxieson the sky.The error is dominated by the sample varianceon large scales(first term in eq.[2])and the"shape noise"onsmall scales.Our assumption of Gaussianity is not applicablefor the angular scales shown in the plot because the scalesplotted are near or below the size of individual halos,but theerrors shown should be a useful reference and have been usedin previous studies.A reliable estimate of the error wouldpresumably require a ray tracing calculation which is beyondthe scope of this paper.3.SUBSTRUCTURE IN THE HALO MODELTo gain a deeper understanding of the simulation results inFigs.1and2,we use the semi-analytic halo model to buildup the nonlinear power spectrum from different kinds of pairsof mass elements that may occur in halos(e.g.Ma&Fry2000;Peacock&Smith2000;Seljak2000;Scoccimarro etal2001).The original halo model assumes that all mass re-sides in virialized,spherical halos without substructures.Onecan then build the matter power spectrum from the differentkinds of pairs of particles that contribute to the2-point clus-tering statistics by writing P(k)=P1h(k)+P2h(k),where the1-halo term P1h contains contributions from particle pairs whereboth particles reside in the same halo,and the2-halo term P2his from pairs where the two particles reside in different halos.The1-halo term is a mass-weighted average of single haloprofiles and dominates on the scales of interest(k 1h Mpc−1)in Fig.1because close pairs of particles are more likely to befound in the same halo.The2-halo term is closely related tothe linear power spectrum and is important only at large sepa-ration(i.e.small k)where a pair of particles is more likely tobe found in two distinct halos.Similarly,the bispectrum canbe constructed from the different classes of triplets of particles(see,e.g.,Ma&Fry2000).The original halo model can be readily extended to take intoaccount a clumpy subhalo component in an otherwise smoothhost halo.Sheth&Jain(2003),e.g.,decompose the original1-halo term into P1h=P ss+P sc+P1c+P2c,where"s"denotessmooth and"c"denotes clump.The smooth-smooth term,P ss,arises from pairs of particles that both belong to the smoothcomponent of the same host halo.This term is identical to theoriginal1-halo term except for an overall decrease in ampli-tude by the factor(1−f)2,where f is the fraction of the totalhalo mass that resides in subhalos.The smooth-clump term,P sc,is due to having one particle in a subhalo(clump)and theother in the host halo(smooth).The1-and2-clump terms,P1cand P2c,come from having both particles in the same subhaloand in two different subhalos,respectively.Explicitly,P ss(k)=(1−f)2¯ρ2 dM N(M)MU(k,M)U c(k,M)× dm n(m,M)mu(k,m)(4)P1c(k)=1¯ρ2 dMN(M)U2c(k,M)× dmn(m,M)mu(k,m) 2(6)where U(k,M),u(k,m),and U c(k,M)are the Fourier trans-forms of the host halo radial density profile,the subhalo radialdensity profile,and the radial distribution of subhalo centers,respectively.N(M)dM gives the number density of host ha-los with mass M,and n(m,M)dm gives the number density ofsubhalos of mass m inside a host halo of mass M.A similarexpression can be written down for the2-halo term P2h,whichis also included in our calculations.Fig.3illustrates the contributions from the individual termsin the halo model.We use the NFW profile(truncated atthe virial radius)for the input host halo U(k,M)and subhalou(k,m),and the concentration c(M)=c0(M/1014M⊙)−0.1withc0=11that wefind to approximate the ART host halos andis identical to Dolag et al(2004)except for a15%increasein amplitude.We use c sub=3for the subhalos to take intoaccount tidal stripping but also compare different values inFig.4below.For the distribution of subhalo centers,U c(k),we compare the profile of NFW with that of Gao et al.(2004),whofind the number of subhalos within a host halo’s virial ra-dius r v to beN(<x)1+acxα,x=r/r v(7)where a=0.244,α=2,β=2.75,c=r v/r s,and N tot is the to-tal number of subhalos in the host.Since this distribution atsmall r is shallower(∝r−0.25)than the inner part of the NFWprofile(∝r−1),its Fourier transform U c(k)at high k is abouta factor of10lower than that of the NFW profile.This decre-ment results in a much lower∆sc and∆2c as shown in Fig.3(dashed vs dotted curves).Wefind the subhalo centers in theART simulation to follow approximately the distribution ofGao et al.although there is a large scatter.4F IG . 