The Vacuum Theta-Angle is Zero in Non-Abelian Gauge Theories

The Principle of Non-Gravitating Vacuum Energy and some of its consequencesE.I.Guendelman∗and A.B.Kaganovich†Physics Department,Ben Gurion University of the Negev,Beer Sheva84105,IsraelAbstractFor Einstein’s General Relativity(GR)or the alternatives suggested up to date,the vacuum energy gravitates.We present a model where a new measureis introduced for integration of the total action in the D-dimensional space-time.This measure is built from D scalarfieldsϕa.As a consequence of sucha choice of the measure,the matter lagrangian L m can be changed by addinga constant while no gravitational effects,like a cosmological term,are induced.Such Non-Gravitating Vacuum Energy(NGVE)theory has an infinite dimen-sional symmetry group which contains volume-preserving diffeomorphisms inthe internal space of scalarfieldsϕa.Other symmetries contained in this sym-metry group,suggest a deep connection of this theory with theories of extended ∗GUENDEL@BGUmail.BGU.AC.IL†ALEXK@BGUmail.BGU.AC.IL1objects.In general the theory is different from GR although for certain choices of L m,which are related to the existence of an additional symmetry,solutions of GR are solutions of the model.This is achieved in four dimensions if L m is due to fundamental bosonic and fermionic strings.Other types of matter where this feature of the theory is realized,are for example:scalars without potential or subjected to nonlinear constraints,massless fermions and point particles.The point particle plays a special role,since it is a good phenomeno-logical description of matter at large distances.de Sitter space is realized in an unconventional way,where the de Sitter metric holds,but such de Sitter space is supported by the existence of a variable scalarfield which in practice destroys the maximal symmetry.The only space-time where maximal symmetry is not broken,in a dynamical sense,is Minkowski space.The theory has non trivial dynamics in1+1dimensions,unlike GR.21IntroductionAs it is known,in the general theory of relativity energy is a source of gravity,whichis described by the metric tensor gµν.This makes an important difference to ideas developed forflat space physics where the origin with respect to which we measure energy does not matter,that is the energy is defined up to an additive constant.For general relativity in contrast,all the energy has a gravitational effect,therefore the origin with respect to which we define the energy is important.In quantum mechanics,there is the so called zero-point energy associated to the zero-pointfluctuations.In the case of quantumfields,such zero-pointfluctuations turn out to have an associated energy density which is infinite.In fact there is a zeropoint vacuum energy-momentum tensor of the form T vacµν=Aηµνinflat space(ηµνis the Minkowski metric),or T vacµν=Agµν+(terms∝R)in curved space.Here A is infinite.Notice that the appearance of an energy-momentum tensor proportional to gµνin Einstein’s equations is equivalent[1]to what Einstein called the‘’cosmological con-stant“or‘’Λ-term“.It was introduced by Einstein[2]in the formRµν−12gµνR−Λgµν=κ2Tµν(1)SuchΛ-term does not violate any known symmetry.Therefore,normally we would not consider excluding it,if we were to apply the arguments usually made in quantum field theory.However,we get into trouble if we note that the natural scale of such a term,obtained on dimensional grounds,is of the order of magnitude of the Planck3density.The problem is more severe once we realize that the zero point vacuumenergy appears as an infinite quantity.Indeed,in order to get agreement with observations,different sources of energy density have to compensate with each other almost exactly to high accuracy,thus creating an acute‘’fine tuning problem“.In order to explain this so called‘’cosmological constant problem“,a variety of ideas have been developed,see for example reviews[3].Among these attempts,pos-sible changes in gravity theory were studied[3],where the result was that the cosmo-logical constant appeared as an integration constant,for example,in‘’nondynamical √−g“models.The reason why such a constant should be picked zero is unclear however.In this paper we will also suggest a modification of gravity theory by imposing the principle that the vacuum energy density,to be identified with the constant part of the lagrangian density,should not contribute to the equation of motion.The realization of this idea in the model considered here,apart from leading to a geometrically interesting new theory,also leads to the possibility of new gravitational effects.2The Model2.1A new measure and generally coordinate invariant action All approaches to the cosmological constant problem have been made under the as-sumption that the invariant measure to be used for integrating the total lagrangian4density in the action is √−gd D x.In the present paper,this particular assumptionwill be modified,and the result will be that,by an appropriate generally coordinate invariant choice of the measure,the theory will not be sensitive to a change in the lagrangian density by the addition of a constant,in contrast to the Einstein-Hilbert action,where such a change generates a cosmological term.Let the measure of integration in a D dimensional space-time be chosen asΦd D x, whereΦis a yet unspecified scalar density of weight1.In order to achieve the result that the vacuum energy does not gravitate,we will start from the demand that the addition of a constant in the lagrangian density does not affect the dynamics of thetheory.This means thatLΦd D x and(L+constant)Φd D x must reproduce thesame equations of motion.This is of course achieved ifΦis a total derivative.The simplest choice for a scalar density of weight1,which is as well a total derivative,may be realized by using D scalarfieldsϕa(x)and then definingΦ≡εa1a2...a D εα1α2...αD(∂α1ϕa1)(∂α2ϕa2)...(∂αDϕaD)(2)Hereεα1α2...αD=1ifα1=0,α2=1...αD=D−1and±1according to whether(α1,α2,...,αD)is an even or an odd permutation of(0,1,...,D−1).Likewise forεa1a2...a D(a i=1,2,...,D)Therefore the total action we will consider isS=(−1κR+L m)Φd D x(3)whereκ=16πG,R is the scalar curvature and we will take L m not to depend on any of the scalarsϕa(x).Notice that if we consider parity or time reversal trans-formations,then S→−S,which does not affect the classical equations of motion.5Quantum mechanically(considering for example the path integral approach),such transformation will transform total amplitudes into their complex conjugates,there-fore leaving probabilities unchanged.Notice thatΦis the jacobian of the mappingϕa=ϕa(xα),a=1,2,...,D.If this mapping is non singular(Φ=0)then(at least locally)there is the inverse mapping xα=xα(ϕa),α=0,1...,D−1.SinceΦd D x=D!dϕ1∧dϕ2∧...∧dϕD we can think Φd D x as integrating in the internal space variablesϕa.Besides,ifΦ=0then there is a coordinate frame where the coordinates are the scalarfields themselves.ThefieldΦis invariant under the volume preserving diffeomorphisms in internal space:ϕ a=ϕ a(ϕb)whereεa1a2...a D ∂ϕ b1∂ϕa1∂ϕ b2∂ϕa2...∂ϕ bD∂ϕaD=εb1b2...b D(4)2.2Equations of motionThe equations of motion obtained by variation of the action(3)with respect to the scalarfieldsϕb areAµb ∂µ(−1κR+L m)=0(5)whereAµb ≡εa1a2...aD−1bεα1α2...αD−1µ(∂α1ϕa1)(∂α2ϕa2)...(∂αD−1ϕaD−1)(6)It follows from(2)that Aµb∂µϕb =D−1δbb Φand taking the determinant of bothsides,we get det(Aµb )=D−DD!ΦD−1.Therefore ifΦ=0,which we will assume in what6follows,the only solution for(5)is−1κR+L m=constant≡M(7)Variation of S g≡−1κRΦd D x with respect to gµνleads to the result[4]δS g=−1κΦ[Rµν+(gµν−∇µ∇ν)]δgµνd D x(8)In order to perform the correct integration by parts we have to make use the scalarfieldχ≡Φ√−g,which is invariant under continuous general coordinate transforma-tions,instead of the scalar densityΦ.Then integrating by parts and ignoring a totalderivative term which has the form∂α(√−gPα),where Pαis a vectorfield,we getδS g δgµν=−1κ√−g[χRµν+gµνχ−χ,µ;ν](9)In a similar way varying the matter part of the action(3)with respect to gµνand making use the scalarfieldχwe can express a result in terms of the standard matterenergy-momentum tensor Tµν≡2√−g∂(√−gL m)∂gµν.Then after some algebraic manipula-tions we get instead of Einstein’s equationsGµν=κ2[Tµν−12gµν(Tαα+(D−2)L m)]+1χD−32gµνχ+χ,µ;ν(10)where Gµν≡Rµν−12Rgµν.By contracting(10)and using(7),we getχ−κD−1[M+12(Tαα+(D−2)L m)]χ=0(11)By using eq.(11)we can now exclude Tαα+(D−2)L m from eq.(10):Gµν=κ2[Tµν+Mgµν]+1χ[χ,µ;ν−gµνχ](12) 7Notice that eqs.(5)and(10)are invariant under the addition to L m a constant piece,since the combination Tµν−12gµν[Tαα+(D−2)L m]is invariant.However byfixing the constant part of the difference L m−M in the solution(7)of eq.(5),we break this invariance.To give a definite physical meaning to the integration constant M, we conventionally take the constant part of L m equal to zero.It is very important to note that the terms depending on the matterfields in eq.(12)as well as in eq.(10)do not containχ-field,in contrast to the usual scalar-tensor theories,like Brans-Dicke theory.As a result of this feature of the NGVE-theory,the gravitational constant does not suffer space-time variations.However,the matter energy-momentum tensor Tµνis not conserved.Actually,taking the covariantdivergence of both sides of eq.(12)and using the identityχα;ν;α=(χ),ν+χαRαν, eqs.(12)and(11),we get the equation of matter non conservationTµν;µ=−2∂L m∂gµνgµα∂αlnχ(13)2.3Volume preserving symmetries and associated conservedquantitiesFrom the volume preserving symmetriesϕ a=ϕ a(ϕb)defined by eq.(4)which for the infinitesimal case impliesϕ a =ϕa+λεaa1...a D∂F a1a2...a D−1(ϕb)∂ϕaD(14)(λ 1),we obtain,through Noether’s theorem the following conserved quantitiesjµV =Aµa(−1κR+L m)εaa1...a D∂F a1a2...a D−1(ϕb)∂ϕaD(15)82.4Symmetry transformations with the total lagrangian den-sity as a parameter and associated conserved quantities Let us consider the following infinitesimal shift of thefieldsϕa by an arbitrary in-finitesimal function of the total lagrangian density L≡−1R+L m,that isϕ a=ϕa+ g a(L), 1(16) In this case the action is transformed according toδS= DAµaL∂µg a(L)d D x=∂µΩµd D x(17)whereΩµ≡DAµa f a(L)and f a(L)being defined from g a(L)through the equationL dg adL =d f adL.To obtain the last expression in the equation(17)it is necessary to notethat∂µAµa≡0.By means of the Noether’s theorem,this symmetry leads to the conserved currentjµL=Aµa(Lg a−f a)≡Aµa LL0g a(L )dL (18)For certain matter models,the symmetry structure is even richer(see discussion of the‘’Einstein symmetry“in the next section).The complete understanding of the group structure and the consequences of these symmetries is not known to us at present,but we will expect to report on this in future publications.93Einstein symmetry and Einstein sector of solu-tions3.1Einstein conditionWe are interested now in studying the question whether there is an Einstein sector of solutions,that is are there solutions that satisfy Einstein’s equations?First of all we see that eqs.(12)coincide with Einstein’s equations with cosmological constantκM only if theχ-field is a constant.From eq.(11)we conclude that this is possible only if an essential restriction on the matter model is imposed:2M+Tαα+(D−2)L m≡2[M+gµν∂L mµν−L m]=0.However we have not found any reasonable matter model where this condition is satisfied for M=0(recall that the constant part of L m is taken to be zero).In the case M=0this condition becomesgµν∂L m∂gµν−L m=0(19)which means that L m is an homogeneous function of gµνof degree one,in any dimen-sion.If condition(19)is satisfied then the equations of motion allow solutions of GR to be solutions of the model,that isχ=constant and Gµν=κTµν.3.2Einstein symmetryIt is interesting to observe that when condition(19)is satisfied,a new symmetry of the action(3)appears.We will call this symmetry‘’Einstein symmetry“(because(19) leads to the existence of an Einstein sector of solutions).Such symmetry consists of10the scalingsgµν→λgµν(20)ϕa→λ−1Dϕa(21) To see that this is indeed a symmetry,note that from definition of scalar curvature it follows that R→λR when the transformation(20)is performed.Since condition (19)means that L m is a homogeneous function of gµνof degree1,we see that under the transformation(20)the matter lagrangian L m→λL m.From this we conclude that(20)-(21)is indeed a symmetry of the action(3)when(19)is satisfied.3.3ExamplesThe situation described in the two previous subsections can be realized for special kinds of bosonic matter models:1.Scalarfields without potentials,includingfields subjected to non linear con-straints,like theσmodel.The general coordinate invariant action for these cases hasthe form S m=L mΦd D x where L m=1σ,µσ,νgµν.2.Matter consisting of fundamental bosonic strings.The condition(19)can be verified by representing the string action in the D-dimensional form where gµνplays the role of a background metric.For example,bosonic strings,according to our formulation,where the measure of integration in a D dimensional space-time is chosen to beΦd D x,will be governed by an action of the form:S m=L stringΦd D x,L string=−TdσdτδD(x−X(σ,τ))√−gdet(gµνXµ,a Xν,b)(22)11whereL string√−gd D x would be the action of a string embedded in a D-dimensionalspace-time in the standard theory;a,b label coordinates in the string world sheet and T is the string tension.Notice that under a scaling(20)(which means that gµν→λ−1gµν),L string→λD−2L string,therefore concluding that L string is a homogeneous function of gµνof degree one,that is eq.(19)is satisfied,if D=4.3.It is possible to formulate the point particle model of matter in a way such that eq.(19)is satisfied.This is because for the free falling point particle a vari-ety of actions are possible(and are equivalent in the context of general relativity).The usual actions are taken to be S=−mF(y)ds,where y=gαβdXαdXβands is determined to be an affine parameter except if F=√y,which is the case ofreparametrization invariance.In our model we must take S m=−mL partΦd4x withL part=−mdsδ4(x−X(s))√−gF(y(X(s)))whereL part√−gd4x would be the action of apoint particle in4dimensions in the usual theory.For the choice F=y,condition(19)is satisfied.Unlike the case of general relativity,different choices of F lead to unequivalent theories.Notice that in the case of point particles(taking F=y),a geodesic equation(andtherefore the equivalence principle)is satisfied in terms of the metric g effαβ≡χgαβevenifχis not constant.It is interesting also that in the4-dimensional case g effαβis invariant under the Einstein symmetry described by eqs.(20)and(21).Furthermore,since for point particles the theory allows an Einstein sector,we seem to have a formulation where at macroscopic distances there will be no difference with the standard GR,but where a substantial difference could appear in micro-physics.The theory could be12useful in suggesting new effects that may be absent in GR and that could constitute non trivial tests of the NGVE-theory and of GR.Deviations from GR may have also interesting cosmological consequences for the early Universe[5]In all the above cases1,2and3,solutions where thefieldχ≡Φ√is constant,−gexist if M=0and then solutions of the eq.(12)coincide with those of the Einstein theory with zero cosmological constant.Theories of fermions(including fermionic string theories)appear also can serve as candidate matter models where there will be an Einstein-Cartan sector of solutions,as will be studied elsewhere.4The Cosmological Constant Problem4.1The de Sitter solution in the context of the NGVE-theory If we allow non constantχ,we expect to obtain effects not present in Einstein gravity and cosmology.For example,as we will see,in the NGVE-theory de Sitter space is realized in an unconventional way,where the de Sitter metric holds,but such de Sitter space is supported by the existence of a variable scalarfieldχwhich in practice destroys the maximal symmetry.Effects of a non constantχcan be studiedfirst in the case where there is no matter(L m=Tµν=0).If we require maximal symmetry of the space-time metric in such a case,thefieldχmust satisfy the conditionχ,µ;ν=cχgµνwhere c is a constant. Geometry allows[6]suchχonly for the value of c=−Rand it is then possible12to have maximally symmetric metric with any value of R=−κM.For example a13de Sitter solution of eqs.(11)and(12)(taking D=4)is ds2=dt2−a2d x2,where a=a0exp(λt),χ=χ0exp(λt)andλ2=κM/12.Let us consider the point particle model(considered at the end of section3) which satisfies the Einstein condition.In this case the physics of the de Sitter space is described by geodesics with respect to the effective metric g eff.Notice that such aαβ=dτ2−τ6d x2,whereτ=τ0exp(λt) metric corresponds to a power law inflation:ds2effwe notice that there are not andλ2=κM/12.By examining the physical metric g effαβthe10Killing vectors of the de Sitter space.We see that although the metric gµνis maximally symmetric,the physical geometry is not maximally symmetric.4.2Particle creation,possible instability of the de Sitterspace and the Parker conditionSome years ago,Parker[7]suggested a possible mechanism,based on particle pro-duction in the early universe,for selecting a zero cosmological constant.The basic assumption Parker made was that of the existence of an underlying theory where the cosmological constant can be dynamically adjusted by a process based on some-thing like the familiar‘’Lenz’s law“,which requires that the equilibrium condition be achieved after the cosmological constant relaxes to a certain value.The idea is based on the fact that for a4-dimensional homogeneous,isotropic cosmological background,there is not real particle creation for massless conformally coupled scalarfields(MCCSF)satisfyingφ+Rφ=0(23)614If there are massless minimally coupled scalarfields(MMCSF)or gravitons,in general particle creation takes place.However,when considering particle creation effect in a given background metric with zero scalar curvature,the MCCSF and MMCSF theories behave in the same way[7].Also for such a background R=0,one expects no graviton production[7].The existence of radiation with Tµµ=0does not affect these conclusions[7].4.3Realization of the Parker cosmological condition in theEinstein sector of the NGVE-theoryIn the context of the NGVE-theory,we have that states with R=0exist among many other possible states,provided the integration constant M is chosen zero and the matter lagrangian on shell equals zero(see eq.(7)).The last condition is satisfied, for example,for the case of massless fermions and for electromagnetic radiation with Tµ=L em=E2−B2=0.Such a state may be realized apparently for the universe (em)µfilled by ultrarelativistic matter.As Parker[7]points out,a de Sitter space,although not satisfying the condition R=0,has a chance however of being stable due to its maximal symmetry.This seems in accordance with the calculations of Candelas and Raine[8].In our case however even this possibility seems to be excluded.Indeed,for the de Sitter space in the NGVE-theory we haveχ=χ(t)=constant which means explicit breaking of maximal symmetry since for a maximally symmetric space a scalarfield must obey[9] the condition∂µχ=0.Therefore we expect that in the NGVE-theory the de Sitter15space suffers from the above mentioned instability towards particle production.Only flat space-time allows the possibility of maximal symmetry since in this caseχmay be constant,which is clear from eq.(11).It is interesting to observe that the Parker condition in the framework of the NGVE-theory,when applied to the above mentioned case of an early universe dom-inated by ultrarelativistic matter(massless fermions and electromagnetic radiation with Tµ=L em=E2−B2=0)is a particular realization of the Einstein (em)µcondition(19).Notice that once the Einstein condition is satisfied,the direct cou-pling of theχ-field with matter disappears(see eq.(11)).When this decoupling does not exist,like for example is apparent from eq.(13),for the small matter perturba-tions around a de Sitter space,we expect a tendency for any homogeneousχstate to loose energy to inhomogeneous degrees of freedom(from the point of view of ther-modynamics a transfer of energy from homogeneous degree of freedom of theχ-field into inhomogeneous degrees of freedom is more preferable than the reverse since the inhomogeneous modes are more numerous).An effective way to describe this would be the introduction of a friction term in the equation of motion forχ.We expect this would lead to the decay of the de Sitter space towards a Friedmann epoch with M=0andχ=constant.The nonequilibrium dynamics explaining the details of how the relaxation of the cosmological constant is achieved,or in our case how the constant M is changed to zero,is a subject for future studies.165DiscussionThere are many directions in which research concerning the NGVE-theory could be expanded.A subject of particular interest consists of the study of the NGVE-theory in1+1dimensions.In this case,the model gives equations that coincide with those of Jackiw and Teitelboim[10]when the constant of integrationκM in the NGVE-theory is identified with the constant scalar curvature which is imposed on the vacuum solutions of that model[10]and where ourfieldχplays the same role,in the equations, as the lagrange multiplierfield in the Jackiw-Teitelboim model[10].Another model that resembles the NGVE-theory studied here is the non dynami-cal √−g theory(NDSQR)(for reviews,see articles of Weinberg and Ng[3]).For theNDSQR-theory,also any de Sitter space is a solution of the theory and the constant curvature of the vacuum solutions also appears as an integration constant.The differ-ences between the NDSQR-theory and the NGVE-theory are however very obvious. To mention just some:(a)The NDSQR-theory does not exist as a non trivial theory in1+1dimensions,while the NGVE-theory does.(b)The4-D de Sitter solutions do not posses the maximal symmetry for the NGVE theory case(due to the fact that the scalarfieldχis not constant)while maximal symmetry is respected in the NDSQR-theory whereflat space and de Sitter space have the same symmetry.(c)In the NGVE-theory,the matter energy-momentum tensor is not covariantly conserved, while in the NDSQR-theory it is.(d)In addition,the NDSQR-theory is for all prac-tical purposes indistinguishable from GR,while the NGVE-theory is really a new physical theory,which could contain an Einstein sector of solutions,but in addition17there is the potential offinding out new gravitational effects.We should also point out that a more thorough study of the infinite dimensional symmetry found here should be made.In particular the restrictions on the possible induced terms in the quantum effective action seem to be strong if the symmetries(14) and(16)remain unbroken after quantum corrections are also taken into account.In particular,symmetry under the transformations(16)seems to prevent the appearance of terms of the form f(χ)Φ(except of f(χ)∝1)in the effective action which although is invariant under volume preserving transformations(14),breaks symmetry(16). The case f(χ)∝1is not forbidden by symmetry(16)and appearance of such a termwould mean inducing a‘’real“cosmological term,i.e.a term of the form √−gΛin theeffective action.However,appearance of such a term seems to be ruled out becauseof having opposite parity properties to that of the action given in(3).Of course,in the absence of a consistently quantized theory,such arguments are only preliminary. Nevertheless it is interesting to note that if all these symmetry arguments are indeed applicable,this would imply that the scalarfieldsϕa can appear in the effective action only in the integration measure,that is they preserve their geometrical role.The physical meaning of the symmetry(16)is puzzling.To get a feeling of the meaning of this symmetry,it is interesting to notice that such transformation becomesnon trivial if L≡−1κR+L m is not a constant,in contrast to what we have studied so far in this paper.For the derivation of eq.(7),which implies L=constant,we have assumed thatΦ=0.AllowingΦ=0in some regions of space-time should be equivalent to allowing for‘’defects“which could be string-like or take the shape18of other extended objects.In such event,the symmetry(16)would become non trivial precisely at the location of such defects,a situation that reminds us of the reparametrization invariance of theories of extended objects.In this context,it becomes then natural to explore the possibility that all the matter could arise as regions of space-time whereΦ=0,i.e.as defects described above.This could be a way to realize an idea of Einstein and Infeld[11]that matter should arise as singular points from a pure gravitational theory.In their words[11]:‘’All attempts to represent matter by an energy-momentum tensor are unsatisfactory and we wish to free our theory from any particular choice of such a tensor.Therefore we shall deal here only with gravitational equations in empty space,and matter will be represented by singularities of the gravitationalfield“.In GR,however,such mechanism could lead only to singularities of the metric,i.e.black holes(if the cosmic censorship hypothesis[12]is correct).Although black holes are interesting objects, they are of course not satisfactory candidates for the description of the matter we see around.Defects that appear in the NGVE-theory are singularities of the measure which are not necessarily singularities of the metric.Furthermore the existence of the symmetry(16)suggests to us a close connection between these singularities and reparametrization invariance of extended objects as mentioned above.Finally,the crucial question concerning the large distance behavior of the model should be analyzed in detail.In particular,the study of general conditions under which the theory contains an Einstein sector of solutions or a set of solutions which deviate very little from those of the Einstein theory must be studied.In this respect,19let us recall that we have already reviewed a number of cases where the Einstein condition and Einstein symmetry hold.In these cases the theory is guaranteed to contain an Einstein sector of solutions.However,it would be interesting to study situations where the answer is not so clear.We have here in mind cases where neither the Einstein condition or the Einstein symmetry are exactly satisfied,but that they could appear only in the long distance behaviour of the theory,without being satisfied by the underlying microscopic theory. This possibility is suggested by the fact that the point particle limit allows a formu-lation consistent with the Einstein symmetry.In the point particle limit however, the underlying microscopic(field theoretic)structure is‘’integrated out“and in this way disappears.This of course suggests that the integration of microscopic degrees of freedom could,under very general circumstances,lead to a macroscopic theory satis-fying the Einstein symmetry.The answer to this last question will of course demand further research.6AcknowledgementsWe would like to thank H.Aratyn,J.Bekenstein,K.Bronnikov,A.Feinstein,J.Friedman, A.Guth,A.Heckler,J.Ib´a˜n ez,C.Kiefer,R.Mann,V.Mostepanenko,L.Parker,D.Pav´o n, J.Perez-Mercader,Y.Peleg and H.Terazawa for interesting conversations.20。

