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核磁共振NMR 高斯计的测绘原理By Philip Keller, Metrolab产品经理瑞士Metrolab公司是精密磁力计的全球市场领导者，在过去的30年中，已经赢得了大型物理实验室和磁共振成像的所有领先厂商的信赖。
磁共振磁强计已经成为世界各地的物理学家，工程师和技术人员日常工具。
最常见的应用包括研究，磁体的制造和测试，标准和校准。
北京华贺技术有限公司作为Metrolab在中国的专业代理与进口公司，全面支持其在中国的市场、销售和售后等服务。
1.NMR 高斯计技术With a resolution approaching 1 ppb (part per billion), Nuclear Magnetic Resonance (NMR) is the gold standard of magnetic measurement. Bellow picture illustrates the technical principle:Principles of NMR magnetic field strength measurement.A proton (hydrogen nucleus) has two possible spin states. In the absence of an external magnetic field, these states are degenerate, but as soon as we apply a field, the spinaligned state is lower energy than the unaligned state. The energy differential ΔE between the two states depends linearly on the magnetic field strength. This exact linear dependence, very nearly independent of all other external factors such as temperature, forms the basis for NMR teslameters.In an NMR teslameter, a coil is wrapped around a sample material rich in hydrogen nuclei – ordinary water works great. This is the "Nuclear" part of NMR. The sample is placed in the magnetic field to be measured ("Magnetic") and irradiated with an RF signal whose frequency gradually increases. When we hit the frequency that corresponds to ΔE, the sample suddenly absorbs energy ("Resonance"). For a field strength of 1 T, this resonance occurs at about 42.5 MHz; this is the gyromagneticratio (γ) for hydrogen nuclei.The resonance is extremely narrow, and so the frequency provides an extremely precise measure of the magnetic field strength.NMR has some overwhelming advantages over other measurement technologies:- extremely precise;- no drift; and- measures total field.That last point is perhaps not obvious. In fact, the protons align themselves with the magnetic field, and the resonance always occurs at B/γ, regardless of how we orient our coil. It turns out, however, that the best coupling between the RF field and the proton spins is achieved when the magnetic field is perpendicular to the coil's axis. In fact, NMR has a blind spot when the coil's axis is exactly aligned with the magnetic field.NMR also has substantial limitations:- Uniform field only: In a field gradient, one edge of the sample will resonate at one frequency, and the opposite edge at another. As the gradient increases, the resonance signal becomes broader and shallower, until it can no longer be detected; this limit typically lies in the range of several hundred to several thousand ppm/cm. In some situations, gradient correction coils can improve this situation.- DC / low-AC fields only: NMR is a relatively slow measurement method, making it unsuitable for measuring rapidly varying fields. Here, we have to distinguish search mode from measurement mode: scanning through a large frequency range to find the resonance requires the field to remain stable for seconds; but once the search is completed, we can track the field and achieve measurement rates of up to about 100 measurements per second.- Low fields require a large sample, ESR or pre-polarization: As the field and, consequently, the energy gap between the spin states tends towards zero, the populations of the two states tend to become equal, and the strength of the resonance diminishes. There are three possible remedies:●Use a very large sample to increase the number of spin-flips.●oPre-polarize the sample in a strong field to populate the spin-aligned state,and then remove this bias field during the measurement.●Use ESR, i.e. the spin of orbital electrons instead of protons, because thesehave a gyromagnetic ratio (γ) three orders of magnitude higher than protons.2.NMR 核磁共振测绘To build an NMR mapper, we need:- NMR probe or probe array. As we will see in the example, a probe array ramatically speeds up the acquisition and simplifies the jig.- Positioning jig.- NMR teslameter (the electronics).The output of an NMR mapper is straightforward:- total field B,- point-sampled,In fact, the size of the "points" are determined by the size of our NMR sample, which is typically a few millimetres in diameter.