3.—Comparison of individual subhalo terms in the halo model.The smooth-clump ∆2sc and 2-clump ∆22c terms depend on the distributionof subhalo centers U c within a host halo,having a much lower amplitude at k >1h Mpc −1when U c has the cored isothermal profile of Gao et al.(2004)compared with the cuspy NFW profile.The smooth-smooth ∆2ss and 1-clump ∆21c terms are independent of U c .See text for parameters used in the model.We use the mass function of Sheth &Tormen (1999)for the host halos N (M )and a power law n (m ,M )∝m −1.9that well approximates the subhalo mass function in the ART sim-ulation.The latter is normalized so that the total mass of subhalos in a host halo adds up to f times the host mass M (f =0.14in Fig.3).To compare the halo model with simula-tions,we set the lower limit on the P ss integral to 1010h −1M ⊙,which is the smallest halo present in the simulation (about ten times the simulation particle mass).The lower limit on the outer integrals of P sc ,P 1c ,and P 2c corresponds to the smallest halo that contains substructure,which we set to the small-est halo that we considered for erasing substructure in §2:2×1012h −1M ⊙.Similarly,the lower limit on the inner inte-grals of these terms is set to the smallest subhalo that can be resolved (i.e.1010h −1M ⊙).Fig.4compares the sum of all the terms in thehalo model with the simulation result from Fig.1.As in Fig.1,we il-lustrate the effects due to substructures by dividing out the power spectrum from the original (smooth)halo model,i.e.,∆2smooth =k 3P ss /[(1−f )2(2π2)],where P ss is given before in eq.(4).Fig.4shows that the halo model is able to reproduce qualitatively the simulation results when the subhalo centers in the halo model are assigned the shallower distribution ofGao et al.The feature of ∆2sub /∆2smooth <1at 1 k 100h Mpc −1is mainly caused by the drop in the smooth-clump term relative to the smooth-smooth term at k 1h Mpc −1shown inFig.3.The ratio ∆2sub /∆2smooth becomes >1only at k 100h Mpc −1when the 1-clump term finally takes over.Fitting the halo model to actual simulation results is clearly not exact in part due to the large scatters in the properties of simulated ha-los,e.g.,the concentration (for both hosts and subhalos),the subhalo mass fraction f ,and the maximum subhalo mass in each host halo.The halo model allows us to study the depen-dence of clustering statistics on these parameters (see Fig.4).In addition,a number of effects are neglected in the current halo model,e.g.,tidal effects are likely to reduce the number of subhalos (modeled by U c of Gao et al.here)as well as theirF IG . 4.—Same ratio of ∆2as in Fig.1but comparing simulation(symbols;same 1012.5h −1M ⊙curve in Fig.1)with halo model predictions (plain curves).The two agree qualitatively when the shallower distribu-tion of Gao et al.for subhalo centers U c (k )is used (bottom 3curves)in the halo model (but not for an NFW U c (k );dotted).The detailed model prediction depends on halo parameters:the solid curve uses the same pa-rameters as in Fig.3;the dashed shows how a larger subhalo concentration(c sub =c sub 0(M /1014M ⊙)−0.1;c sub 0=11vs 3)steepens the curve at high k ;the dash-dotted shows how a smaller subhalo mass fraction f (0.1vs.0.14)raises the dip.outer radii (not modeled here)towards host halo centers;a larger amount of stripped subhalo mass may also be deposited to the inner parts of the hosts,resulting in a radius-dependent subhalo mass fraction f within the host.Fig.4also shows that the halo model predicts the oppo-site effect due to substructure (i.e.∆2sub /∆2smooth >1at all k )if the subhalo centers U c (k )are assumed to follow the NFW distribution like the underlying dark matter.The sign of this effect is consistent with the previous subhalo model study of Dolney et al.