高一英语天文术语单选题30题1. The ______ is the largest planet in our solar system.A. EarthB. MarsC. JupiterD. Venus答案：C。

解析：在太阳系中，木星（Jupiter）是最大的行星。

地球（Earth）、火星（Mars）和金星（Venus）都比木星小，所以A、B、D选项错误。

2. Which of the following is a satellite of the Earth?A. The SunB. The MoonC. MarsD. Jupiter答案：B。

解析：月球 The Moon）是地球的卫星。

太阳 The Sun）是恒星，火星（Mars）和木星（Jupiter）是行星，它们都不是地球的卫星，所以A、C、D选项错误。

3. The ______ is closest to the Sun.A. MercuryB. VenusC. EarthD. Mars答案：A。

解析：水星（Mercury）是离太阳最近的行星。

金星（Venus）、地球 Earth）和火星 Mars）距离太阳都比水星远，所以B、C、D 选项错误。

4. Which planet is known as the "Red Planet"?A. EarthB. MarsC. JupiterD. Saturn答案：B。

解析：火星 Mars）被称为“红色星球”，因为它的表面呈现出红色。

地球（Earth）不是“红色星球”，木星（Jupiter）和土星 Saturn）也不是，所以A、C、D选项错误。

5. A ______ is a huge ball of gas that gives off light and heat.A. planetB. satelliteC. starD. comet答案：C。

解析：恒星（star）是巨大的气态球体，能发出光和热。

Features / BenefitsOverviewThe MPS150 is an easy to use, yet highly-precise manual probe platform for wafers and substrates up to 150 mm. It supports a wide variety of applications and accessories. The modular and flexible design allows to configure and individualize the system to match application requirements. With the System Integration for Measurement Accuracy (SIGMA™) kit, MPS150 can be seamlessly integrated with third-party instrumentation, ensuring the shortest signal bining the MPS150 probe system with our measurement expertise, FormFactor provides pre-configured application-focused probing solutions for a variety of applications, and an integrated measurement solution for accurate S-parameter measurements, which include everything you need to achieve accurate measurement results in the shortest time, with maximum confidence.Note: For physical dimensions and facility requirements, refer to the MPS150 Facility Planning Guide.Mechanical PerformanceChuck StageTravel155 mm x 155 mm (6 in. x 6 in.)Resolution 5 µmPlanarity over 150 mm (6 inch)< 10 µmLoad stroke, Y axis90 mmZ height adjustment range10 mmZ contact / separation / load stroke0-3 mm adjustableTheta travel (standard)360°Theta travel (fine)± 8°Theta resolution7.5 x 10-3 gradientManual Microscope Stage (On Bridge)Travel range50 mm x 50 mm (2 in. x 2 in.) / 150 mm x 100 mm (6 in. x 4 in)Resolution≤ 5 µm (0.2 mils)Scope lift Manual, tilt-back or linear pneumaticProgrammable Microscope Stage*Travel range50 mm x 50 mm (2 in. x 2 in.)Resolution0.25 µm (0.01 mils)Scope lift Programmable 130 mm* Electronics box for manual systems (P/N 157-137) requiredPlaten SystemPlatenPlaten space (typical)Universal platen: space for up to four DPP2xx/DPP3xx/DPP4xx/RPP210 or up to twelve DPP105 positionersUniversal platen with optional probe card adapter: space for up to eight DPP2xx/DPP3xx/DPP4xx/RPP210or up to sixteen DPP105 positionersMMW platen: space for up to four RPP305 or two LAP positionersZ-Height adjustment range Maximum 40 mm (depending on configuration)Minimum platen-to-chuck height16 mm (universal platen)Separation lift200 µmSeparation repeatability< 1 µmVertical rigidity / force 5 µm / 10 N (0.2 mils / 2.2 lb.)Accessory mounting options Universal platen: magnetic, vacuumRF-platen: bolt-down, magneticWafer ChuckStandard Wafer ChuckDiameter150 mmMaterial Stainless steelDUT sizes supported Shards or wafers 25 mm (1 in.) through 150 mm (6 in.)Vacuum ring diameter Universal: 4 mm, 7 mm, 22 mm, 42 mm, 66 mm, 88 mm, 110 mm, 132 mmStandard: 22 mm, 42 mm, 66 mm, 88 mm, 110 mm, 132 mmVacuum ring actuation Universal: all connected in meander, center hole 1.5 mm diameterStandard: mechanically selected, center hole 1.0 mm diameterChuck surface Planar with centric-engraved vacuum groovesSurface planarity≤ ± 3 µmRigidity< 15 µm / 10 N @ edgeRF Wafer ChuckDiameter150 mm with two additional AUX chucksMaterial Stainless steel with HF/OPTO surface (flat with 0.7 mm holes)DUT sizes supported Main: single DUTs down to 3 mm x 5 mm size or wafers 25 mm (1 inch) through 150 mm (6 inch)AUX: up to 18 mm x 26 mm (1 in. x 0.7 inch) eachVacuum hole sections (diameter)22 mm, 42 mm, 66 mm, 88 mm, 110 mm, 132 mm (four holes in center with 2.5 mm x 4.3 mm distance) Vacuum hole actuation Mechanically selectedChuck surface Planar with 0.7 mm diameter holes in centric sectionsSurface planarity≤ ± 3 µmRigidity< 15 µm / 10 N @ edgeTriax Wafer ChuckDiameter150 mm with three additional AUX chucks (two with vacuum fixation)Material Stainless steelDUT sizes supported Main: wafers 50 mm through 150 mmAUX: up to 18 mm x 26 mm (1 inch x 0.7 inch) eachVacuum hole sections (diameter)50 mm, 100 mm, 150 mm (2 inch, 4 inch, 6 inch)Vacuum hole actuation3x vacuum switch unitChuck surface Planar with 0.4 mm diameter holes in centric sectionsSurface planarity≤ ±5 µmNon-Thermal ChucksNote: Results measured with non-thermal chuck at standard probing height (10,000 µm) with chuck in a dry environment. Moisture in the chuck may degrade performance.MPS-CHUCK150-COAXOperation voltage Standard: in accordance with EC 61010, certificates for higher voltages available upon requestIsolation*> 2 GΩCapacitance100 pF* Factory test with multimeter with maximum 2 GΩ range.Non-Thermal Chucks (continued)MPS-CHUCK150-RFOperation voltage Standard: in accordance with EC 61010, certificates for higher voltages available upon request Isolation (Signal-Shield)> 200 GΩCapacitance (Signal-Shield)80 pFMPS-CHUCK150-TRIAX1In Purged Shield Enclosure Open2Humidity2< 30%50%Leakage (1 sigma)< 50 fA< 200 fALeakage (average)NA NALeakage (P-P)< 100 fA< 1000 fAResistance (F-G)> 1 TΩ> 1 TΩResistance (G-S)> 1 TΩ> 1 TΩResistance (F-S)> 1 TΩ> 1 TΩResidual capacitance @ 3 pA Tx< 20 pF< 20 pFCapacitance @ 300 pA (F-G)< 400 pF< 400 pFCapacitance @ 300 pA (G-S)< 400 pF< 400 pFTRIAXIAL PROBE ARMS1Standard Triaxal Arm (PN 100525)Advanced Triax Option (PN 157-450 and DCP)In Purged Shield Enclosure In Purged Shield EnclosureHumidity3< 30%< 30%Leakage (1 sigma)< 5 fA< 2 fAResistance (F-G)> 20 TΩ> 50 TΩResistance (G-S)> 4 TΩNAResidual capacitance @ 3 pA Tx< 1 pF< 0.3 fFCapacitance @ 300 pA (F-G)< 300 pF< 150 pFCapacitance @ 300 pA (G-S)< 400 pF< 200 pFCOAXIAL PROBE ARMS1Coaxial Probe Arm (PN 100561)Open / Ambient2, 4Resistance (Signal-Shield)> 20 TΩCapacitance (Signal-Shield)< 200 pF1. T est conditions: B1500 with SMU B1517, triax test cables and adapter ground unit (104-337). Resistor test setup: 10 V HR Mode PCL Factor 15.Capacitor test setup: 3 pA / 300 pA HR Mode PCL Factor 4. Leakage test setup: 10 V HR Mode PCL Factor 40.2. Depending on DC-/AC-noise environment.3. Environment data (not specification data).4. Depending on humidity.Thermal Chuck PerformanceNote: For details on facility requirements, refer to the Facility Planning Guide for your thermal system.MPS-TC150-CTX-300C1Triax @ 30°C Triax @ 200°C Triax @ 300°C Breakdown voltage2a Force-to-guard≥ 500 V≥ 500 V≥ 500 VGuard-to-shield≥ 500 V≥ 500 V≥ 500 VForce-to-shield≥ 500 V≥ 500 V≥ 500 V Resistance3a Force-to-guard≥ 1 x 1012≥ 1 x 1011≥ 5 x 109Guard-to-shield≥ 1 x 1011≥ 1 x 1010≥ 1 x 109Force-to-shield≥ 5 x 1012≥ 2 x 1011≥ 5 x 109 Chuck leakage4≤ 100 fA≤ 10 pA≤ 300 pA Residual capacitance≤ 50 pFSettling time6 @ 10 V 50 fA500 ms (typical)MPS-TC150-CTX-300C (using coax-triax adapter)1, 5Coax @ 30°C Coax @ 200°C Coax @ 300°C Breakdown voltage2a≥ 500 V≥ 500 V≥ 500 V Resistance3a Signal-to-shield≥ 1 x 1012≥ 1 x 1011≥ 5 x 109 Chuck leakage4≤ 600 fA≤ 15 pA≤ 1 nA Residual capacitance≤ 600 pFMPS-TC150-RF-300C1, 5Coax @ 30°C Coax @ 200°C Coax @ 300°C Breakdown voltage2a≥ 500 V≥ 500 V≥ 500 V Resistance3a Signal-to-shield≥ 1 x 1012≥ 1 x 1011≥ 5 x 109 Chuck leakage4≤ 600 fA≤ 15 pA≤ 1 nA Residual capacitance≤ 600 pFMPS-TC150-200C1Triax @ 30°C Triax @ 200°CBreakdown voltage2b Force-to-guard≥ 500 V≥ 500 VGuard-to-shield≥ 500 V≥ 500 VForce-to-shield≥ 500 V≥ 500 VResistance3b Force-to-guard≥ 5 x 1012≥ 5 x 1011Guard-to-shield≥ 2 x 1012≥ 8 x 1010Force-to-shield≥ 7 x 1012≥ 5 x 1011Chuck leakage4≤ 35 fA≤ 40 fAResidual capacitance6≤ 20 pFSettling time7 @ 10 V 50 fA500 ms (typical)Thermal Chuck Performance (continued)MPS-TC150-200C (using coax-triax adapter)1, 5Coax @ 30°C Coax @ 200°CBreakdown voltage2b≥ 500 V≥ 500 VResistance3b Signal-to-shield≥ 5 x 1012≥ 5 x 1011Chuck leakage4≤ 600 fA≤ 7.5 pAResidual capacitance6≤ 600 pF1. P erformance values determined using EMV shielded chamber. Actual value depend on electromagnatic surrounding and shielding situation of the probestation.2a. For fully-baked chuck: 90°C for 60 minutes + 200°C for 240 minutes + 300°C for 480 minutes.2b. For fully-baked chuck: 90°C for 60 minutes + 200°C for 800 minutes3a. For fully-baked chuck: 90°C for 60 minutes + 200°C for 240 minutes + 300°C for 480 minutes; controller on; 21-23C° environment with ≤ 50% humidity.3b. For fully-baked chuck: 90°C for 60 minutes + 200°C for 800 minutes; 21-23C° environment with ≤ 50% humidity.4. O verall leakage current is comprised of two separate components: 1) offset, and 2) noise. Offset is the DC value of current due to instrument voltageoffset driving through isolation resistance. Noise is low frequency ripple superimposed on top of offset and is due to disturbances in the probe station environment.*****************************************************************************************************************(1σ).5. Chuck: Guard-Shield shorted, B1500: triax, guard open.6. Depends on test environment7. Settling time is measured with B1500 with SMUB1517 - ST@10V CMI program or equivalentTransition TimeHeating Cooling30°C to 100°C°100°C to 200°C200°C to 300°C300°C to 200°C200°C to 100°C100°C to 30°C MPS-TC150-CTX-300C145 sec155 sec300 sec145 sec245 sec1525 secMPS-TC150-RF-300C180 sec300 sec540 sec165 sec310 sec1650 secMPS-TC150-200C155 sec260 sec na na120 sec425 secMPS-TC150-CTX-300C and MPS-TC150-RF-300C SpecificationsTemperature range+ 30°C to 300°CTemperature accuracy± 0.1°C (with calibrated controller)Temperature resolution0.1°CTemperature uniformity≤ 0.5°C @ 30°C, ≤ 3.0°C @ 300°CChuck flatness≤ 30 μm (0.12 mils) @ +30°C to 300°CAudible noise< 58 dB(A) (normal operation); < 79 dB(A) (max. cooling mode)MPS-TC150-200CTemperature range+ 30°C to 200°CTemperature accuracy± 0.5°CTemperature resolution0.1°CTemperature uniformity≤ ±1°C (30°C - 200°C)Chuck flatness≤ 30 μm (0.12 mils) @ +30°C to 200°CAudible noise< 54 dB(A) (normal operation); < 68 dB(A) (max. cooling mode)Ordering InformationPre-Configured Application-Focused PackagesEPS150 COAX / COAX PLUS EPS150TRIAX EPS150RFEPS150MMW EPS150FA EPS150TESLAIntegrated Measurement SolutionRFgeniusPart Number DescriptionEPS150COAX150 mm manual probing solution for DC parametric testEPS150COAXPLUS150 mm manual probing solution for DC parametric test (including platen lift)EPS150TRIAX150 mm manual probing solution for low-noise measurementsEPS150RF150 mm manual probing solution for RF applicationsEPS150MMW150 mm manual probing solution for mmW, THz and load pull applicationsEPS150FA150 mm manual probing solution for failure analysisRFgenius-xx*RFgenius education kit, turn-key solution for measurements up to 4.5/6.5/9/14/20/26.5 GHz 181-669FormFactor certified laptop for RFgenius-xx (optional)*** Enter the frequency range for a VNA of your choice. Example: RFgenius-4 for 4.5 GHz. RFgenius-26 for 26.5 GHz.** M inimum requirement for a laptop to be supplied by a user: Windows 7 or 10 (64 bit), Intel i5 6th Gen or newer, 4 GB memory or more (16 GB recommended),2 GB disk space or more, 1024 x 768 resolution, USB 3.o port.Corporate Headquarters 7005 Southfront Road Livermore, CA 94551Phone: © Copyright 2018 FormFactor, Inc. All rights reserved. FormFactor and the FormFactor logo are trademarks of FormFactor, Inc. All other trademarks are the property of their respective owners.All information is subject to change without notice.MPS150-DS-0518Regulatory ComplianceCertificationCE, cNRTLus, CBWarrantyWarranty* Fifteen months from date of delivery or twelve months from date of installation Service contracts Single and multi-year programs available to suit your needs*See FormFactor’s T erms and Conditions of Sale for more details.。