- very high precision.Well below 1 ppm, in the best case approaching 1 ppb.Computational post-processing depends very much on the application. The typical postprocessing for MRI applications is described in the following section.Close-up of an NMR probe array. Each probe – one of them is circled – is mounted on itsown circuit card. Such probe arrays typically contains 24 or 32 probes (maximum 96).3.NMR核磁共振测绘–案例The most widespread use of NMR mapping relates to the development, manufacturing and installation of MRI (Magnetic Resonance Imaging) magnets. These can be permanent, resistive, or superconducting magnets, with a typical field strength between 0.2 and 7 T.Technically, the preferred shape is a torroid, but for improved access to the patient, or for a less claustrophobic feel, C-shaped magnets are sometimes used. Most modern full-body systems from the major manufacturers use superconducting torroids, 1.5 or 3 T, as illustrated in Figure 12.Example of modern full-body MRI scanner (Philips Achieva).The homogeneity of the field in the imaging region must typically be guaranteed to within a few ppm. Since minor, unavoidable manufacturing variations cause inhomogeneities generally two orders of magnitude greater than that, the homogeneity must be adjusted in a process called shimming.The overall shimming procedure is to map the field, analyze the map, adjust the field with iron shims and/or shim-coil current adjustments, and to remap the field to verify the results.If necessary, this process is repeated until the specified homogeneity is achieved. The same process, and usually the same equipment, is used in R&D, manufacturing and installation. The measurement is extremely sensitive, and obscure effects such as the passing of an overhead crane or the return current of a nearby train can cause hugeerrors.NMR mapping jigs for torroid- and C-shaped MRI magnets, respectively.The probe arrays and jigs shown in Figure 11 and Figure 13 generate a map of thetotal field on the surface of a sphere. As long as there are no currents or magneticmaterial inside this sphere, and assuming the direction of the field is known, the fieldat every point inside the sphere can be calculated from Maxwell's equations. Generally we use an expansion in spherical harmonics to perform this computation.It is worth noting that the jigs shown are much simpler that in the previous examples. Fundamentally, there are two reasons for this:- Using a probe array reduces the required motion to a single dimension.- Partly because the field is so uniform, and partly because the NMR sample points are fairly large, the requirements on the positioning precision are much less –typically 0.1mm. Compare that to the 0.1 μm for the Hall mapper example!4.问答To summarize our observations from these different examples of magnetic mapping, here is a small check-list of key questions to ask if you want (rather, need) to build a mapper:- Use: R&D, production, field service?It makes a big difference if a system is to be used once in a while for R&D, or all the time in production, or packed up in a suitcase for field service.- Measurement: field components, total field, integral, gradient?Do you really need Bx, By, Bz, or do you really need B, or an integral or gradient of B?By choosing the appropriate measurement technology, you may be able to speed up the acquisition as well improve your precision.- Field: strength, uniformity, AC/DC, stability?The characteristics of your field also play an important role in the choice of measurement technology.- Precision: 10% or 10 ppm?…as does the precision required.- Positioning: access, range, precision, reproducibility?The design of your jig is as important as the choice of magnetic sensor. What sort of access do you have to the region to be measured? What positioning precision do you need? How reproducible must the positioning be?- Environment: vacuum, cryogenic?The environment changes dramatically depending on whether you're in a lab, on a production floor or in the field. In addition, magnetic systems are often combined with vacuums and cryogenic temperatures. Hall effect sensors, for example, don't work at liquid-helium temperatures.- Speed: cost, external error sources, human error?Making a fast mapper may not cost more; for example, we saw that the simplification of the jig may more than make up for the costs of a sensor array. In addition, the improved speed dramatically reduces external and human error.。