(2004),which assumed the same NFW profile for the subhalo centers and the hosts and obtained a matter power spectrum that had a higher amplitude for all k when the substructure terms were included.Their results differ slightly from ours because of different integration limits.Subhalos in recent simulations like that of Gao et al.,however,show a much shallower radial distribution in the central regions of the host halos,and inclusion of gas dynamics appears to have little effect on the survivability of subhalos (Nagai &Kravtsov 2005).The shallow distribution is apparently due to tidal disruptions,even though the precise shape of the distri-bution is still a matter of debate (e.g.,Zentner et al.2005).We have also experimented with a third distribution U c (k )that has the NFW form but is less concentrated.We are able tobring ∆2sub /∆2smooth below unity only when the concentration is reduced by a factor of more than 2.5,and only when this reduction factor is increased to ∼100would we get a com-parable dip as the curves for ART simulation and Gao et al.in Fig.4.It is interesting to see if we can mimic the behav-ior of the ART simulation without using subhalos in the halo model.We try replacing the one-halo term,P 1h ,by one that is a simple superposition of a Gao et al.profile and the usual NFW profile.This accounts for the fact that ∼90%of the mass is in a smooth NFW profile and that ∼10%is in sub-halos,which follow a flatter profile.One would not expect the high-k regime to agree as it is dominated by the subha-5los(the1-clump term,specifically).The intermediate range, 1 k 100h Mpc−1,is dominated by the host halo itself,but wefind no similarity in this range either.Subhalos are there-fore needed if the halo model is to recreate the ART results.4.DISCUSSIONThe purpose of this work is to provide a physical under-standing of the effects of substructures on clustering statistics. By experimenting with dark matter substructures in a cosmo-logical simulation with5123particles,we have shown that the power spectra of matterfluctuations and weak lensing shear can change by up to∼12%(and up to∼24%in the bispec-trum)if a significant amount of substructures is not resolved in a simulation.When a larger mass fraction of the host halos is in the form of lumpy subhalos,wefind the effect is to lower the amplitude of the matter and weak lensing power spectra at the observationally relevant ranges of k∼1to100h Mpc−1 and l 105,and to raise the amplitude on smaller scales.A similar drop in power is also seen in our analytic halo-subhalo model when the subhalo centers U c within a host halo are dis-tributed with a shallower radial profile than the underlying dark matter(as expected due to tidal effects).A way to un-derstand the drop involves looking at where the dense regions are.When U c has an NFW form the subhalos basically trace the smooth background.Thus,there is never a decrease in power when the smooth-smooth and smooth-clump terms are added because dense regions are in nearly the same relative positions.When we use a shallower profile for U c,the sub-halos are not as numerous in the denser inner regions of the background halo.This decrease in the overlap between dense clump regions and the dense inner regions causes the drop in power.We have quantified the effects of substructures on clustering statistics by erasing substructures in an N=5123simulation. An important related question is whether N=5123,single-mass resolution simulations such as the one used in our study has sufficient resolution to measure the power spectrum to the few-percent accuracy required by future surveys.Note that at least hundreds of particles and force resolution of∼kilo-parsec are required to ensure subhalo survival against tidal forces,placing stringent requirements on the dynamic range of simulations.Multi-mass resolution simulations designed for subhalo studies,on the other hand,do not give reliable predictions for P(k)on quasi-linear scales due to compro-mised resolution outside highly clustered regions.The fact that the curves in Figs.1and2continue to change at the few-percent level each time the mass threshold is lowered by 0.5dex from1012.5to1010.5h−1M⊙suggests that subhalos of M 1010.5h−1M⊙may still be affecting the power spectra at a comparable level and that N>5123would be required.We alsofind>3%changes in P(k)at k∼10h Mpc−1in the halo model as the minimum subhalo mass in the integration limit of eq.