2. The model, symmetries and the Dyson-Schwinger equations The model we will deal with contains two SU (2) isodoublets ψ1 and ψ2 and is described by the following Lagrangian a a ¯2 τ ψ1 ) . ¯1 i/ ¯2 i/ ¯1 τ ψ2 )(ψ (1) L=ψ ∂ ψ1 + ψ ∂ ψ2 + G(ψ 2 2 In eq.(1) τ a are the Pauli matrices and G is a positive coupling. The symmetries of the model can be summarized as follows : i) SU (2) ψ1 ψ2 ψ1 ψ2 ψ1 ψ2 ψ1 ψ2 → → → → → → e 2 θ τ ψ1 i a a e 2 θ τ ψ2 eiα ψ1 ψ2 , ψ1 eiβ ψ2
.
Σ
We are interested in the possible nontrivial solutions of eqs.(4). These are given by i)
(2) Σ(1) a = Σa = 0 (1) Σ0
, , d4 k 1 4 2 (2π ) k + Σ2 0 , , d4 k (2π )4 1 k2 + Σ
In order to study the dynamical symmetry breaking we will use in a first approach the Dyson-Schwinger equations in the one-loop approximation. Using the notation S −1 (p) = p /−Σ , (2) where Σ = Σ0 + τa Σa , we obtain Σij =

五年级英语宇宙探索发现单选题50题1. The ____ is the only planet known to have life.A. MarsB. MoonC. EarthD. Sun答案解析：C。

本题考查对星球相关词汇的认识。

选项A“Mars”是火星，目前没有发现有生命存在。

选项B“Moon”是月球，它是地球的卫星，不是行星，也没有生命。

选项C“Earth”地球，是我们所知道的唯一有生命的行星，符合题意。

选项D“Sun”是太阳，它是恒星，不是行星，更没有生命。

2. Which planet is called the "Red Planet"?A. VenusB. MarsC. JupiterD. Saturn答案解析：B。

这题考查特定星球的别名相关词汇。

选项A“Venus”是金星，它没有“Red Planet”这个别名。

选项B“Mars”火星，因其表面呈现红色，被称为“Red Planet”，正确。

选项C“Jupiter”是木星，与“Red Planet”无关。

选项D“Saturn”是土星，也不是“Red Planet”。

3. The Moon is a ____ of the Earth.A. starB. planetC. satelliteD. comet答案解析：C。

本题考查月球与地球关系相关的词汇。

选项A“star”是恒星，月球不是恒星。

选项B“planet”是行星，月球不是行星。

选项C“satellite”卫星，月球是地球的卫星，正确。

选项D“comet”是彗星，与月球的性质完全不同。

4. Which planet has a big red spot?A. MarsB. JupiterC. NeptuneD. Uranus答案解析：B。

这里考查对星球特征相关词汇的掌握。

选项A“Mars”火星没有大的红斑。

选项B“Jupiter”木星有一个很大的红斑，正确。

五年级英语天文现象单选题50题1. There are eight planets in the solar system. Which one is the biggest?A. EarthB. JupiterC. MarsD. Venus答案：B。