a r X i v :a s t r o -p h /0310699v 3 13 F eb 2004The Uncertainty in Newton’s Constant and Precision Predictions of the PrimordialHelium AbundanceRobert J.ScherrerDepartment of Physics and Astronomy,Vanderbilt University,Nashville,TN37235The current uncertainty in Newton’s constant,G N ,is of the order of 0.15%.For values of the baryon to photon ratio consistent with both cosmic microwave background observations and the primordial deuterium abundance,this uncertainty in G N corresponds to an uncertainty in the primordial 4He mass fraction,Y P ,of ±1.3×10−4.This uncertainty in Y P is comparable to the effect from the current uncertainty in the neutron lifetime,τn ,which is often treated as the dominant uncertainty in calculations of Y P .Recent measurements of G N seem to be converging within a smaller range;a reduction in the estimated error on G N by a factor of 10would essentially eliminate it as a source of uncertainty the calculation of the primordial 4He abundance.Big Bang nucleosynthesis (BBN)represents one of the key successes of modern cosmology [1,2].In recent years,the BBN production of deuterium has emerged as the most useful constraint on the baryon density in the universe,both because of observations of deuterium in (presumably unprocessed)high-redshift QSO absorption line systems (see Ref.[3],and references therein),and the fact that the predicted BBN yields of deuterium are highly sensitive to the baryon density.These arguments give a baryon density parameter Ωb h 2,of [3]Ωb h 2=0.0194−0.0234,(1)which is in excellent agreement with the baryon den-sity derived by the WMAP team from recent cosmic mi-crowave background observations [4]:Ωb h 2=0.022−0.024.(2)Given these limits on the baryon density,BBN predicts the primordial abundances of 4He and 7Li.Because the 4He abundance is particularly sensitive to new physics beyond the standard model,a comparison between the predicted and observed abundances of 4He can be used to constrain,for example,neutrino degeneracy or extra relativistic degrees of freedom (see,e.g.,Refs.[5,6]).For this reason,it is useful to obtain the most accurate possible theoretical predictions for the primordial 4He mass fraction,Y P .The primordial production of 4He is controlled by the competition between the rates for the processes which govern the interconversion of neutrons and protons,n +νe ↔p +e −,n +e +↔p +¯νe ,n ↔p +e −+¯νe ,(3)and the expansion rate of the Universe,given by˙R3πG N ρ1/2.(4)In BBN calculations,the weak interaction rates are scaled offof the inverse of the neutron lifetime,τn .When these rates are faster than the expansion rate,the neutron-to-proton ratio (n/p )tracks its equilibrium value.As the Universe expands and cools,the expan-sion rate comes to dominate and n/p essentially freezes out.Nearly all the neutrons which survive this freeze-out are bound into 4He when deuterium becomes sta-ble against photodisintegration.Following the initial calculations of Wagoner,Fowler,and Hoyle [7],numer-ous groups examined higher-order corrections to the 4He production.The first such systematic attempt was un-dertaken by Dicus et al.[8],who examined the effects of Coulomb and radiative corrections to the weak rates,finite-temperature QED effects,and incomplete neutrino ter investigations included more detailed ex-amination of Coulomb and radiative corrections to the weak rates [9,10,11,12],finite-temperature QED ef-fects [13],and incomplete neutrino decoupling [14],as well as an examination of the effects of finite nuclear mass [15].These effects were systematized by Lopez and Turner [16](see also Ref.[17]),who argued that all the-oretical corrections larger than the effect of the uncer-tainty in the neutron lifetime had been accounted for,yielding a total theoretical uncertainty ∆Y P <0.0002.Assuming an uncertainty of ±2sec in the neutron life-time,the corresponding experimental uncertainty in Y P is ∆Y P =±0.0004.Similar results were obtained in Ref.[17].Two relevant changes have occurred since the publica-tion of Refs.[16,17].First,the estimated uncertainty in the neutron lifetime has decreased,with the current value being [18]τn =885.7±0.8sec .(5)Second,the estimated uncertainty in the value of G N has increased .The value currently recommended by CO-DATA (Committee on Data for Science and Technology)is [19]G N =6.673±0.010×10−8cm 3gm −1sec −2.(6)This represents a factor of twelve increase over the pre-vious recommended uncertainty [20],and is primarily due to an anomalously high value for G determined by Michaelis,Haars,and Augustin [21].(See Table 1).2Reference6.67407(22)Quinn,et al.(2001)[30]6.674215(92)Luo et al.(1999)[32]6.6742(7)Schwarz et al.(1999)[34]6.6749(14)Kleinevoss et al.(1999)[36]6.673(10)CODATA(1986)[20]3[13]A.J.Heckler,Phys.Rev.D49,611(1994).[14]S.Dodelson and M.S.Turner,Phys.Rev.D46,3372(1992).[15]R.E.Lopez,M.S.Turner,and G.Gyuk,Phys.Rev.D56,3191(1997).[16]R.E.Lopez and 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武汉轻工大学学报Journai of Wuhan Polytechnio University V c S.38Nr.5Oct.2019第38卷第5期2019年10月文章编号：2095N386(2019)05-0006-06DOI：10.3969/j.issn.2095N386.2019.05.002天麻酸奶中天麻素和天麻＜元含量的测定黄先敏，甘会廷,韩立乾,孙建美（昭通学院农学与生命科学学院，云南昭通657000）摘要:以实验所做出的天麻酸奶为试验材料，对其中的天麻素和天麻昔元的含量进行测定分析，为天麻酸奶的生产利用和推广提供理论依据。