(3)is lowered to107h−1M⊙(although the exact predic-tions are sensitive to the slope of the subhalo mass function, which is assumed to be−1.9here.)Careful convergence stud-ies with higher resolution aided by insight from this study and detailed semi-analytic models for halo substructure will likely be needed to determine N.There are other challenges to predicting accurately the weak lensing signal on single halo scales.The effect of neutrino clustering could cause a rise in weak lensing convergence of ∼1%atℓ∼2000(Abazajian et al.2005).Two recent groups have investigated different aspects of baryon effects.White (2004)found that baryonic contraction and its subsequent im-pact on the dark matter distribution is capable of causing an increase in the weak lensing convergence power of a few per-cent atℓ 3000.Zhan&Knox(2004),on the other hand,use the fact that the hot intracluster medium does not follow the dark matter precisely and predict an opposite effect:a sup-pression of weak lensing power of a few percent atℓ 1000. Unlike the effects of substructure and neutrino clustering,the baryon effects cause departures from the pure dark matter weak lensing signal that only get larger with increasingℓ. We thank M.Boylan-Kolchin,W.Hu,D.Huterer,C.Vale, and P.Schneider for useful discussions.BH is supported by an NSF Graduate Student Fellowship.CPM is supported in part by NSF grant AST0407351and NASA grant NAG5-12173.A VK is supported by NSF grants AST-0206216and 0239759,NASA grant NAG5-13274,and the Kavli Institute for Cosmological Physics at the University of Chicago.REFERENCESAbazajian,K.,Switzer,E.,R.,Dodelson,S.,Heitmann,K.,Habib,S.2005, Phys.Rev.D,71,043507Bartelmann M.&Schneider P.2001,Phys.Rep.,340,291Bullock,J.S.et al.2001,MNRAS,321,559Dolag,K.,Bartelmann,M.,Perrotta,F.,Baccigalupi,C.,Moscardini,L., Meneghetti,M.,Tormen,G.2004,A&A,416,853Dolney,D.,Jain,B.,&Takada,M.2004,MNRAS,352,1019Gao,L.,White,S.D.M.,Jenkins,A.,Stoehr,F.,Springel,V.2004,MNRAS, 355,819Ghigna,S.,Moore,B.,Governato,F.,Lake,G.,Quinn,T.,Stadel,J.2000, ApJ,544,616Huterer,D.,&Takada,M.2005,astro-ph/0412142Jing,Y.P.,Suto,Y.2002,574,538Kaiser,N.1998,ApJ,498,26Klypin,A.,Gottloeber,S.,Kravtsov,A.V.,Khokhlov,M.1999a,ApJ,516, 530Klypin,A.,Kravtsov,A.V.,Valenzuela,O.,&Prada,F.1999b,ApJ,522,82 Kravtsov,A.V.,Klypin,A.A.,&Khokhlov,A.M.1997,ApJS,111,73 Kravtsov,A.V.&Klypin,A.A.1999,ApJ,520,437Ma,C.-P.&Fry,J.2000,ApJ,543,503Massey,R.et al.2004,AJ,127,3089Moore,B.et al.1999,ApJ,524,L19Nagai,D.,Kravtsov,A.V.2005,ApJ,618,557Navarro,J.,Frenk,C.,White,S.D.M.1996,ApJ,462,563Peacock,J.,A.,Smith,R.,E.2000,MNRAS,318,1144Scoccimarro,R.,Sheth,R.,Hui,L.,Jain,B.2001,ApJ,546,20Seljak,U.2000,MNRAS,318,203Sheth,R.&Jain,B.2003,MNRAS,345,529Sheth,R.&Tormen,G.1999,MNRAS,308,119Smith,R.E.et al.2003,MNRAS,341,1311Smith,R.E.,Watts,P.I.R.2005,MNRAS,360,203Tasitsiomi,A.,Kravtsov,A.V.,Wechsler,R.H.,Primack,J.R.2004,ApJ, 614,533Tormen,G.,Diaferio,A.,Syer,D.1998,MNRAS,299,728White,M.2004,Astroparticle Phys.,22,211Zentner,A.et al.2005,ApJ,in press,astro-ph/0411586Zhan,H.&Knox,L.2004,ApJ,616,L75。

第 21 卷 第 7 期2023 年 7 月Vol.21，No.7Jul.，2023太赫兹科学与电子信息学报Journal of Terahertz Science and Electronic Information TechnologyG波段行波管电子枪设计与实验李莹，边兴旺，张琳，宋博文，潘攀，蔡军(中国电子科技集团公司第十二研究所微波电真空器件国家级重点实验室，北京100015)摘要：设计了用于G波段行波管的聚焦极调制皮尔斯电子枪，电子注电压20 kV，电流50.9 mA，注腰半径0.056 mm，射程10.3 mm。

利用热-结构耦合分析和电子注轨迹仿真方法，分析了热形变对电子枪性能造成的显著影响。

为了消除电子枪热形变的影响，设计了装配模具进行补偿，并得到了实验验证。

该电子枪已用于多种G波段行波管，解决了关键部件技术问题。