本题考查太阳系中行星的大小知识。

地球（Earth）不是最大的行星；火星（Mars）比木星小；金星（Venus）也比木星小。

木星 Jupiter）是太阳系中最大的行星。

2. The sun is a star. What gives the sun its energy?A. WaterB. CoalC. Nuclear fusionD. Wind答案：C。

本题涉及太阳能量来源的知识。

水（Water）、煤炭（Coal）和风（Wind）都不是太阳的能量来源。

太阳的能量来自核聚变（Nuclear fusion）。

3. Which planet is known as the "Red Planet"?A. MercuryB. SaturnC. MarsD. Uranus答案：C。

本题考查对行星特征的了解。

水星（Mercury）不是红色的；土星（Saturn）有环，但不是红色的；天王星（Uranus）也不是红色的。

火星 Mars）表面呈现红色，被称为“红色星球”。

4. How many moons does Saturn have?A. 53B. 62C. 82D. 100答案：C。

本题考查土星卫星数量的常识。

土星有82 颗卫星，A 选项53 颗、B 选项62 颗、D 选项100 颗均不符合实际情况。

5. Which is the closest planet to the sun?A. MercuryB. VenusC. EarthD. Mars答案：A。

本题考查太阳系行星与太阳的距离。

金星 Venus）、地球 Earth）、火星 Mars）距离太阳都比水星远，水星 Mercury）是距离太阳最近的行星。

Symbol complete（符号大全）Symbol Daquan 2010-07-22 12:29Formulas and notations in mathematical physics: Alpha alpha: Alfa AlphaBeta beta beta: BetaGamma gamma gamma: GammaDelta DelteEpsilon epsilon: episilon EpsilonSome of the zeta Jieta: ZetaEpsilon ETA: yita EtaTheta theta theta: ThetaI l: erota IotaKappa kappa Kapa: KappaA: Lamuda Lambda.Mu Mu: Bartholomew MuUpsilon V: Ao NuE: Roxy Xi.April: Mike Omicron / European roundPi Pi: send PiP P: soft RhoSigma: Sigma SigmaT: t TauR V: Yu Puxilong UpsilonPhi Phi: Fai PhiX x: ChiOnly psi pusai: PsiOmega Omega: Omega OmegaSymbol complete:(1) the number of symbols: such as: I, 2 + I, a, x, natural logarithm base e, PI pi.Such as: (2) operational symbol plus (+) and minus (-) sign, (* or *), division (or / /), the union of two sets (U), (a), Reagan (intersection), log (log, LG, LN), (:), differential ratio (d), integral (formula).(3) the relationship between symbols: such as "=" is equal to "value" or "," is the approximate symbol, not equal to is not equal, ">" is greater than the symbol, "<" is less than the symbol, "said variable trend," ~ "is similar to" Te "is congruent symbol. No," "parallel" is "an" symbol is the vertical symbol, "/" is "and" the proportion of symbols, symbols belong to.(4) a combination of symbols: such as parentheses (brackets) "," [] "braces" {} "line"-"(5) the nature of symbols such as a "+", "-" sign, the absolute value of the symbol """(6) ellipsis: (a) such as triangle, sine (SIN), X function (f (x)), limit (LIM), because (dreams), so (H0), sum (sigma), product (II), from each N element R from all the different elements the number of combinations (C), power (aM), factorial (!) Etc..Symbolic meaningH-infinity infinityPI.The absolute value of the |x| functionU set withA set intersectionIs greater than or equal toIs less than or equal toIt is less than or equal to the congruenceLn (x) the logarithm based on eLG (x) with 10 as the base of the logarithmFloor (x) on the integral functionCeil (x) under the integral functionX mod y for remainderDecimal part X - floor (x)Formula F (x) x integralFormula [a:b]f (x) integral to B a x.P equals 1, or 0[1 = k = n]f (k) of the N sum, can be extended to many Such as: Sigma [n, is, prime][n < 10]f (n)Sigma Sigma [1 = I = J = n]n^2Lim f (x) (x->) limitF (z) f on M's order derivative function of ZC (n:m) combination number, n take MP (n:m) permutationsM|n m divisible nM m and n n t coprimeA A a belongs to the set AThe number of elements in the #A collection AJunior physics formula:Physical quantity (unit) formula; deformation of remark formulaSpeed V (m/S) v= S: distance /t: timeGravity G (N) G=mg M: mass g:9.8N/kg or 10N/kgThe density of =m/V m (kg/m3) P: quality: Volume VThe resultant force is the same as F (N): F and =F1+F2In the opposite direction: when F is the opposite of =F1 - F2,F1>F2Buoyancy F float(N) F, floating =G matter - G, depending on the G: the gravity of the object in the liquidBuoyancy F float(N) F floating =G matter, this formula applies onlyObject floating or suspendedBuoyancy F float(N) F =G =m g= P floating row row row row row: G gV liquid liquid gravityPlatoon M: the quality of the liquidP: liquid liquid densityPlatoon V: the volume of the liquid(that is, the volume immersed in a liquid)Lever balance conditions F1L1=, F2L2, F1: power L1: power armF2: resistance L2: resistance armFixed pulley F=GS=h F: the pull of the free end of the ropeG: gravity of objectsS: the distance at which the end of the rope movesH: the distance that an object risesMoving pulley F= (G object +G wheel)S=2, h, G objects: the gravity of objectsG wheel: the gravity of the moving pulleyPulley block F= (G, +G wheel)S=n H N: the number of segments of the rope by moving the pulley Mechanical work W(J) W=Fs F: forceS: the distance traveled in the direction of forceUseful work, W, yesTotal W total W =G HW total =Fs applies pulley block verticallyMechanical efficiency = x 100%Power P(W) P=W: work!T: timePressure P(Pa) P=F: stressS: force areaLiquid pressure P(Pa) P= P GH P: liquid densityH: depth (from liquid level to desired point)Vertical distanceHeat Q(J) Q=cm T C: the specific heat capacity of material quality: MT: temperature change valueFuel combustionHeat Q (J) Q=mq M: qualityQ: calorific valueCommon Physics Formulas and important knowledge pointsI. physical formulaUnit) deformation of formula remark formulaSeries circuitCurrent I (A) I=I1=I2=...... Current is equal everywhere Series circuitVoltage U (V) U=U1+U2+...... Series circuitPartial pressure actionSeries circuitResistor R (omega) R=R1+R2+......Parallel circuitCurrent I (A) I=I1+I2+...... The current trunk is equal to theSum of branch currents (shunt)Parallel circuitVoltage U (V) U=U1=U2=......Parallel circuitResistor R (omega) = + +......Ohm's law I=Current and voltage in a circuitProportional to, inversely proportional to the resistance Current definition I=Q: the amount of charge (Coulomb)T: time (S)Electrical work W(J) W=UIt=Pt U: voltage I: currentT: time P: electric powerElectrical power P=UI=I2R=U2/R U: voltage I: currentR: resistanceElectromagnetic wave velocity and waveLong, the relationship between the frequencies of C= lambda V C:Unit formula of physical quantityName, symbol, name, symbolThe quality is m kg kg m=pvThe temperature is t degrees Celsius, C degrees CelsiusSpeed v m / sec, m/s v=s/tDensity p kg / M 3 kg/m3 p=m/vForce (gravity) F Newton (cow) N G=mgThe pressure is P Pascal (PA) Pa P=F/SWork W Joule (focus) J W=FsPower P watt (W) w P=W/tCurrent I ampere (an) A I=U/RVoltage U volts (volts) V U=IRResistance R ohm (OU) R=U/IElectrical work W Joule (focus) J W=UItElectrical power P watts (Watts) w P=W/t=UIHeat Q Joule (coke) J Q=cm (T-T degrees)Specific heat C Jiao / (kg degree C) J/ (kg degrees C)In the vacuum, the speed of light is 3 * 108 meters per secondG 9.8 Newton / kg15 degrees C air speed of 340 meters per secondCompilation of Physics Formulas for junior high school [mechanical part]1, speed: V=S/t2, gravity: G=mg3, density: P =m/V4, pressure: p=F/S5, liquid pressure: p= P GH6, buoyancy:(1) F float = F - F (pressure difference)(2) F floating = G - F (apparent gravity);(3) F floating = G (floating, suspended)(4), the Archimedes principle: F floating =G = P liquid gV 7, leverage balance conditions: F1 L1 = F2 L28, ideal slope: F/G = h/L9. Ideal pulley: F=G/n10, actual pulley: F = (G + G moving) / N (vertical direction) 11, work: W = FS = Gh (raise the object)12, power: P = W/t = FV13, work principle: W hand = W machine14, the actual total machinery: W = W is W extra15, mechanical efficiency: ETA = W /W total16 pulley block efficiency:(1) nF, ETA = G/ (vertical direction)(2), ETA = G/ (G + G) (vertical direction without friction)(3), ETA = f / nF (horizontal)[heat part]1, heat absorption: Q absorption = Cm (T - t0) = Cm, delta T2 heat release: Q = Cm (t0 - t) = Cm = t3, calorific value: q = Q/m4, the efficiency of furnace and heat engine: ETA = Q the effective use of /Q fuel5, heat balance equation: Q = Q suction6, thermodynamic temperature: T = T273K[electrical part]1, current strength: I = Q, electricity /t2, resistance: R= P L/S3 Ohm's Law: I = U/R4 Joule's law:(1) Q = I2Rt universal formula)(2) Q = UIt = Pt = UQ electric = U2t/R (pure resistance formula) 5 、 series circuit:(1) I = I1 = I2(2), U = U1U2(3), R = R1R2(4) U1/U2 = R1/R2 (partial pressure formula)(5) P1/P2 = R1/R26 、 parallel circuit:(1), I = I1I2(2) U = U1 = U2(3), 1/R = 1/R11/R2 [R = R1R2/ (R1R2)](4) I1/I2 = R2/R1 (shunt formula)(5) P1/P2 = R2/R17 fixed resistance:(1) I1/I2 = U1/U2(2) P1/P2 = I12/I22(3) P1/P2 = U12/U228 electric work:(1) W = UIt = Pt = UQ (universal formula)(2) W = I2Rt = U2t/R (pure resistance formula)9 electric power:(1) P = W/t = UI (universal formula)(2) P = I2R = U2/R (pure resistance formula) [common physical quantity]1, speed of light: C = 3 * 108m/s (in vacuum)2, sound speed: V = 340m/s (15 DEG C)3, the human ear distinguish echo: more than 0.1s 4, gravity acceleration: g = 9.8N/kg = 10N/kg5, the standard atmospheric pressure value:760 mm mercury column = 1.01 * 105Pa6, the density of water: P = 1 * 103kg/m37. Freezing point of water: 0 DEG C8. Boiling point of water: 100 DEG C9. The specific heat of water:C = 4.2 * 103J/ (kg DEG C)10, yuan charge: e = 1.6 * 10-19C11, a dry battery voltage: 1.5V12, a section of lead-acid battery voltage: 2V13, for human safety voltage: less than 36V (less than 36V)14 、 voltage of power circuit: 380V15 、 home circuit voltage: 220V16, unit conversion:(1) 1m/s = 3.6km/h(2) 1g/cm3 = 103kg/m3(3) and 1kW = H = 3.6 * 106J;Compilation of Physics Formulas for junior high school [mechanical part]1, speed: V=S/t2, gravity: G=mg3, density: P =m/V4, pressure: p=F/S5, liquid pressure: p= P GH6, buoyancy:(1) F float = F - F (pressure difference)(2) F floating = G - F (apparent gravity);(3) F floating = G (floating, suspended)(4), the Archimedes principle: F floating =G = P liquid gV 7, leverage balance conditions: F1 L1 = F2 L28, ideal slope: F/G = h/L9. Ideal pulley: F=G/n10, actual pulley: F = (G + G moving) / N (vertical direction) 11, work: W = FS = Gh (raise the object)12, power: P = W/t = FV13, work principle: W hand = W machine14, the actual total machinery: W = W is W extra15, mechanical efficiency: ETA = W /W total16 pulley block efficiency:(1) nF, ETA = G/ (vertical direction)(2), ETA = G/ (G + G) (vertical direction without friction)(3), ETA = f / nF (horizontal)[heat part]1, heat absorption: Q absorption = Cm (T - t0) = Cm, delta T2 heat release: Q = Cm (t0 - t) = Cm = t3, calorific value: q = Q/m4, the efficiency of furnace and heat engine: ETA = Q the effective use of /Q fuel5, heat balance equation: Q = Q suction6, thermodynamic temperature: T = T273K[electrical part]1, current strength: I = Q, electricity /t2, resistance: R= P L/S3 Ohm's Law: I = U/R4 Joule's law:(1) Q = I2Rt universal formula)(2) Q = UIt = Pt = UQ electric = U2t/R (pure resistance formula) 5 、 series circuit:(1) I = I1 = I2(2), U = U1U2(3), R = R1R2(4) U1/U2 = R1/R2 (partial pressure formula)(5) P1/P2 = R1/R26 、 parallel circuit:(1), I = I1I2(2) U = U1 = U2(3), 1/R = 1/R11/R2 [R = R1R2/ (R1R2)](4) I1/I2 = R2/R1 (shunt formula)(5) P1/P2 = R2/R17 fixed resistance:(1) I1/I2 = U1/U2(2) P1/P2 = I12/I22(3) P1/P2 = U12/U228 electric work:(1) W = UIt = Pt = UQ (universal formula)(2) W = I2Rt = U2t/R (pure resistance formula) 9 electric power:(1) P = W/t = UI (universal formula)(2) P = I2R = U2/R (pure resistance formula) [common physical quantity]1, speed of light: C = 3 * 108m/s (in vacuum)2, sound speed: V = 340m/s (15 DEG C)3, the human ear distinguish echo: more than 0.1s4, gravity acceleration: g = 9.8N/kg = 10N/kg5, the standard atmospheric pressure value:760 mm mercury column = 1.01 * 105Pa6, the density of water: P = 1 * 103kg/m37. Freezing point of water: 0 DEG C8. Boiling point of water: 100 DEG C9. The specific heat of water:C = 4.2 * 103J/ (kg DEG C)10, yuan charge: e = 1.6 * 10-19C11, a dry battery voltage: 1.5V12, a section of lead-acid battery voltage: 2V13, for human safety voltage: less than 36V (less than 36V)14 、 voltage of power circuit: 380V15 、 home circuit voltage: 220V16, unit conversion:(1) 1m/s = 3.6km/h(2) 1g/cm3 = 103KEncyclopedia of mathematical symbols:(1) the number of symbols: such as: I, 2+i, a, x, natural logarithm base e, pi.Such as: (2) operational symbol plus (+) and minus (-) sign, (* or *), division (or / /), the union of two sets (U), (a), the intersection of root (V), (log, LG, log LN), than (:). Differential (DX), integral (formula).(3) the relationship between symbols: such as "=" is equal, "is" is the approximate symbol, not equal to is not equal, ">" is greater than the symbol, "<" is less than the symbol, "said," variable trend, "~" is similar to "=" symbols are congruent. "The" "symbol is parallel," t "is the vertical symbol," / "is directly proportional to the symbols (not inversely proportional to the symbol, but can be used as a symbol with reciprocal" and "inversely) is a symbol of" C "or" C below a bar "is" contained "symbols.(4) a combination of symbols: such as parentheses "(in parentheses)" "" "," {} "horizontal braces"-"(5) the nature of symbols: such as a "+", "-" sign, the absolutevalue of the symbol """(6) ellipsis: (a) such as triangle, sine, cosine (SIN) (COS), X function (f (x)), limit (LIM), dreams because (a foot stand, stand (two) said so, foot standing, can stop) the sum (sigma), product (II), from each n elements of the R elements removed all the different number of combinations (C (R) (n) (A), power, Ac, Aq, x^n), factorial (!) Etc..(7) other symbols: alpha, beta, gamma and so forthThe origin of mathematical symbols:For example, the plus sign used to have several, and now the universal "+" number.The "+" is evolved from the Latin "et" (meaning of "harmony"). In sixteenth Century, Italy scientist Tartaglia in Italian "PLU" (and meaning) the first letter said, "Mu" grass have become the last "+"."-" is evolved from the Latin "minus" (minus) meaning. The abbreviation m, and then the omission of the letter, becomes "-".Some people say, liquor merchants "-" said how much the barrel of wine sold. Later, when the new wine is poured into the barrel, in the "-" with a vertical, meaning that the cancellation of the original lines, this became a "+".By fifteenth Century, the German mathematician Wei Demeiofficially confirmed: "+" is used as a plus, "-" used as a minus sign.Once a dozen times, now general two. One is "X", which was first proposed by British mathematician Okut in 1631, and was first invented by British mathematician, Hector ott. German mathematician Leibniz said: "X" number like the Latin alphabet "X" against, and in favor with "No.". He also said "are" put forward by. But this symbol is now applied to set theory.In eighteenth Century, American mathematician Oude Levin, the "X" as a symbol of multiplication. He thought that the "X" was "+" tilted to write, another sign of increasing."," first as a minus sign, long popular in continental europe. Until 1631 the British mathematician aucuy special "said in addition to or better than, other people" - "(except line) said in addition. Later, the Swiss mathematician Raha in his book "algebra", according to the people to create, will be officially "/" as a case.Square root Latin "Radix used" (root) and the two letters together and said that at the beginning of the seventeenth Century, the French mathematician in his "geometry", the first time the "tick" said reagan. "V" is from the Latin word line "R", "-" is the line.In sixteenth Century the French mathematician dimension leaves special "=" said the difference between the amount of two. But the British University of Oxford mathematics, Professor Leo Calder think any rhetoric, with two parallel and equal to theequivalent linear representation is the most appropriate, and equal to the symbol "=" from the beginning of 1540 to use.In 1591, Veda, a French mathematician, used the symbols in the diamond to be accepted gradually. Seventeenth Century German Leibniz made extensive use of "=", he is still used in geometry "~" similar, "=" said."Greater than" and less than "< <" is the 1631 British famous mathematician mathematician, "Rui Rui" created. As for the "more than", "less than", "and" the three symbols appear, is very very late. "{}" brackets and brackets "," is one of the founders of algebra Zhide created wei.Any number comes from the word "any" in English, because both lowercase and uppercase are prone to confusion, so capitalize the first letter of the word and turn it upside down, as shown.A mathematical symbol of a mathematical symbolSuch as: I, 2+i, a, x, natural logarithm base e, pi.Operational symbolAs a plus (+) and minus (-) sign, (* or *), division (or / /), the union of two sets (U), (a), the intersection of root (V), (log, LG, log LN), than (:), differential, integral (DX) (formula), (PHI) and curve integral.Relational symbolSuch as "=" is the sign "=" is the approximate symbol, not equal to is not equal, ">" is greater than the symbol, "<" is less than the symbol, "or" is greater than or equal to the symbol (can also be written as "less than", "less than") is less than or equal to the symbol (can also be written "using"),. "," said variable trend, "~" is similar to "=" symbols are congruent, "" parallel "is" an "symbol is the vertical symbol," / "is directly proportional to the symbols (not inversely proportional to the symbol, but can be used as a symbol with reciprocal inverse)" this is "symbol"? "Is" contained "symbols.Combination symbolAs in parentheses, "()) brackets [[]]","{}" horizontal braces"-"Property symbolAs a "+", "-" sign, the absolute value of the symbol "| |" sign ""Ellipsis(a) such as triangle, triangle (Rt delta), sine cosine (SIN), (COS), X function (f (x)), limit (LIM), angle (angle),Because of dreams, (a foot stand, stand)* so (two feet standing, can stop) the sum (sigma), product (II),from each n elements of the R elements removed all the different number of combinations (C (R) (n) (A), power, Ac, Aq, x^n), factorial (!) Etc..(7) other symbols: alpha, beta, gamma and so forthExpress existence",For any given"The meaning of mathematical symbols:Symbolic (Symbol) meaning (Meaning)= equal to is equal toIs not equal to is not equal to not equal< less than is less than> greater than is, greater, thanParallel is parallel to ||Greater than or is greater than or equal to is equal toLess than or is less than or equal to is equal toIt is less than or equal to the congruencePi Pi|x| absolute value absolute, value, of, XSimilar to is similar toIs equal to (especially = congruent for triangle) "is far greater than the number"Far less than number"U UnionA intersectionIncluded inThe circleDiameter of phiBeta betaH-infinity infinityLn (x) the logarithm based on eLG (x) with 10 as the base of the logarithmFloor (x) on the integral functionCeil (x) under the integral functionX mod y for remainderX - floor (x) decimal partFormula F (x) DX integralFormula [a:b]f (x) DX A to B integralThe use of mathematical symbols:P equals 1, or 0[1 = k = n]f (k) of the N sum, can be extended to many Such as: Sigma [n, is, prime][n < 10]f (n)Sigma Sigma [1 = I = J = n]n^2Lim f (x) (x->) limitF (z) f on M's order derivative function of ZC (n:m) combination number, n take MP (n:m) permutationsM|n m divisible nM m and n n t coprimeA A a belongs to the set AThe number of elements in the #A collection A。