实验结果显示天麻与乳酸菌共同发酵后，发酵物中仍含有天麻素和天麻昔元。
关键词:天麻酸奶;天麻素;天麻昔元;含量;反相高效液相色谱法中图分类号:TS201.2文献标识码：AMeasurement of gastrodin and gastrodigenin in Gastrodia elata Bl yoghurt HUANG Xian-min.,GAN Hui-ting,HAN Li-qian,SUN Jian-mei(College of Agriculturo and Life Science,Zhaotong University,Zhaotong,657000,China)Abstract：The Gastrodia elata BI yoghurt made in laboratoro was used as the experimentai materiai,O s mecsure the content of gastrodin and gastrodioenin in Gastrodia elata BI yoghui powdco,which provided a theoreticoi basis fof the production,utilization and promotion of Gastrodia elata BI yorhuri.AOs the co-femientation of Gastrodia elata BI and lactic acid bacteaa,tar femientation product stili contains gastrodin and gastrodiaenia.Key words:Gastrodia elata BI%gastrodin%gastrodiaenin%content%reversed phass high perfomianco liquia chroma-iogoaphy1引言天麻（Gastuodia elatr BI）是我国传统名贵中药［1］，已有千年的药用历史，被誉为“治风之神药”&2-'（天麻中含有天麻素⑷、天麻昔元［5］、巴利森昔&6'、对k基苯甲醛切、对k基苯甲酸［8'及天麻多糖［9］等多种活性物质，其中主要的活性物质为天麻素和天麻昔元&10N1'。
湍流长度尺度英文Turbulence Length ScalesTurbulence is a complex and fascinating phenomenon that has been the subject of extensive research and study in the field of fluid mechanics. One of the key aspects of turbulence is the concept of turbulence length scales, which refers to the range of different-sized eddies or vortices that are present in a turbulent flow. These length scales play a crucial role in understanding and predicting the behavior of turbulent flows, and they have important implications in a wide range of engineering and scientific applications.The smallest length scale in a turbulent flow is known as the Kolmogorov length scale, named after the Russian mathematician and physicist Andrey Kolmogorov. This length scale represents the size of the smallest eddies or vortices in the flow, and it is determined by the rate of energy dissipation and the kinematic viscosity of the fluid. The Kolmogorov length scale is typically denoted by the Greek letter η (eta) and can be expressed as η = (ν^3/ε)^(1/4), where ν is the kinematic viscosity of the fluid and ε is the rate of energy dissipation.The Kolmogorov length scale is important because it represents the scale at which viscous forces become dominant and energy is dissipated into heat. Below this length scale, the flow is considered to be in the dissipation range, where the eddies are too small to sustain their own motion and are rapidly broken down by viscous forces. The Kolmogorov length scale is therefore a critical parameter in the study of turbulence, as it helps to define the range of scales over which energy is transferred and dissipated within the flow.Another important length scale in turbulence is the integral length scale, which represents the size of the largest eddies or vortices in the flow. The integral length scale is typically denoted by the symbol L and is a measure of the size of the energy-containing eddies, which are responsible for the bulk of the turbulent kinetic energy in the flow. The integral length scale is often determined by the geometry of the flow domain or the boundary conditions, and it can be used to estimate the overall scale of the turbulent motion.Between the Kolmogorov length scale and the integral length scale, there is a range of intermediate length scales known as the inertial subrange. This range is characterized by the presence of eddies that are large enough to be unaffected by viscous forces, but small enough to be unaffected by the large-scale features of the flow. In this inertial subrange, the energy is transferred from the large eddies to the smaller eddies through a process known as the energycascade, where energy is transferred from larger scales to smaller scales without significant dissipation.The energy cascade is a fundamental concept in turbulence theory and is described by Kolmogorov's