关键词：G波段行波管；电子枪；热形变中图分类号：TN124 文献标志码：A doi：10.11805/TKYDA2021433Design and experiment research on electron gun of G band traveling wave tubeLI Ying，BIAN Xingwang，ZHANG Lin，SONG Bowen，PAN Pan，CAI Jun (National Key Laboratory of Science and Technology on Vacuum Electronics，The 12th Research Institute of China ElectronicsTechnology Group Corporation，Beijing 100015，China)AbstractAbstract：：A focus electrode modulation Pierce gun for G band traveling wave tube is designed, witha beam voltage of 20 kV, current of 50 mA, waist radius of 0.056 mm, and a waist position of 10.3 mm.The impact of thermal deformation on the performance of the electron gun is analyzed by using thermal-structure coupling analysis and electron beam trajectory simulation method. In order to eliminate theinfluence of thermal deformation, an assembly fixer for compensation is designed and verified byexperiments. The electron gun has been applied in a variety of G band traveling wave tube, and hassolved technical problems of the key component.KeywordsKeywords：：G band traveling wave tube；electron gun；thermal deformation太赫兹(0.1~10 THz)频谱资源丰富，在高分辨力实时成像、抗干扰保密通信以及高速高数据率传输等方面具有重要的应用前景[1-2]。

物探专业术语中英⽂对照lunar tide 太阴潮solar tide 太阳潮turbulence 湍流spectrum of turbulence 湍流谱turbulent diffusion 湍流扩散turbulent dissipation 湍流耗散turbulent exchange 湍流交换turbulent mixing 湍流混合twilight 曙暮光wind shear 风切变yield function 产额函数zonal circulation 纬向环流zonal wind 纬向风airglow ⽓辉MST radar MST雷达，对流层、平流层、中层⼤⽓探测雷达。

aeronomy ⾼空⼤⽓学deviative absorption 偏移吸收non-deviative absorption ⾮偏移吸收after-effect of [magnetic] storm 磁暴后效Chapman layer 查普曼层Appleton anomaly 阿普尔顿异常equatorial anomaly ⾚道异常winter anomaly 冬季异常magneto-ionic theory 磁离⼦理论buoyancy frequency 浮⼒频率D - region Ｄ区E - region Ｅ区F - region Ｆ区F1 layer Ｆ1层F1 ledge Ｆ1缘F2 layer Ｆ2层Chapman production function 查普曼⽣成函数Cowling conductivity 柯林电导率Pedersen conductivity 彼得森电导率Hall conductivity 霍尔电导率direct conductivity 直接电导率cosmic radio noise 宇宙射电噪声riometer 宇宙噪声吸收仪critical frequency 临界频率dissociative recombination 离解性复合dynamo region 发电机区evanescent wave 消散波fade 衰落fadeout, blackout [短波通讯]中断ordinary wave 寻常波extraordinary wave ⾮寻常波Faraday rotation 法拉第旋转field-aligned irregularity 场向不规则结构Harang discontinuity 哈朗间断impedance probe 阻抗探针incoherent scattering radar ⾮相⼲散射雷达ionospheric storm 电离层暴ionosonde 电离层测⾼仪virtual height 虚⾼true height 真⾼digisonde 数字式测⾼仪ionogram 电离图polar cap absorption, PCA 极盖吸收sudden ionospheric disturbance, SID 突发电离层骚扰spread F 扩展 Fsporadic E 散见 E 层top-side sounder 顶视探测仪bottom-side sounder 底视探测仪travelling ionospheric disturbance, TID 电离层⾏扰short wave fadeout, SWF 短波突然衰落sudden frequency deviation, SFD [短波]频率急偏sudden phase anomaly, SPA 突发相位异常characteristic wave 特征波cross-modulation 交叉调制total electron content, TEC 电⼦总含量ambipolar diffusion 双极扩散eclipse effect [⽇]⾷效应skip distance 跳距outer space 外层空间interplanetary space ⾏星际空间interstellar space [恒]星际空间deep space 深空solar-terrestrial space ⽇地空间solar-terrestrial physics ⽇地物理学one-hop propagation ⼀跳传播quasi-transverse propagation 准横传播quasi-longitudinal propagation 准纵传播maximum usable frequency, MUF 最⼤可⽤频率geomagnetism 地磁[学] main field 主磁场inclination, dip angle 磁倾⾓declination 磁偏⾓agonic line 零偏线aclinic line 零倾线magnetic isoclinic line 等磁倾线magnetic chart 磁图isomagnetic chart 等磁图isomagnetic line 等磁强线isoporic line, isopore 等年变线magnetic isoanomalous line 等磁异常线geomagnetic pole 地磁极dip pole 磁倾极magnetic local time 磁地⽅时magnetic dipole time 磁偶极时central dipole 中⼼偶极⼦dipole coordinate 偶极⼦坐标corrected geomagnetic coordinate 修正地磁坐标north magnetic pole 磁北极south magnetic pole 磁南极invariant latitude 不变纬度dip equator 倾⾓⾚道eccentric dipole 偏⼼偶极⼦magnetogram 磁照图magnetically quiet day, q 磁静⽇magnetically disturbed day, d 磁扰⽇secular variation 长期变化solar daily variation, S 太阳⽇变化disturbed daily variation, Sd 扰⽇⽇变化storm-time variation, Dst 暴时变化magnetic disturbance 磁扰magnetic bay 磁湾扰magnetic crochet 磁钩扰magnetic storm 磁暴gradual commencement [magnetic] storm 缓始磁暴sudden commencement [magnetic] storm 急始磁暴sudden commencement 急始initial phase 初相main phase 主相recovery phase 恢复相magnetic substorm 磁亚暴expansive phase 膨胀相equivalent current system 等效电流系internal field 内源场external field 外源场aurora 极光aurora australis 南极光aurora borealis 北极光auroral oval 极光卵形环auroral belt 极光带subauroral zone 亚极光带Alfvēen layer 阿尔⽂层cleft, cusp 极隙pseudo-trapped particle 假捕获粒⼦radiation belt, Van Allen belt 辐射带⼜称“范艾伦带”。