划片机作业手册-----Disco Automatic Dicing Saw 9890501 发表于: 2005-11-26 22:17 来源: 半导体技术天地(disco)1.0 TitleDisco Automatic Dicing Saw2.0 PurposeThe Disco Automatic Dicing Saw is a precision machine used to cut semiconductor wafers into individual chips or dice. Wafers are held to the chuck table by means of vacuum and t he chuck can accommodate wafers with diameters from 2" to 6 ". The maximum table stroke (left-right movement of the chu ck table) is 160 mm (6 5/16"). The cutting range is 20.4 mm to 153 mm in 1 mm increments (0.8" to 6" in 0.025" increme nts). The cutting feed speed is variable from 0.3 to 10 mm/ sec. (0.012" to 12"/sec).The dicing wheel is mounted on a high frequency air-bearingspindle with an average rotation speed of 30,000 rpm. The range of depth left uncut is variable, and ranges from 0.00 5 mm to 19.995 mm (0.0002" to 0.7872") in steps of 0.005 mm (0.0002") increments. (Do not use a Z-index of less than 0.07 mm without consulting a superuser.)Following each cut, the Disco uses stored parameters to aut omatically index the wafer along the Y-axis. The maximum sp indle stroke (forward-backward movement of spindle) is 160 mm (6 5/16"), and the variable spindle index ranges from 0. 002 mm to 99.998 mm (0.0001" to 4") in indexing steps of 0. 002 mm (0.0001") increments.3.0 ScopeThere are four fixed sawing modes available:MODE AThe cut is made only in one direction as the chuck moves fr om right to left (down cut).MODE BThe cut is made in both directions along the X-axis (down c ut/up cut).MODE CThis mode also cuts in both directions along the X-axis, bu t the blade descends within the range of 0.005-19.995 mm al ong the Z-axis when the chuck table moves from left to righ t. Use this mode for cuts deeper than 650 microns.MODE DThis mode is constructed with a DRESS, which uses a dress b oard, and a PRE-CUT, which uses a dummy wafer.Dicing tape and hoops are available in the Microlab. Tape c an be found on a dispenser in 432b, and hoops are stored be neath the disco saw. Dicing tape is recommended for all dic ing operations and is required for through wafer cuts.4.0 Applicable Documents5.0 Definitions and Process Terminology6.0 Safety7.0 Statistical/Process Data8.0 Available Process, Gases, Process Notes 8.1 Cutting Blades In UseSilicon BladeSemitec Corp. PN S2525kerf (width of cut) = .64 microns or .0025”Maximum depth of cut = 640 microns or .025”Ceramics, saphire, crystal substrateDicing Technology, PN CX-004-270-040-Hkerf .004”, 50-70 micron abrasive, 1 mm or .040” exposureRecommended cutting speed, best cut: ..25 mm/sec, Z-index: . 7, .04Maximum cutting speed: .5 mm/sec (more chipping)GlassDicing Technology, PN CX-010-600-060 Jkerf .010”, 22-36 micron abrasive, 1.5 mm or .060” exposu reRecommended cutting speed, best cut: .5 mm/sec, Z-index: .7, .04Maximum cutting speed: 1 mm/sec9.0 Equipment Operation9.1 Operating PrecautionsSilicon particles (shipped pieces) produced by dicing opera tion will coat your samples, if you do not use a protective layer. These are sharp edged particles, which can easily p enetrate the underlying structure, and are very difficult o r impossible to remove. It is highly recommended that you c oat your wafers with 1-2 micrometers of photoresist as a sa crificial layer that can trap and later remove particles (p ost dicing operation). You can use the manual spinner (head way) or the automated track systems (SVG) to perform this c oating.Chapter 1.3 of the manual, module 6 (MOD6) provides and ove rview of the resist coating procedure, if you are not famil iar with this process. Please note that there is no need fo r HMDS treatment of wafers surface (skip Section A). Once w afer is diced you can easily remove your resist layer along with the particles in a acetone bath followed by isopropan ol and a DI rinse/dry steps (soak samples for 2 minutes in acetone, DI rinse, then 2 minutes in isopropanol followed by DI rinse).Before operating the saw, be sure to verify the following:9.1.1 The blade is intact. If you attempt to c ut a wafer with a damaged blade, it may cause severe damage to the spindle. You may change the blade by following the procedure posted on the wall. Be careful not to apply exces sive force to the spindle. Use the torque driver that is ke pt by the saw.9.1.2 The AUTOBREAKER CONTROL switch (located on the right side of the main body) is turned on (in the UP position).9.1.3 The air is on and is being supplied at 8 0 psi (or more).9.1.4 The water is on.9.1.5 The STANDBY light is on.During operation, make sure:9.1.6 Your wafer is no more than 550 um thick. If you are cutting thick wafers, wafer stacks, etc., you m ust use MODE C. Otherwise, the saw blade will scrape along your wafer on the return stroke, damaging your wafer, the b lade, and possibly the spindle. Similarly, never attempt to make a cut that is deeper than the exposed amount of saw b lade, since this will place a high load on the spindle and possibly damage it.Dicing blades are made of thin material and cannot be used for side grinding. If you are dicing a sample (a half wafer, etc), which has a pre-existing flat edge parallel to the c utting direction, be very careful not to let the blade inde x over and try to cut right along the edge of the sample. T he lateral forces that are induced in the blade will easily peel it off the blade holder.9.1.7 Cooling water is being supplied to the c utting area, at a flow rate of at least 0.3 lpm.9.1.8 Always perform a Setup after changing the blade. Otherwise, if the new blade is at all larger than the old blade, it may cut into the chuck.Note: Spindle ShutdownThere are two ways to stop the spindle from rotating. Press ing the button SPINDLE will turn off the spindle and preser ve the height setting. Pressing the EM STOP will stop the s pindle, raise it, return it to the home position and erase the height information.If a blade is to be changed, it is imperative to use EM STO P rather than spindle to stop rotation so new height inform ation is programmed following the blade change.NEVER TURN OFF THE DISCO WHILE THE SPINDLE IS TURNING.FIRST STOP THE SPINDLE ROTATION WITH ONE OF THE ABOVE METHO DS.9.2 Initial Set-UpBefore beginning the actual operation, the saw must be "set -up". This allows the machine to verify the zero reference point along the Z-axis (i.e. verifies the chuck height). Th is procedure is done without a wafer on the chuck table as the presence of a wafer may cause damage to either the blad e or the wafer. Be sure that there is no water present on t he surface of the chuck table. The procedure is as follows:9.2.1 Check that the spindle cover is on tight ly. Press the SPINDLE button (the LED should now be lit). V erify that the spindle is rotating.9.2.2 Press the ILLUMINATION button to turn on the lights to the microscope.9.2.3 Press the VACUUM button (the LED should now be lit).9.2.4 Press the SET UP button. This will cause the blade to rise along the Z-axis and stop at the limit o f travel along the Z-axis. The chuck table will now move toand stop at approximately the center of the Y-axis. The ch uck table will then move along the X-axis from the left to the SET UP position and stop. The blade will descend along the Z-axis and touch the surface of the chuck table, then i mmediately rises to form a gap equal to the amount entered into the Z INDEX. The chuck table will now move along the X -axis to the position of the microscope and stop. The SET U P lamp will now come on to indicate the completion of the S ET UP operation.9.3 ProgrammingThere is space available for storing 10 different programs (Prog.#0-#9). Programmable parameters include:►MODE of cutting►CUT STRK: length of the cutting stroke►CUT SPD: speed of cut (see Table I for settings)►Y-IND: stepping index in Y►Z-IND: distance to be left uncut as measured up from the chuck zero reference point►Theta-IND: angle that the wafer is rotated betwe en cuts done for block1 and for block2The following is a detailed example of the procedure for en tering data:9.3.1 Press the INCH/MM button to select units. The INCH will light to indicate all parameters will be set in inches, while the MM will light to indicate the selecti on of mm (for this exercise choose mm).9.3.2 Press FIX, and the current cutting MODE will be displayed.9.3.3 Press the MODE button until the desired MODE is displayed (for this exercise select A).9.3.4 Press the PROG# key and use the numerickeypads to enter the desired program number (for this examp le enter 1).9.3.5 Press the C (clear) key. This will erase all current parameters entered for the selected program.9.3.6 The CUT STRK LED should now be blinking to indicate that this is the current parameter for programm ing. The first data that you enter will be the value for th e desired cutting pattern, which is square. The cut stroke remains the same length and is equal to the diameter of the wafer. Entering a 0 will give the square pattern. This dat a is shown in the BLOCK display.9.3.7 The CUT-STRK LED should still be blinking to indicate that it is the current parameter for programm ing. The CUT-STRK is usually equivalent to the wafer diamet er, and is the length of the desired cut (the center of the chuck is used to determine where the cut begins; e.g. for a 100mm stroke the cut will begin 50mm to one side of the c enter and continue 50mm beyond the center). Use the keypad to enter the desired value (for this example enter 100 for100 mm).9.3.8 Press the W key to write (enter) the data.9.3.9 The CUT-SPD LED should now be blinking t o indicate that it is the current parameter for programming. Check Table I for the value to enter to get the desired X-axis speed. Use the numeric keypads to enter the desired va lue. For this exercise enter 15. Note: Be careful when sele cting a value to enter as too great a speed will break the blade!9.3.10 Press the W key to write (enter) the data.9.3.11 The Y-IND LED should now be blinking to indi cate that it is the current parameter to program. Use the n umeric keypads to enter the desired cutting index (in mm) f or block1. Be sure to use the decimal point if necessary. F or this example, enter 10.880 (if you are unsure of the cor rect value for the Y-INDEX, you can measure this distance u sing the DATA SEL button as detailed in Section 9.6).9.3.12 Press the W key to write (enter) the data.9.3.13 Y-IND LED is still blinking to indicate that it is waiting to be programmed. Use the numeric keypads to enter the desired cutting index (in mm) for block2. For th is example, enter 10.880. Note: block2 cuts will be the fir st ones made when using the FULL AUTO mode.9.3.14 Press the W key.9.3.15 The Z-IND LED should now be blinking to indi cate that it is the current parameter for programming. Use the numeric keypad to enter the desired value. The value en tered (in mm) is the depth left UNCUT as measured up from t he chuck. Dicing tape thickness of 125 microns should be ta ken into consideration. When using dicing tape, through wat er cuts can be achieved with a Z-index no less than the min imum recommended 0.07 mm. For this exercise, enter 0.15.9.3.16 Press the W key.9.3.17 The Theta-IND LED should now be blinking. Use the numeric key to enter in the desired value for the ang le, which the chuck will rotate, between cuts made for bloc k2 and block1. This value will almost always be 90, so ente r this value.9.3.18 Press the W key. Programming is completed.To view your program, press the SHIFT key successively to d isplay each parameter. If a parameter must be changed, firs t press the C/E key and then re-enter the data. Be sure to press the W key to enter the new data.9.4 Operating ModesThere are two different modes of operation: (1) fully autom atic (FULL AUTO), and (2) semi automatic (SEMI AUTO). Both modes use the currently selected program for determining cu tting parameters.9.4.1 FULL AUTOThe fully automatic mode will cut both channels (after wafe r alignment) as indicated in the following cutting sequence: Channel 1 manual alignment -> Manual rotation to Channel 2 -> Channel 2 manual alignment -> Channel 2 automatic cutti ng -> Automatic rotation to Channel 1 -> Channel 1 automati c cutting. The FULL AUTO button must be on (LED will be lit) while aligning, and cutting is initiated with the START/ST OP button. The blade cooling water turns 'on' at this point. Adjust water flow with the control knob on the rotameter. You can temporarily halt the cutting operation to inspect t he cut by depressing the START/STOP button. This turns cool ing water off. Once the START/STOP button has been depresse d, cutting will continue until the current cut is made all the way across the wafer, then the chuck will move under th e microscope for viewing. Pressing the START/STOP button ag ain will reinitiate cutting and the chuck will automaticall y index to the position for the next cut. Leaving it stoppe d too long may cause it to halt completely and revert to ma nual mode, so be careful to quickly do any required inspect ions.9.4.2 SEMI AUTOSEMI AUTO mode allows you to align each cut before it is ma de, or you can use it to automatically index and cut the wa fer after only a single alignment is made. Note: SEMI AUTO will not automatically rotate the wafer. In SEMI AUTO mode you begin by manually aligning the wafer, then you depress the SEMI AUTO button (water to the blade will begin to spra y at this point). To initiate cutting, press one of the Y m ovement arrows. Adjust water flow with rotameter control kn ob. Cutting will begin along the same path by which you ali gned the wafer, and will then automatically index in the sa me direction as the Y movement arrow you used to initiate c utting. If you wish to halt the cutting process, depress ei ther of the following buttons: SEMI AUTO, REPEAT, INDEX, or JOG/SCAN (for the Y axis). The blade will continue the cut across the wafer then the chuck will move under the scope for viewing. The cooling water will stop. You can then use the INDEX and Y arrow buttons (which will move the chuck in the selected Y direction the amount which is stored for th e Y-IND in the current program) or JOG/SCAN to move the waf er to the next desired position, align the wafer and make a nother cut. This process can be repeated as many times as desired.9.4.3 Align the microscope cross hair to the b lade.Note: The two knobs near the microscope on the disco a re (1) focus and (2) front-back kerf width adjustment (if t he cut is not being made where the microscope says it shoul d be). Lab techs suggest users never touch the kerf adjustm ent. It's almost never necessary to use the focus either.9.5 Wafer AlignmentAfter entering your program and deciding on the type of ope rating mode to use, the next step is to prepare your wafer for dicing.Dicing tape can be used with hoops (snap ring set) to bette r control the dicing process. A set of dicing hoops (an inn er hoop and an outer hoop) will hold the dicing tape tightl y over the hoops. First, place a square of dicing tape, adh esive side up on the inner loop. Second, force the outer hoop over the inner hoop from the adhesive side of the dicing tape. The result should be a tight surface of dicing tape ready to accept a wafer. Please do not take the dicing ring s (hoops) away from the disco station. Snap rings and dicin g tape should be kept in 432C, the room adjacent to the Dis co station.Now place your wafer on the chuck and align it precisely:9.5.1 For FULL AUTO mode, depress the FULL AUT O button (LED will light).9.5.2 With the VACUUM off, center your wafer o n the chuck.9.5.3 Depress the VACUUM button to turn on vac uum (LED will light) to the wafer and check the vacuum gaug e--it should be in the green range with a wafer on the chuc k.9.5.4 Maneuver the microscope over the wafer (the scope will be positioned over the center of the chuckautomatically if FULL AUTO is enabled when you turn on the VACUUM).9.5.5 Use the Theta JOG/SCAN and arrow buttons to align your wafer in theta. Be sure to press the arrow b utton, which is outlined in green last, as this enters the position into the Disco's memory.9.5.6 Use the Y-Axis JOG/SCAN and arrow button s to precisely align your wafer in Y. Be sure to press the arrow button, which is outlined in green last, as this will enter the position into the Disco's memory. For SEMI AUTO, you are now ready to begin cutting by pressing the SEMI AU TO button (water to the blade will begin to spray), and the desired Y arrow button.9.5.7 For FULL AUTO mode, depress ROTATION and one of the theta direction arrows to rotate the wafer in p reparation for block2 alignment. Repeat steps 9.5.5 and 9.5.6 for precise alignment. (Remember to press the arrow butto n, which is outlined, in green last!) Press the START/STOP button to initiate automatic cutting.9.6 Measuring Distance Along the Y-AxisIf you are unsure of the precise value to enter for the Y-I ND, the Disco has a feature, which allows you to measure di stances along the Y-Axis as detailed in the following:9.6.1 Using the Y and Theta JOG/SCAN arrows, p osition your wafer at the desired starting point for beginn ing measurements.9.6.2 Press the DATA SEL button.9.6.3 Press the 1 button on the numeric keyboa rd. The data panel will now display zeros to indicate that this is the zero starting point.9.6.4 Make sure that the Y JOG/SCAN is enabled (LED will be lit), and use the arrow buttons to move the w afer to the desired measurement location.9.6.5 Data displayed on the panel is the measured Y-Axis movement in mm (or inches if this is the selecte d unit option). A negative value indicates that movement is toward the front of the machine, while positive indicates movement to the rear.9.6.6 Record this value (it will disappear whe n you disable this feature) for use when programming Y-IND.9.6.7 Press the SHIFT button to disable the Y-Axis distance measurement feature.9.7 Actions Dangerous to DiscoBe sure that you understand the following ways that the mac hine can be damaged, and be careful not to make these mista kes:9.7.1 The air-bearing spindle can be galled and ruined if it is rotated by hand when the 80 psi air is no t on. For example, if you change the blade without first tu rning on the power to the machine (so air flows to the spin dle), the bearing surfaces will rub against each other andbe damaged. So the first thing you must always do before to uching the spindle is to turn on the power, and wait a few seconds for the air pressure to come up.9.7.2 If you try to make a cut that is deeper than the length of the blade, then the flange will ride up on the substrate being cut, and the spindle may spin inside the hub and become galled. Blades become shorter with use, so inspect the blade before use to make sure that it is lo nger than the cut depth you need.9.7.3 If you change the blade and then start t o cut without redoing the set-up, you may cut into the tabl e (if the new blade is longer than the old one), or the fla nge may hit the wafer if the new blade is shorter than the old one.9.7.4 The needle on the chuck vacuum gauge sho uld be in the blue area. If it is in the red, the wafer may not be held adequately and can be moved by the force of cu tting. This will break the blade.9.8 Shut-Down ProceduresWhen finished with the saw, please shut it down as follows:9.8.1 Press the SPINDLE button to bring the sp indle to a controlled stop (LED will go out).9.8.2 Press the ILLUMINATION button to disable the lights to the microscope (LED will go out).9.8.3 After the spindle has stopped, press EM STOP. This will raise the blade up out of the way.9.8.4 Clean and dry the chuck and surrounding area with clean wipes. Be careful not to hit and damage the blade!9.8.5 Turn off the AUTOBREAKER CONTROL switche s (DOWN position).9.8.6 Disable disco on the wand.9.9 Final Blade Inspection Before Leaving the DiscoThe blade will wear while you are using it. It will be shor ter, and may be partially broken, so you must give it the s ame close inspection when leaving the saw that you did when arriving and making sure that the blade is ok to use. If t he blade is bad (as explained below) it is your responsibil ity to change it before you leave the saw.9.9.1 Blade LengthIf the blade length is less than 0.5 mm it should be thrown away since the next user may try to cut through a wafer th at is thicker than this. Then the hub would hit the wafer, and break it, and gall the shaft. The rate at which blade l ength wears away increases with feed rate, so if you want t o maximize blade life, select a slower traverse speed.9.9.2 Broken BladesReport broken blades using FAULTS when spares are not available to the next user.Sometimes sections of the blade get knocked out, but the re st of the blade is still intact. If a replacement blade is available, the broken blade should be replaced. If no repla cement is available (as when the office is locked on weeken ds), a broken blade can still be used. It is weaker, so a s lower traverse speed should be used to keep it from breakin g completely.When handling the blades, remember to only touch the hub. I f you touch the cutting edge, or hit it against something, you can bend it or knock pieces of it out.10.0 Troubleshooting Guidelines11.0 Figures and Schematics12.0 AppendicesIMPORTANT NOTEFor the resin-bonded (black) blade, cut speed must be 2 mm/ sec or less (speed value of 7 or lower).For the metal-bonded (shiny) blade, cut speed must be 10 mm /sec or less (speed value of 15 or lower).DISCO Study GuideBe sure to know...1. Start-up and Pre-Start-up procedures.2. Setting up the Z-axis zero position.3. Cutting in different modes.4. Changing the blade.5. Safety for the user.6. Actions "dangerous to disco".7. Choosing the correct blade.8. Blade-related problems and troubleshoo ting.9. Cutting all the way through a wafer, c utting thick wafers.10. Starting and stopping the spindle.11. When to use Set-up.12. Minimum Z-index, air pressure, water flow.13. Entering the program.14. Shutdown procedure.15. Aligning the optics.16. Troubleshooting the display.17. Choosing a reasonable cut speed划片机作业手册-----迪斯科自动切割锯9890501发表于：2005-11-26 22:17来源：半导体技术天地（迪斯科）1.0标题迪斯科自动切割锯2.0目的迪斯科全自动切割锯用于切割半导体晶圆切割成单个芯片或骰子是一种精密的机器。