famous 1941 theory, which predicts that the energy spectrum in the inertial subrange should follow a power law with a slope of -5/3. This power law relationship has been extensively verified through experimental and numerical studies, and it has important implications for the modeling and prediction of turbulent flows.In addition to the Kolmogorov and integral length scales, there are other important length scales in turbulence that are relevant to specific applications or flow regimes. For example, in wall-bounded flows, the viscous length scale and the boundary layer thickness are important parameters that can influence the turbulent structure and behavior. In compressible flows, the Taylor microscale and the Corrsin scale are also relevant length scales that can provide insight into the characteristics of the turbulence.The understanding of turbulence length scales is crucial for a wide range of engineering and scientific applications, including fluid dynamics, aerodynamics, meteorology, oceanography, and astrophysics. By understanding the different length scales and their relationships, researchers and engineers can better predict andmodel the behavior of turbulent flows, leading to improved designs, more accurate simulations, and a deeper understanding of the fundamental principles of fluid mechanics.In conclusion, turbulence length scales are a fundamental concept in the study of turbulent flows, and they play a crucial role in our understanding and modeling of this complex and fascinating phenomenon. From the Kolmogorov length scale to the integral length scale and the inertial subrange, these length scales provide valuable insights into the structure and dynamics of turbulence, and they continue to be an active area of research and exploration in the field of fluid mechanics.。
单矢量水听器水中多目标方位跟踪方法张维;尚玲【摘要】The direction of arrival (DOA) of multiple targets was acquired by solving non-liner correlation equations involving acoustic pressure and particle velocity with quantum particle swarm algorithm.In order to improve the precision, the DOA tracks of multiple targets were fitted with the method of least squares, the prediction model was found and then the DOA tracks were optimized by Kalman filter.The results indicate that the DOA of multiple targets can be resolved with the single vector hydrophone and the results should be expressed by statistic characteristics.The maximum number of unknown sources is 7.As the number increases, the DOA error is more serious.When the signal to noise ratio is higher, the resolution ratio and precision are also higher and the deviation is smaller.More importantly, the precision of DOA can be improved effectively by the method of data fitting and the Kalman filter.%采用量子粒子群求解声压和质点振速组成的非线性相关方程组,实现多目标声源方位的估计.为提高精度,应用最小二乘法对测量结果进行拟合并建立预测模型,通过卡尔曼滤波对方位轨迹进行优化.结果表明:单矢量水听器能够同时分辨多个目标方位,解算结果应使用统计特性表示;采用本方法最多能分辨7个目标,目标个数越多,方位误差越大;信噪比越高,分辨率和精度越高,偏差越小;通过数据拟合然后卡尔曼滤波的方法能够有效提高目标方位跟踪精度.【期刊名称】《国防科技大学学报》【年(卷),期】2017(039)002【总页数】6页(P114-119)【关键词】多目标方位;单矢量水听器;卡尔曼滤波;最小二乘法;量子粒子群【作者】张维;尚玲【作者单位】中国船舶重工集团公司第七一〇研究所, 湖北宜昌 443003;中国船舶重工集团公司第七一〇研究所, 湖北宜昌 443003【正文语种】中文【中图分类】TN911.7单个矢量水听器能同时拾取声压和质点振速信息，在各向同性噪声背景中，采用平均声强器[1-2]、最大似然检测[3-4]、互谱法[5]就可以对目标进行定向。
a r X i v :a s t r o -p h /0304102v 2 6 M a y 2003Measurements of Proton,Helium and Muon Spectraat Small Atmospheric Depths with the BESSSpectrometerK.Abe a ,∗,1,T.Sanuki a ,K.Anraku a ,2,Y .Asaoka a ,3,H.Fuke a ,S.Haino a ,N.Ikeda b ,M.Imori a ,K.Izumi a ,T.Maeno b ,4,Y .Makida c ,S.Matsuda a ,N.Matsui a ,T.Matsukawa b ,H.Matsumoto a ,J.W.Mitchell d ,A.A.Moiseev d ,J.Nishimura a ,M.Nozaki b ,S.Orito a ,5,J.F.Ormes d ,M.Sasaki c ,6,E.S.Seo e ,Y .Shikaze b ,T.Sonoda a ,R.E.Streitmatter d ,J.Suzuki c ,K.Tanaka c ,K.Tanizaki b ,T.Yamagami f ,A.Yamamoto c ,Y .Yamamoto a ,K.Yamato b ,T.Yoshida c ,K.Yoshimura c a The University of Tokyo,Bunkyo,Tokyo 113-0033,Japan b Kobe University,Kobe,Hyogo 657-8501,Japan c High Energy Accelerator Research Organization (KEK),Tsukuba,Ibaraki 305-0801,Japan d National Aeronautics and Space Administration (NASA),Goddard Space Flight Center,Greenbelt,MD 20771,USA.e University of Maryland,College Park,MD 20742,USA f Institute of Space and Astronomical Science (ISAS),Sagamihara,229-8510,Japan1IntroductionPrimary cosmic rays interact with nuclei in the atmosphere,and produce atmo-spheric secondary particles,such as muons,gamma rays and neutrinos.It is impor-tant to understand