∗ †
E-mail address: ikishimo@post.kek.jp E-mail address: tomo@asuka.phys.nara-wu.ac.jp
1
Introduction
String field theory is established as a framework for exploring nonperturbative structures in string theory. Motivated by Sen’s conjecture [1, 2], many people studied classical solutions extensively and intriguing results were provided in bosonic open string field theory [3, 4]. In the supersymmetric case, the most promising theory is formulated in terms of the Wess-ZuminoWitten (WZW) like action proposed by Berkovits [5, 6], which has no problem with contact term divergences [7]. This open superstring field theory is a sufficient framework to elucidate nonperturbative phenomena of the Neveu-Schwarz (NS) sector. Indeed, the tachyon vacuum and kink solutions were found in the superstring field theory by using the level truncation scheme [6, 8, 9, 10, 11]. On the analytical side, there are some attempts to construct exact solutions in terms of a half string formulation [12], a pregeometrical formulation [13, 14], a conjecture of vacuum superstring field theory [15, 16, 17, 18, 19] and an analogy with integrable systems [20]. In the present paper we construct analytic classical solutions in the open superstring field theory using techniques developed in bosonic open string field theory [21, 22, 23]. The resulting solution consists of the identity string field, ghost fields and an operator associated with a current. Taking ∂X (z ) as the current, we find that the action expanded around the solution can be transformed to the original action by a string field redefinition. In the redefined theory, however, the momentum is shifted in the string field and then the classical solution can be related to a background Wilson line. Generically, we anticipate that our solutions correspond to marginal boundary deformed backgrounds as in the bosonic case. The analytic solutions are useful for studying gauge structure in string field theory. In bosonic string field theory, the analytic solution corresponding to Wilson lines can be represented as a “locally” pure gauge, and then we find that a “locally” pure gauge configuration in string field theory corresponds to a marginal deformation in conformal field theory [21, 22, 23]. This correspondence is a natural generalization of that of low energy effective theories. Later we will see that the solution in the superstring field theory shares this feature of the bosonic theory. Marginal deformations in string field theory were often studied using the level truncation scheme. We see that the effective potential for a marginal field becomes flatter as the truncation level is increased [24, 25, 26, 27, 28, 29], and then the vacuum energy of the analytic solution must vanish. Unfortunately, we encounter a difficulty in calculating the vacuum energy in the bosonic theory. Though the vacuum energy formally vanishes, it is given as a kind 1

This bound is usually interpreted as a bound on the vacuum energy density in QFT1 : |ρvac | < 10−29 g/cm3 ∼ 10−47 GeV 4 ∼ 10−9 erg/cm3 (3)
By contrast, theoretical estimates of various contributions to the vacuum energy density in QFT exceed the observational bound by at least 40 orders of magnitude. This large discrepancy constitutes the cosmological constant problem. More generally, one can distinguish at least three different meanings to the notion of a cosmological constant problem: 1. A ‘physics’ problem: QFT vacuum ↔ Λ. Various contributions to the vacuum energy density are estimated from the quantum field theories which describe the known particles and forces. The vacuum energy density associated with these theories is believed to have experimentally demonstrated consequences and is therefore taken to be physical real. The cosmological implications of this vacuum energy density follows when certain assumptions are made about the relation between general relativity and QFT. 2. An ‘expected scale’ problem for Λ. Dimensional considerations of some future theory of quantum gravity involving a fundamental scale – e.g. the Planck scale – lead physicists to expect that the cosmological constant, as well as other dimensional quantities, is of the order ∼ 1 in Planck units (for example, Λ should be of the order of Planck energy densities).2 3. An ‘astronomical’ problem of observing Λ. Astronomers and cosmologists may refer to the ‘cosmological constant problem’ as a problem of whether a small cosmological constant is needed to reconcile various cosmological models with observational data. Although we will indicate how these different notions of the cosmological constant problem are related, we shall in this paper be almost exclusively concerned with the first of these formulations. Accordingly, when we refer to the term ‘cosmological constant problem’ we normally mean 1. In this manuscript we critically discuss the origin of the QFT vacuum concept (see also [48, 49]), and attempt to provide a conceptual and historical clarification of the cosmological constant problem. The paper is organized as follows: We first trace the historical origin of the cosmological constant problem in the QFT context. We

This means there are more shakes in a second. (b) Humans have existed for a fraction of 106 years/1010 years = 10−4 . That fraction of a day is 10−4 (24 hr) 60 min 1 hr 60 s 1 min = 8.64 s.
The percentage error of the approximation is then 3.1416 × 107 s − 3.1558 × 107 s = −0.45 %. 3.1558 × 107 s E1-6 (a) 10−8 seconds per shake means 108 shakes per second. There are 365 days 1 year 24 hr 1 day 60 min 1 hr 60 s 1 min = 3.1536 × 107 s/year.
2
E1-8 We will wait until a day’s worth of minutes have been gained. That would be (24 hr) 60 min 1 hr = 1440 min.
The clock gains one minute per day, so we need to wait 1,440 days, or almost four years. Of course, if it is an older clock with hands that only read 12 hours (instead of 24), then after only 720 days the clock would be correct. E1-9 First find the “logarithmic average” by log tav = = = Solve, and tav = 54.8 seconds. E1-10 After 20 centuries the day would have increased in length by a total of 20 × 0.001 s = 0.02 s. The cumulative effect would by the product of the average increase and the number of days; that average is half of the maximum, so the cumulative effect is 1 2 (2000)(365)(0.02 s) = 7300 s. That’s about 2 hours. E1-11 Lunar months are based on the Earth’s position, and as the Earth moves around the orbit the Moon has farther to go to complete a phase. In 27.3 days the Moon may have orbited through 360◦ , but since the Earth moved through (27.3/365) × 360◦ = 27◦ the Moon needs to move 27◦ farther to catch up. That will take (27◦ /360◦ ) × 27.3 days = 2.05 days, but in that time the Earth would have moved on yet farther, and the moon will need to catch up again. How much farther? (2.05/365) × 360◦ = 2.02◦ which means (2.02◦ /360◦ ) × 27.3 days = 0.153 days. The total so far is 2.2 days longer; we could go farther, but at our accuracy level, it isn’t worth it. E1-12 (1.9 m)(3.281 ft/1.000 m) = 6.2 ft, or just under 6 feet, 3 inches. E1-13 (a) 100 meters = 328.1 feet (Appendix G), or 328.1/3 = 10.9 yards. This is 28 feet longer than 100 yards, or (28 ft)(0.3048 m/ft) = 8.5 m. (b) A metric mile is (1500 m)(6.214 × 10−4 mi/m) = 0.932 mi. I’d rather run the metric mile. E1-14 There are 300, 000 years 365.25 days 1 year 24 hr 1 day 60 min 1 hr 60 s 1 min = 9.5 × 1012 s 1 log(5 × 1017 ) + log(6 × 10−15 ) , 2 1 log 5 × 1017 × 6 × 10−15 , 2 √ 1 log 3000 = log 3000 . 2

Abstract The main principles of two-dimensional quantum field theories, in particular two-dimensional QCD and gravity are reviewed. We study non-perturbative aspects of these theories which make them particularly valuable for testing ideas of four-dimensional quantum field theory. The dynamics of confinement and theta vacuum are explained by using the non-perturbative methods developed in two dimensions. We describe in detail how the effective action of string theory in non-critical dimensions can be represented by Liouville gravity. By comparing the helicity amplitudes in four-dimensional QCD to those of integrable self-dual Yang-Mills theory, we extract a four dimensional version of two dimensional integrability.
2 48 49 52 54 56
5 Four-dimensional analogies and consequences 6 Conclusions and Final Remarks

{"001 [] CIF30 input/output communication error"}, 输入输出及通讯报警信息.{"002 [0E09] Auxiliaries circuits not active - W1"}, 辅助启动没被激活.{"003 [0E12] Insufficient air pressure - W1"}, 压缩空气压力不足{"004 [0E13] Insufficient main vacuum - W1"}, 真空环境未满足{"005 [] The Machine is running"}, 设备正在运行{"006 [0E05] Printer safety covers open (PRINT) - W1"}, 安全门打开(无法运行){"007 "},{"008 [2E07] Oven safety covers open (OVEN) - W1"}, 烘箱安全盖打开{"009 [1E03] Loader unit safety cover close (LOAD) - W1"}, 上料安全门关闭{"010 [FILE] Error in accessing DATA file"}, 获取数据文件有误{"011 [FILE] Error in accessing AXIS (axis parameter file)"}, 获取轴参数文件有误{"012 "},{"013 [Vis] Alarm vision system"}, 视觉系统报警{"014 [Axis] Error with remote status request ELMO"}, 报警与远程状态请求elmo{"016 [Axis] Check page 42-Elmo Manual; Error with ELMO MG "},请检查第4-2 elmo手册;检查电机{"018 [] Machine A hasn't been reset"}, 设备A无法复位{"019 [] Machine B hasn't been reset"}, 设备B无法复位{"021 End of roll paper on left table"},纸偏左{"022 End of roll paper on right table"}, 台纸偏右{"023 Paper is cut on friction roll (left table)"}, 左台纸剪切发生磨擦{"024 Paper is cut on friction roll (right table)"}, 右台纸剪切发生磨擦{"027 [] Machine A hasn't been reset"}, 设备A没有复位{"028 [] Machine B hasn't been reset"}, 设备B没有复位{"030 [] Machine A Stopped"}, 设备A停止{"031 [] Machine B Stopped"}, 设备B停止{"032 [] Machine A in MANUAL mode"}, 设备A在手动模式{"033 [] Machine B in MANUAL mode"}, 设备B在手动模式{"034 [] Machine A in STEP by STEP mode"}, 设备A在步进模式{"035 [] Machine B in STEP by STEP mode"}, 设备B在步进模式{"049 [1E06] Up sucker sensor (LOAD) - W0"}, 上料抓手上位传感器{"050 [21MG] Print Table Axis Homing"}, 旋转电机复位原点{"051 [22MG] Print Head X Axis Homing"}, 印刷头X轴复位原点{"052 [23MG] Print Head Y Axis Homing"}, 印刷头Y轴复位原点{"053 [24MG] Print Head THETA Axis Homing"}, 印刷头THETA轴复位原点{"054 [25MG] Print Head Z Axis Homing"}, 印刷头Z轴复位原点{"055 [26MG] Squeegee Input/Output Axis Homing"}, 刮刀前/后复位原点{"056 [27MG] Squeegee Up/Down Axis Homing"}, 刮刀上/下复位原点{"061 [10MG] Print Walking Beam Axis Homing"}, 印刷上料行走臂电机复位原点{"062 [28MG] Oven Walking Beam Axis Homing"}, 烘箱行走臂电机复位原点{"063 [29MG] Oven Front Clamps Axis Homing"}, 烘箱前抓手复位原点{"064 [30MG] Oven Rear Clamps Axis Homing"}, 烘箱后抓手复位原点{"067 [36MG] Input Walking Beam Axis Homing"}, 输入行走臂电机复位原点{"068 [31MG] Oven Clamps Up/Down Axis Homing"}, 烘箱抓手上/下电机复位原点{"069 [12MG] Right Pickup Front Clamp 1 Axis Homing"},电机右前抓手"1"复位到原点{"070 [13MG] Right Pickup Rear Clamp 1 Axis Homing"}, 电机右后抓手"1"复位到原点{"071 [14MG] Right Pickup Front Clamp 2 Axis Homing"}, 电机右前抓手"2"复位到原点{"072 [15MG] Right Pickup Rear Clamp 2 Axis Homing"}, 电机右后抓手"2"复位到原点{"073 [17MG] Left Pickup Front Clamp 1 Axis Homing"}, 电机左前抓手"1"复位到原点{"074 [18MG] Left Pickup Rear Clamp 1 Axis Homing"}, 电机左后抓手"1"复位到原点{"075 [19MG] Left Pickup Front Clamp 2 Axis Homing"}, 电机左前抓手"2"复位到原点{"076 [20MG] Left Pickup Rear Clamp 2 Axis Homing"}, 电机左后抓手"2"复位到原点{"079 [36MG] Magazine Up/Down Axis Homing"}, 承载盒上下复位到原点{"105 [1E10] Piece presence on walking beam (LOAD) - W1"}, 上料行走臂后短上有硅片{"106 [1E10] Piece presence on walking beam (LOAD) - W0"}, 行走臂上前短有硅片{"107 [1E01] Magazine unit in backward position (LOAD) - W1"},承载盒位置靠后{"108 [1E02] Magazine unit in forward position (LOAD) - W1"}, 承载盒位置靠前{"109 [] Waiting to screen blocked"}, 等待锁网版{"110 [] Waiting to CYCLE START"}, 等待周期开始{"111 [] Waiting to CYCLE RESET"}, 等待周期复位{"112 [] Waiting to RESET ALARM"}, 等待报警复位// {"115 [1E06] Pickup suckers up (LOAD) - W1"}, 上料吸片抓手高位{"116 [0E14] Walking beam up (PRINT) - W1"}, 行走臂高位{"117 [0E15] Walking beam down (PRINT) - W1"}, 行走臂低位{"123 [0E31] Item 2 automatic cycle - W1"}, 2道自动循环{"124 [0E28] Item 2 position OK - W1"}, 2道的位置确定{"125 [0E29] Item 2 piece request - W1"},2道硅片请求{"126 [0E29] Item 2 piece request - W0"} ,2道硅片请求{"127 [1E04] Upper piece presence on magazine (LOAD) - W1"},承载盒上有硅片{"128 [] Magazine empty (LOAD)"}, 上料承载盒为空{"129 [] Wait magazine on loader unit (LOAD)"}, 上料等待承载盒进装载单元{"130 [1E01] Magazine unit in backward position (LOAD) - W1"},上料承载盒在靠后位置{"131 [1E02] Magazine unit in forward position (LOAD) - W0"},上料承载盒在靠前位置{"132 [1E09] Double piece presence on walking beam (LOAD) - W0"},两片硅片在行走臂上{"133 [1E07] Pickup in walking beam position (LOAD) - W1"}, 抓手在行走臂位置{"134 [1E08] Pickup in magazine position (LOAD) - W1"}, 抓手在承载盒位置{"135 [1E05] Magazine presence on loader unit (LOAD) - W1 change magazine"},承载盒在进料单元，换盒{"145 [0E36] Walking beam up (OVEN) - W1"}, 烘箱行走臂上位{"146 [0E37] Walking beam down (OVEN) - W1"}, 烘箱行走臂下位{"148 [2E00] Forward pickup clamps at 0 pos. (OVEN) - W1"}, 烘箱前抓手在O位{"149 [2E01] Backward pickup clamps at 0 pos. (OVEN) - W1"}, 烘箱后抓手在O位{"150 [2E04] Driving motor fault (OVEN) - W1"}, 烘箱启动电机失败{"151 [2E05] Motor at correct step (OVEN) - W1"}, 烘箱电机运行正常{"152 [2E05] Motor at correct step (OVEN) - W0"}, 烘箱电机运行正常{"153 [2E06] Motor slow speed (OVEN) - W1"}, 烘箱电机低速运转{"154 [2E06] Motor slow speed (OVEN) - W0"}, 烘箱电机低速运转{"160 [Cal] Camera calibration calculation error"}, 摄像校对计算误差{"161 [Cal] Linear calibration error during camera calibration"}, 摄像线型校对有误{"162 [Cal] Angular calibration error during cameracalibration"},摄像角校正有误{"163 [All] Alignment error"}, 对准有误{"164 [Cal] Calibration error"}, 较准有误{"165 [2E09] Oven max temperature - W1"}, 烘箱最大温度{"166 [Oven] Waiting to reach temperature oven"}, 等待到达烘箱设定温度{"167 [Oven] Alarm sensor channel A"}, 报警传感器A道{"168 [Oven] Alarm sensor channel B"}, 报警传感器B道{"169 [Oven] Alarm sensor channel C"}, 报警传感器C道{"170 [Oven] Alarm sensor channel D"} 报警传感器D道{"173 [2E10] Fan motor fault (oven) - W1"}, 烘箱电机风扇故障{"174 [2E11] Clogged filter switch (oven) - W0"}, 过滤器开关堵塞{"184 [Oven] Max temperature alarm channel A"}, 传感器A道最大温度报警{"185 [Oven] Max temperature alarm channel B"}, 传感器B道最大温度报警{"186 [Oven] Max temperature alarm channel C"}, 传感器C道最大温度报警{"187 [Oven] Max temperature alarm channel D"}, 传感器D道最大温度报警{"192 [Oven] Oven temperature cycle in progress"}, 烘箱进行温度循环{"193 [Oven] Oven temperature cycle finished"}, 烘箱温度循环结束{"195 [Paper] Left paper algoritm alarm"}, 左台纸算法报警{"196 [Paper] Right paper algoritm alarm"}, 右台纸算法报警{"198 [Print] Reset MACCHINE A in progress"}, MACCHINE A正在复位{"199 [Oven] Reset MACCHINA B in progress"}}; MACCHINE B正在复位"0 Elmo Driver NON OPERATIONAL", 驱动板卡报警信息"1 Power supply under voltage", 供电电压低于所需电压"2 Power supply over voltage", 供电电压高于所需电压"3 Motor short circuit", 电机短路"4 Amplifier overheating", 放大器过热"5 Motor failure", 电机故障"6 Current limit (LC)", 电流受限"7 Stack overflow or CPU exception", 堆栈溢出或CPU异常"8 Stopped by a limit switch", 限压停止"9 Main encoder error", 主编码器错误"10 Auxiliary encoder error", 辅助码器错误"11 The peak current has been exceeded", 超过峰值电流"12 External inhibit", 外围受限"13 Digital hardware failure", 数码硬件故障"14 Digital hall sensor", 数字化霍尔传感器"15 Speed error exceeded", 超速"16 Position error exceeded", 超过位置误差"17 Inconsistent database", 数据库数据记录不统一// "18 Life guarding failure", 生命保卫失效"19 Failed to find electrical zero", 找不到零点"20 Speed limit exceeded", 超速"21 Position limit exceeded",超过位置误差"22 Cannot tune the current offsets", 不能调动目前的偏差"23 Time-out PDO2 message",PDO2 无信息输出"24 Motor hardware fault", 电机硬件故障"25 Position positive limit exceeded", 设备位置超出上限受限位置"26 Position negative limit exceeded", 设备位置超出下限受限位置"27 Wait axis in position window", 等待电机在复位原点位置窗口"28 CAN communication error", 扫描通讯错误"29 Error PDO2 message code:" pdo2讯息代码错误。

a r X i v :1006.2321v 1 [a s t r o -p h .C O ] 11 J u n 2010Mon.Not.R.Astron.Soc.000,000–000(0000)Printed 14June 2010(MN L A T E X style file v2.2)Gravitational lensing in a non-uniform plasmaG.S.Bisnovatyi-Kogan 1,2⋆and O.Yu.Tsupko 1,2⋆1Space Research Institute of Russian Academy of Sciences,Profsoyuznaya 84/32,Moscow 1179972NationalResearch Nuclear University MEPhI,Kashirskoe Shosse 31,Moscow 115409,Russia14June 2010ABSTRACTWe develop a model of gravitational lensing in a non-uniform plasma.When a grav-itating body is surrounded by a plasma,the lensing angle depends on the frequency of the electromagnetic wave,due to dispersion properties of plasma,in presence of a plasma inhomogeneity,and of a gravity.The second effect leads,even in a uniform plasma,to a difference of the gravitational photon deflection angle from the vacuum case,and to its dependence on the photon frequency.We take into account both effects,and derive the expression for the lensing angle in the case of a strongly nonuniform plasma in presence of the gravitation.Dependence of the lensing angle on the pho-ton frequency in a homogeneous plasma resembles the properties of a refractive prism spectrometer,which strongest action is for very long radiowaves.We discuss the ob-servational appearances of this effect for the gravitational lens with a Schwarzschild metric,surrounded by a uniform plasma.We obtain formulae for the lensing angle and the magnification factors in this case and discuss a possibility of observation of this effect by the planned VLBI space project Radioastron.We also consider models with a nonuniform plasma distribution.For different gravitational lens models we compare the corrections to the vacuum lensing due to the gravitational effect in plasma,and due to the plasma inhomogeneity.We have shown that the gravitational effect could be detected in the case of a hot gas in the gravitational field of a galaxy cluster.Key words:gravitation –gravitational lensing:strong –gravitational lensing:weak –gravitational lensing:micro –plasmas.1INTRODUCTIONThe photon deflection angle in vacuum,in the Schwarzschild metric with a given mass M ,is determined,for small deflec-tion angles ˆα≪1,by a formula ˆα=4GMb ,(1)where b is the impact parameter,and b ≫R S ,R S =2GM/c 2is the Schwarzschild radius (Landau &Lifshitz 1993;Misner,Thorne &Wheeler 1973;Schneider,Ehlers &Falco 1992).When the impact parameter is close to its critical value,corresponding to the capture of the photon by the black hole,the expression for the deflection angle is more complicated (Darwin 1959;Misner et al.1973;Virbhadra &Ellis 2000;Bozza et al.2001;Bisnovatyi-Kogan &Tsupko 2008).It is interesting to consider the gravitational lensing in a plasma,because in space the light rays mostly propagate through this medium.In an inhomogeneous plasma pho-tons move along the curved trajectories,because a plasma⋆E-mail:gkogan@iki.rssi.ru (GSBK);tsupko@iki.rssi.ru (OYuT)is a dispersive medium with a permittivity tensor depend-ing on its density (Landau &Lifshitz 1960).In the disper-sive nonuniform medium a photon trajectory depends also on the photon frequency,and this effect has no relation to the gravity.The photon deflection in a non-homogeneous plasma,in presence of gravity,has been considered by Bliokh &Minakov (1989),Muhleman,Ekers &Fomalont (1970),Lightman et al.(1979).The consideration was done in a linear approximation,when the two effects:the vacuum deflection due to the gravitation,and the deflection due to the non-homogeneity of the medium,have been considered separately.The first effect is achromatic,the second one de-pends on the photon frequency if the medium is dispersive,but equals to zero if the medium is homogeneous.A general theory of the geometrical optics in a curved space-time,in arbitrary medium,is presented in the book of Synge (1960).On the basis of his general approach we have developed the model of gravitational lensing in plasma.In our previous work (Bisnovatyi-Kogan &Tsupko 2009)we have shown,that in a nonlinear approach a new effect ap-pears.Even in the homogeneous plasma,the gravitational deflection angle really depends on the frequency of the pho-ton,and is different from the vacuum case.We have derived2G.S.Bisnovatyi-Kogan and O.Yu.Tsupkothe expression for the deflection angle of the photon in a weak gravitationalfield,in a weakly inhomogeneous plasma.In this work we use more general approach and derive the deflection angle for the photon moving in a weak grav-itationalfield,in the Schwarzschild metric,in the arbitrary inhomogeneous plasma.Such approach is more appropriate for the propagation in a cosmic plasma,because plasma den-sity changes significantly,from the density of the interstel-lar medium to the density of a black hole neighborhood. We consider here only the situation,when the whole deflec-tion angle,from the combined plasma and gravity effects, remains small.In the section2we derive a general expres-sion for the deflection angle in the inhomogeneous plasma,in the curved space-time.In the section3we discuss in details the important case of the weak Schwarzschildfield with a spherically symmetric distribution of plasma,and derive the formula for the deflection in this situation.Our approach al-lows us consider two effects simultaneously:the difference of the gravitational deflection in plasma from the vacuum case and the non-relativistic effect(refraction)connected with the plasma inhomogeneity.In the paper of Kulsrud&Loeb (1992)it was shown that in the homogeneous plasma the photon wave packet moves like a particle with a velocity equal to the group velocity of the wave packet,and with a mass equal to the plasma frequency.In the section4we show,that our result for a homogeneous plasma follows also from this approach.In the section5we discuss the obser-vational appearances for a Schwarzschild point-mass lens, surrounded by a uniform plasma(effect of gravitational ra-diospectrometer).In particular,we obtain formulae for the magnification factors in this case.We also estimate a pos-sibility of observation of this effect by the planned VLBI space project Radioastron.In the section6we consider the models with the nonuniform plasma distribution.For differ-ent gravitational lens models we compare the corrections to the vacuum lensing due to the gravity effect in plasma and due to the plasma inhomogeneity.After the publication of our previous work (Bisnovatyi-Kogan&Tsupko2009)two papers con-cerning the effect of amplification of gravitational deflection in dispersive medium were published(Dressel et al.2009; Linet2009).These papers have nothing to do with as-trophysics,authors calculate the vertical deflection of a light ray in a medium with strong frequency-dependent dispersion in a uniform gravitationalfield,and estimate such effect for the laboratory experiments with the Earth gravity.In the paper of Linet(2009)the Synge method of calculation is used.2DEFLECTION ANGLE IN THEINHOMOGENEOUS PLASMA INPRESENCE OF GRA VITYLet us consider a static space-time with a metric ds2=g ik dx i dx k=gαβdxαdxβ+g00 dx0 2,(2) i,k=0,1,2,3,α,β=1,2,3.Here g ik does not depend on time.Let us assume that the gravitationalfield is weak,so we can writeg ik=ηik+h ik,h ik≪1,h ik→0under xα→∞.(3)Hereηik is theflat space metric(−1,1,1,1),and h ik is a small perturbation.Note(Landau&Lifshitz1993),that g ik=ηik−h ik,ηik=ηik,h ik=h ik.(4) Let us consider,in this gravitationalfield,a static inhomo-geneous plasma with a refraction index n,which depends on the space location xα,and the photon frequencyω(xα):n2=1−ω2em=K e N(xα).(5)Hereω(xα)is the frequency of the photon,which depends on the space coordinates x1,x2,x3due to the presence of the gravitationalfield(gravitational red shift).We denote ω(∞)≡ω,e is the charge of the electron,m is the electron mass,ωe is the electron plasma frequency,N(xα)is the elec-tron concentration in inhomogeneous plasma,and we do not assume that N(∞)=0.The optics in a curved space-time,in a medium,was developed by Synge(1960).It was shown that,for the static case,the connection between the phase velocity u,and a4-vector of the photon momentum p i,using of the refraction index of medium n,n=c/u,is written asc2(p0√(p0)2,(7)and obtain the usual relation between the space and time components of the4-vector of the photon (Landau&Lifshitz1960;Zhelezniakov1977;Ginzburg 1970),(pα)2=n2(p0)2.(8) For a static medium in a static gravitationalfield,we have (Synge1960,see also Møller1972):p0 −g00=−1c¯hω,(10)whereω≡ω(∞).The components of the4-vector p i,during an arbitrary motion in a non-homogeneous medium,in aflat space are written asp i=(p0,pα)= ¯hωc eα ,p i=(p0,pα)=−¯hωc eα,n2=1−ω2eGravitational lensing in a non-uniform plasma3where e α=p α/p and e α=p α/p (p =c 2√c 2√c 2c 2,v 2ef f =p 2c 2ω2(x α)c 2=n 2c 2.(12)Thus the effective photon velocity equals to the group ve-locity of the photon in plasma v gr =∂(nω)−g 00c p 0,(14)p ef f =c 2−m 2ef f c2=n ¯h ω(x α)2g ij p i p j −(n 2−1) p 0dλ=∂Wdλ=−∂W2g ij p i p j +ω2e ¯h 2dλ=g αβp β,dp α2g ij ,αp i p j −1c 2ω2e,α,(19)or dx αdλ=−12g 00,αp 20−1c 24πe 2c,0,0,n ¯h ωc,0,0,n ¯h ωdλ=n ¯h ωn ¯h ω.(22)The deflection angle is determined by achange of 3-vectore α,so let us express the second equation in (20)through the e α.We obtain successively n ¯h ωdz=−12g 00,αp 20−1c 2K e N ,α,(23)d (ne α)dz+nde αdz=−e αdn2c 2c 2K e N ,α.(25)In the right hand side of this equation we use the componentsfrom (21).We are interested in the components of 3-vector e α,e 3=1,which are orthogonal to the initial direction of the propagation,at α=1,2.In the right hand side of (25)we use the null approximation with e α=ing (4),we obtain:de α2c 2c 2+h 00,α¯h2ω2c 2K e N ,α,(26)de α2h 33,α+1n 2ω2K e N ,α.(27)And for the deflection angle ˆαα=e α(+∞)−e α(−∞)weobtain:ˆαα=11−(ω2e /ω2)−K e N ,α2∞−∞(h 33,α+h 00,α)dz,α=1,2.(29)4G.S.Bisnovatyi-Kogan and O.Yu.TsupkoFor the axially symmetric problem,it is convenient to introduce the impact parameter b relative to the point mass,which remains constant in the null approximation for the photon moving along the axis z .The plasma has a spherically-symmetric distribution around the point mass,with the concentration N =N (r ).In the axially symmet-ric situation the position of the photon is characterized by b and z ,and the absolute value of the radius-vector is r = b 2+z 2.We have the following ex-pression for the deflection angle in the plane perpendicular to direction of the unperturbed photon trajectory:ˆαb =1r ××dh 331−(ω2e /ω2)dh 00ω2−ω2edN (r )1−R S /r+r 2(dθ2+sin 2θdϕ2).(31)In theweak field approximation this metric is written as (Landau &Lifshitz 1993)ds 2=ds 20+R Sr,h αβ=R Srcos 2θ.(33)Here s αis a unit vector in the direction of the radius-vector r α=(x 1,x 2,x 3),the components of which are equal to directional cosines,the angle θis the polar angle be-tween 3-vector r α=r α,and z -axis,and s 3=cos θ=z/r =z/√b−11−(ω2e /ω2)R S bω2−ω2ebdrdz.(34)To demonstrate the physical meaning of different termsin (34),we write this expression under condition 1−n =ω2e /ω2≪1.Carrying out the expansion of terms with the plasma frequency,we obtain:ˆαb =−2R S2R S br 3dz −−1ω2∞−∞1drdz −1ω4∞−∞ω2edrdz.(35)The first term is a vacuum gravitational deflection.The second term is an additive correction to the gravitational deflection,due to the presence of the plasma.This term is present in the deflection angle both in the inhomoge-neous and in the homogeneous plasma,and depends on the photon frequency.The third term is a non-relativistic de-flection due to the plasma inhomogeneity (the refraction).This term depends on the frequency,but it is absent if the plasma is homogeneous.The forth term is a small additive correction to the third term.If we use the approximation1−n =ω2e /ω2≪1,and neglect small second and the forth terms,we obtain a separate input of the two effects:the vacuum gravitational deflection,and the refraction deflec-tion in the inhomogeneous plasma.Calculation of the re-fraction deflection for a power-law concentration was given in our previous work (Bisnovatyi-Kogan &Tsupko 2009),see also Bliokh &Minakov (1989),Muhleman et al.(1970),Thompson et al.(1994),Lightman et al.(1979).Note that the refraction in the inhomogeneous plasma with N (r )=N 0(R 0/r )h ,where N 0=const,R 0=const,h =const =0,leads to the refraction deflection angle αr ,which is oppo-site to the gravitational deflection (Bliokh &Minakov 1989;Bisnovatyi-Kogan &Tsupko 2009).For ω≫ωe we have:αr =1mN 0R 0πΓh22,Γ(x )=∞t x −1e −t dt.(36)For the arbitrary n one needs to use the expression (34)which is valid in a general case.The main approximation used here,is the smallness of the deflection angle,what can be satisfied even if the concentration N changes significantly,or if the refraction index n is not close to the unity.The most interesting result following from our calculation is that even in the case of the homogeneous plasma the photon deflec-tion angle differs from the vacuum case,and depends on the plasma and photon frequency.Indeed,for ωe =const we obtain from (34)ˆαb =−R S1−(ω2e /ω2).(37)This formula is valid only for ω>ωe ,because the waves with ω<ωe do not propagate in the plasma (Ginzburg 1970).Here ˆαb <0.This means that the light ray is bent in the direction of the gravitation center,as it occurs in the vacuum.Thus the presence of plasma increases the grav-itational deflection angle.This formula is valid under the condition of smallness of ˆαb ,but this condition allows the second term in brackets to be much larger than the first one.Gravitational lensing in a non-uniform plasma5 So,the gravitational deflection in plasma can be significantlylarger than in the vacuum.This effect has a general relativis-tic nature,in combination with the dispersive properties ofplasma.Such effect may happen only for radio frequencyphotons,because optical frequencies are much higher thanthe plasma frequencyωe,so the effect would be negligible.In the literature on gravitational lensing theory the de-flection angle is determined usuallyasa positiveone(1),andisdefinedasthedifferencebetweentheinitialand thefinalray directionsˆα=e in−e out,where e is the unit tangent vector of a ray(Schneider et al.1992).Therefore,if we use this definition,we will have the expression with the opposite sign:ˆα=R S1−(ω2e/ω2) ,(38)which turns into the deflection angle for vacuum2R S/b, whenω→∞.4ANALOGY BETWEEN A PHOTON IN PLASMA,AND A MASSIVE PARTICLE Using the analogy between the motion of a photon in the homogeneous plasma,and a massive particle in the grav-itationalfield(12),(14)we may easilyfind the deflection angle of the photon in plasma,produced by a point mass,in a weakfield approximation.A test massive particle passing with the velocity v near a spherical body with a mass M, having the impact parameter b≫R S,deflects to the angle αm defined as(Misner et al.1973;Lightman et al.1979):αm=R Sβ2 ,β=v2R SD ds1+1D d D s==θ0 2 1+14ω2eθ0=θpl0−θ04ω2eν2,(43)whereνis the photon frequency in Hz,ω=2πν.The formula(43)gives the difference between the deviation angle of theradio wave with a frequencyν,and the optical image,whichmay be described by the vacuum formula(40).Let us estimate the possibility of observa-tion of this effect by the planned project Ra-dioAstron(see the RadioAstron web page athttp://www.asc.rssi.ru/radioastron/index.html).TheRadioastron is the VLBI space project led by the AstroSpace Center of Lebedev Physical Institute in Moscow.The payload is the Space Radio Telescope,based onthe spacecraft Spektr-R.For the lowest frequency of theRadioastron,ν=327·106Hz,the angular differencebetween the vacuum and the plasma images is about10−5arcsec,when the plasma density on the photon trajectory,in the vicinity of the gravitational lens is of the order of6G.S.Bisnovatyi-Kogan and O.Yu.TsupkoN e ∼5·104cm −3.this angular resolution is supposed to be reached in the project Radioastron.The magnification of the image increases with increas-ing of the deflection angle,therefore different images may have different spectra in the radio band,when the light prop-agates in regions with different plasma density.The magni-fication is determined by the deflection law (Schneider et al.1992).Let us demonstrate it on the example of the point-mass lensing.The magnification factor of the primary image µ+,located at the same side as the source relative to the lens,and of the secondary image µ−,located at the opposite side,depend on the angular position of the source.Corresponding formulae can be found in Schneider et al.(1992)µ+=1y 2+44y y 2+4+y−2.(45)Here y =β/θ0,where βis the angular position of the source relative to the line passing through the observer and the lens.The total magnification of the source is equal to µtot =µ++µ−=y 2+2y 2+4.(46)Consideration of the total magnification factor is important for the microlensing events when the separated images are not resolved,and the only observable effect is changing of the flux from the source due to lensing.In the case of lensing in plasma we can rewrite theseformulae,using ˜y =β/θpl0instead y :µpl +=1˜y 2+44˜y ˜y 2+4+˜y −2,(48)µpl tot =µpl ++µpl−=˜y 2+2˜y 2+4,(49)where ˜y =βθ011−(ω2e /ω2)−1/2==y11−(ω2e /ω2)−1/2.(50)At large βthe total amplification factor goes to unity,be-cause the influence of the lens on the light propagation be-comes negligible.For the Schwarzschild lens at a small angle β,the amplification is inversely proportional to the angle β,and is proportional to the angular radius of the Einstein ring,which increases with decreasing frequency,approach-ing infinity at the plasma frequency.As βgoes to zero,the amplification increases,formally unrestrictedly for the point source.Let us consider the magnification in plasma,when ω2e /ω2≪1.Carrying out the expansion of the expression (47),(48),(49),and (50),we obtain the additional terms which arise in the case of the plasma,as compared to the case of thevacuum:Figure 1.The ratio µpl +/µ+of the magnification of the primary image in presence of plasma to the same value in vacuum (lower curve),and the ratio µpl −/µ−of the magnification of the secondary image in presence of plasma to the same value in vacuum (upper curve).Curves are plotted for ω=√y (y 2+4)3/2ω2ey (y 2+4)3/2ω2ey (y 2+4)3/2ω2e2ωe ,according to (44),(47).Theupper curve in Fig.1is the ratio of the magnification of the secondary image in presence of plasma µpl −to the same value in vacuum µ−,according to (45),(48).As y approaches zero,the ratio of the magnifications µpl +/µ+and µpl−/µ−becomes constant V +,depending on the frequency V +=µpl +µ−=θpl11−(ω2e /ω2).(54)This value is equal2at ω=√θ04=11−(ω2e /ω2)2.(55)This value is equal 9/4at ω=√Gravitational lensing in a non-uniform plasma7 In the ideal case,when two images of the same sourceare formed by rays propagating through the uniform plasmawith different concentrations,the spectra of two imagesshould be different.In the achromatic lensing the ratio offluxes should be the same at all frequenciesµopt+=µrad+,µopt−=µrad−,so thatµopt+/µopt−=µrad+/µrad−.The presenceof plasma leads to larger amplification at lower frequencies, so if the ratio offluxes in optics and in lower radio bandof two lensing images is differentµopt+/µopt−=µrad+/µrad−,itmay be related to plasma influence,so that the image with larger relative radioflux propagates through the plasma with larger density.In Fig.2two cases are shown for the value (µpl+/µ+)/(µpl−/µ−),as a function ofω/ωe,for differentfixed y.In thefirst one the plasma density is two times larger for rays forming the main image,and in the second case the ra-tio of densities is opposite.While the vacuum valueµ+/µ−does not depend on the frequency,one of these two behaviors is expected for the ratio offluxes of two images as a function of the frequency.In the considered ideal case this plot should give the information about the ratio of plasma densities,and when the image with lower relative radioflux is formed by vacuum lensing,it would be possible to obtain the absolute value of the plasma density through which propagate rays from the image with higher relative radioflux.From Fig.2we see that the spectral dependences can have different forms for different y:while the dashed line is less than unity,the solid line can be both larger and less than unity.In Fig.2a in case when the light rays correspond-ing to primary image go through the densier plasma,we see that for smaller frequencies the primary image is more mag-nificated,relative to the vacuum magnification,due to the plasma presence than the secondary image,see solid line. In opposite case,when the light rays corresponding to the secondary image pass through greater density,we see that for the small frequencies the secondary image is more mag-nificated,therefore the dashed line is less than unity.For bigger y both curves are less than unity.In Fig.2b,c we see that with increasing of y the solid line goes to the region, which is lower than unity.In Fig.3we plot the same de-pendence for the case,when the plasma density is ten times larger for rays forming the main image,and the second curve corresponds to the opposite ratio in densities.In the case, when the difference between densities is larger(comparing with situation in Fig.2),effects connected with plasma are greater.Here the solid line remains above unity for greater values of y than for the situation described in Fig.2.We should note,that for y 1the secondary image is very de-magnified(Schneider et al.1992,2006),so in a real situation we will have behaviour like on Fig.2a and Fig3a,and ratio of densities can be uniquely defined.More detail can be found in Appendix1.In this section we have discussed in details new ob-servational effects,connected with the gravitational deflec-tion in a homogeneous plasma.In reality the distribution of plasma around the gravitating objects is non-homogeneous, and there is a deflection connected with the medium inho-mogeneity.For the plasma density profile decreasing with the distance from center,the refraction deflection has a sign opposite to the gravitational one.Therefore the refraction and gravitational deflection in the nonuniform plasma par-tially cancel each other,and the value and the sign of the resulting angle depend on the particular configuration of the gravitational lens.In the following section we consider situ-ations of lensing with the non-uniform plasma distribution. 6MODELS WITH NONUNIFORM PLASMA DISTRIBUTION6.1Singular isothermal sphereLet us consider a simple model of singular isothermal sphere(Binney&Tremaine1987;Chandrasekhar1939) which is often used in the lens modeling of galax-ies and clusters of galaxies(Schneider et al.1992,2006; Bartelmann&Schneider2001;Wambsganss1998).The density distribution is written asρ(r)=σ2v2Gb.(57) The deflection due to a axisymmetric mass distribution with the impact parameter b is equal to the Einstein angle for the mass M(b),where M(b)is the projected mass enclosed by the circle of the radius b.In another words it is the mass inside the cylinder with the radius b(Clark1972; Bliokh&Minakov1989;Schneider et al.1992,2006).So we for this case we should rewrite formula(35)substituting M(b):ˆαb=4GM(b)c2ω2∞ω2eω2∞1drdz+K e brdN(r)Gπb.(59)So the vacuum gravitational deflection due to the singular isothermal sphere is constant:ˆα1=4πσ2v8G.S.Bisnovatyi-Kogan and O.Yu.TsupkoFigure 2.The value (µpl +/µ+)/(µpl−/µ−),as a function of ω/ωe ,for different fixed y .ωe +is the plasma frequency corresponding to the plasma concentration N +,which rays forming primary image go through.ωe −is the plasma frequency corresponding to the plasma concentration N −,which rays forming primary image go through.The solid curve is plotted for ωe +=ωe 0√2,itcorresponds to N +/N −=1/2.Figure 3.The value (µpl +/µ+)/(µpl−/µ−),as a function of ω/ωe ,for different fixed y .The solid curve is plotted for ωe +=ωe 0√10,it corresponds to N +/N −=1/10.N (r )=ρ(r )Gravitational lensing in a non-uniform plasma9 of matter,not only plasma particles.Thus,the plasma fre-quency is equal toω2e=K e N(r)=K eω2c2K er3dz==b2σ2vκm pσ2v(b2+z2)5/2.(63)Integration of such expressions can be performed using Gradshteyn&Ryzhik(1965),and the properties of theΓ-function:∞dzhb h+1√2+1Γ h3σ2vκm pσ2vω2κm pσ2v(z2+b2)2=−1κm pσ2vˆα3 =8c2.(67) 6.2Non-singular isothermal gas sphereLet us consider a gravitational lens model of an isothermal sphere,in which the singularity at the origin is replaced by afinite core(Hinshaw&Krauss1987;Wu1996):ρ(r)=σ2v1+r22πGr2c,(68)where r c is the core radius.The corresponding projected surface mass density for this model isΣ(b)=σ2vb2+r2c.(69)The total projected mass within b and the vacuum gravita-tional deflection angle are:M(b)=πσ2vb2+r2c−r c ,(70)ˆα1=4πσ2v b2+r2c−r cc2ω2K e2πG∞dzc2ω2K e2πG∞dz(z2+b2)3/2(z2+b2+r2c)is reduced toI1=11r2c(b2+r2c(1−x2)) dx.(73)Integration can be performed with using of Dwight(1961):I1=1r3c√√c2ω2GK eb2+r2c−r c ×(75)× 1r3c√√ω212πG∞dz4σ2vκm pbc2ω2K e2ω2K er c;(77)and for b≫r c,similar to the case of the singular isothermalsphere,we haveˆα2=8π2Gρ20κm pr4c2ω2K eb2.(78)Introducing the mass of the uniform core M c=4πc2,we obtain the ratio ofthese angles asˆα22r c(r c≫b), ˆα2r c(r c≪b).(79)In the realistic cases ˆα210G.S.Bisnovatyi-Kogan and O.Yu.Tsupko6.3Plasma sphere around a black holeLet us consider a black hole of mass M 0,surrounded by the electron-proton plasma.We will consider a case,when we can neglect the self-gravitation of the plasma particles,compared to the gravity of a central black hole.Let us find,in the newtonian approximation,a density distribution of the plasma in the gravitational field a central point mass M 0.The equation of hydrostatic equilibrium for spherically symmetric mass distribution of a isothermal gas with the equation ofstateP =ρℜT in the field of the central mass is (Binney &Tremaine 1987;Chandrasekhar 1939)ℜTdr =−GM 0ω2ℜT1dr=−K e br 3N (r ),(81)where N (r )=ρ(r )/m p is the plasma concentration.If we compare it with expressions for ˆα2and ˆα3in (58)and takeinto account that ω2e =(4πe 2/m )N (r )=K e N (r ),we obtain thatˆα2c 2.(82)We see that this ratio does not depend on the value of the central mass M 0.For the boundary condition ρ(r 0)=ρ0(83)we obtain from the equation (80)the density distribution ρ(r )=ρ0eGM 0r−1r−1ℜT.(84)For angles ˆα2and ˆα3we obtain:ˆα2=2GM 0bm pρ0e−Bω2m pB ρ0e−B(b 2+z 2)3/2eBb 2+z 2dz.(87)Calculation of Int 2can be found in Appendix 2.While the temperature of the non-self-gravitating sphere may have arbitrary values,the plasma effects may be comparable,and even less than the GR plasma effects.It is due to the fact,that with increasing temperature the plasma density can become arbitrary uniform,with corresponding decreasing of non-uniform plasma effect for refraction.We have used newtonian non-relativistic description of the gas sphere,but from the arguments listed above it is clear,that this conclusion remains valid also in the correct relativistic consideration.6.4Plasma in a galaxy clustersIn a galaxy cluster the electron distribution may be more homogeneous due to large temperature of electrons.An ap-propriate approach for this case is to consider a singular isothermal sphere as a model for the distribution of the grav-itating matter,neglecting the mass of plasma,and to find a plasma density distribution from the solution of the equation of the hydrostatic equilibrium of plasma in the gravitational field of a singular isothermal sphere.In this approximation the density distribution of the gravitating matter has a form ρgr (r )=σ2vc 2.(89)For the mass inside a sphere with a radius r we have M (r )=2σ2vρdρr.(91)For the boundary condition ρ(r 0)=ρ0we obtain the plasma density from the equation (91)as ρ(r )=ρ0rℜT.(92)The angles ˆα2and ˆα3are calculated using formula (64),so we haveˆα2=2σ2v π√c 2ω2(s +1)K e 2+1)2)ρ0r 0ω21(z 2+b 2)s/2+1=(94)=−K e√ω2m pΓ(s 2)2)ρ0r 0ˆα3=σ2v 2+1)Γ(s Γ(s2)Γ(s 2).(95)Under the condition s ≪1what corresponds to 2σ2v ≪ℜT ,the expressions are simplified toˆα2=2πσ2vm pρ0rℜT ω2K ebs,(97)ˆα2c 2.(98)If relativistic plasma is present in a galaxy cluster,for exam-ple in jets from AGNs,the plasma GR effects may be larger than the effects of the nonuniform plasma.If the distribu-tion of plasma is not spherically symmetric,there may be distribution of plasma with the density gradient opposite to the direction of the gravitational force,for example,in the。

高一英语天文知识单选题40题1.The largest planet in our solar system is_____.A.MercuryB.VenusC.JupiterD.Earth答案解析：C。

在太阳系中木星是最大的行星。

选项A 水星是最小的行星；选项 B 金星大小与地球类似；选项 D 地球不是最大的行星。

2.The planet known as the Red Planet is_____.A.MarsB.SaturnC.UranusD.Neptune答案解析：A。

火星被称为红色星球。

选项B 土星有美丽的环；选项C 天王星；选项D 海王星。

3.Which planet is closest to the sun?A.MercuryB.VenusC.EarthD.Mars答案解析：A。

水星是距离太阳最近的行星。

选项B 金星；选项C 地球；选项D 火星。

4.The planet with the most moons is_____.A.JupiterB.SaturnC.UranusD.Neptune答案解析：A。

木星拥有最多的卫星。

选项B 土星也有很多卫星，但不如木星多；选项C 天王星；选项D 海王星。

5.Which planet is known as the Morning Star or Evening Star?A.VenusB.MarsC.JupiterD.Saturn答案解析：A。

金星有时在早晨出现，被称为启明星，有时在傍晚出现，被称为长庚星。

选项B 火星；选项C 木星；选项D 土星。

6.The planet that has a ring system is_____.A.SaturnB.UranusC.NeptuneD.Earth答案解析：A。

土星有明显的环系统。

选项B 天王星也有环，但不如土星明显；选项C 海王星也有环；选项D 地球没有环。

7.Which planet is similar in size to Earth?A.VenusB.MarsC.JupiterD.Saturn答案解析：A。

高三英语天文学概念单选题50题1. The largest planet in our solar system is ____.A. VenusB. JupiterC. MarsD. Earth答案：B。

解析：本题考查太阳系行星的相关知识以及对形容词最高级的理解。

在太阳系中，木星（Jupiter）是最大的行星。

选项A 金星 Venus）不是最大的行星；选项C火星 Mars）也不是最大的行星；选项D地球 Earth）同样不是最大的行星。

2. Which planet is known as the "Red Planet"?A. SaturnB. MarsC. NeptuneD. Uranus答案：B。

解析：本题考查特定行星的别称相关的天文学概念以及单词的记忆。

火星（Mars）被称为“红色星球”，因为其表面富含氧化铁而呈现红色。

选项A土星 Saturn），有美丽的光环；选项C海王星（Neptune）和选项D天王星（Uranus）都不是被称为“红色星球”的行星。

3. The Earth has only one natural satellite, which is ____.A. the MoonB. IoC. EuropaD. Ganymede答案：A。

解析：本题考查地球的卫星这一天文学概念以及对单词的认知。

地球只有一个天然卫星，那就是月球（the Moon）。

选项B 木卫一（Io）、选项C木卫二（Europa）和选项D木卫三（Ganymede）都是木星的卫星，而不是地球的卫星。

4. Which planet is closest to the Sun?A. MercuryB. VenusC. MarsD. Jupiter答案：A。

解析：本题考查太阳系行星与太阳的距离关系这一概念以及对单词的掌握。

水星（Mercury）是离太阳最近的行星。

选项B 金星 Venus）距离太阳比水星远；选项C火星 Mars）距离太阳更远；选项D木星（Jupiter）距离太阳是比较远的，是太阳系中较大的行星。

矿产资源开发利用方案编写内容要求及审查大纲
矿产资源开发利用方案编写内容要求及《矿产资源开发利用方案》审查大纲一、概述
㈠矿区位置、隶属关系和企业性质。

如为改扩建矿山, 应说明矿山现状、
特点及存在的主要问题。

㈡编制依据
(1简述项目前期工作进展情况及与有关方面对项目的意向性协议情况。

(2 列出开发利用方案编制所依据的主要基础性资料的名称。

如经储量管理部门认定的矿区地质勘探报告、选矿试验报告、加工利用试验报告、工程地质初评资料、矿区水文资料和供水资料等。

对改、扩建矿山应有生产实际资料, 如矿山总平面现状图、矿床开拓系统图、采场现状图和主要采选设备清单等。

二、矿产品需求现状和预测
㈠该矿产在国内需求情况和市场供应情况
1、矿产品现状及加工利用趋向。

2、国内近、远期的需求量及主要销向预测。

㈡产品价格分析
1、国内矿产品价格现状。

2、矿产品价格稳定性及变化趋势。

三、矿产资源概况
㈠矿区总体概况
1、矿区总体规划情况。

2、矿区矿产资源概况。

3、该设计与矿区总体开发的关系。

㈡该设计项目的资源概况
1、矿床地质及构造特征。

2、矿床开采技术条件及水文地质条件。