these interactions to investigate cosmic-ray phenomena inside the atmosphere.For precise study of the atmospheric neutrino oscillation[1],it is crucial to reduce uncertainties in hadronic interactions,which are main sources of systematic errors in the prediction of the energy spectra of atmospheric neutrinos. At small atmospheric depths below a few ten g/cm2,production process of muons is predominant over decay process,thus we can clearly observe a feature of the hadronic interactions.In spite of their importance,only a few measurements have been performed with modest statistics because of strong constraints of short obser-vation time of a few hours during balloon ascending periods from the ground to the balloonfloating altitude.In2001,using the BESS spectrometer,precise measurements of the cosmic-ray fluxes and their dependence on atmospheric depth were carried out during slow descending from4.5g/cm2to28g/cm2for12.4hours.The growth curves of the cosmic-rayfluxes were precisely measured.The results were compared with the predictions based on the hadronic interaction models currently used in the atmo-spheric neutrinoflux calculations.2BESS spectrometerThe BESS(B xperiment with a S pectrometer)de-tector[2,3,4,5,6]is a high-resolution spectrometer with a large acceptance to per-form precise measurement of absolutefluxes of various cosmic rays[7,8,9],as well as highly sensitive searches for rare cosmic-ray components.Fig.1shows a schematic cross-sectional view of the BESS instrument.In the central region,a uniform magneticfield of1Tesla is provided by a thin superconducting solenoidal coil.The magnetic-rigidity(R≡Pc/Ze)of an incoming charged particle is mea-sured by a tracking system,which consists of a jet-type drift chamber(JET)and two inner-drift-chambers(IDC’s)inside the magneticfield.The deflection(R−1)iscalculated for each event by applying a circularfitting using up-to28hit-points, each with a spatial resolution of200µm.The maximum detectable rigidity(MDR) was estimated to be200GV.Time-of-flight(TOF)hodoscopes provide the veloc-ity(β)and energy loss(d E/d x)measurements.A1/βresolution of1.4%was achieved in this experiment.For particle identification,the BESS spectrometer was equipped with a threshold-type aerogel Cherenkov counter and an electromagnetic shower counter.The refractive index of silica aerogel radiator was1.022,and the threshold kinetic energy for proton was3.6GeV.The shower counter consists of a plate of lead with two radiation lengths covering a quarter area of the lower TOF counters,whose output signal was utilized for e/µidentification.The data acquisition sequence is initiated by afirst-level TOF trigger,which is a simple coincidence of signals in the upper and lower TOF counter.In order to build a sample of unbiased triggers,one of every four events were recorded.The TOF trigger efficiency was evaluated to be99.4%±0.2%by using secondary proton beam at the KEK12GeV proton synchrotron.In addition to the TOF trigger,an auxiliary trigger is generated by a signal from the Cherenkov counter to record par-ticles above threshold energy without bias or sampling.An efficiency of Cherenkov trigger were evaluated as a ratio of the Cherenkov-triggered events among the un-biased trigger sample.It was95.1%for relativistic particles(β→1).Forflux determinations,the Cherenkov-triggered events were used only above9.5GV for protons,11.1GV for helium nuclei,and0.90GV for muons.Below these rigidities, the TOF-triggered events were used.3BalloonflightThe BESS-2001balloonflight was carried out at Ft.Sumner,New Mexico,USA (34◦49′N,104◦22′W)on24th September2001.Throughout theflight,the vertical geomagnetic cut-off rigidity was about4.2GV.The balloon reached at a normal floating altitude of36km at an atmospheric depth of4.5g/cm2.After a few hours, the balloon started to lose thefloating altitude and continued descending for more than13hours until termination of theflight.During the descending period,data were collected at atmospheric depths between4.5g/cm2and28g/cm2.The atmo-spheric depth was measured with accuracy of±1g/cm2,which comes mainly from an error in absolute calibration of an environmental monitor system.Fig.2shows a balloonflight profile during the experiment.4Data analysis4.1Data reductionWe selected“non-interacted”events passing through the detector without any inter-actions.The non-interacted event was defined as an event,which has only one iso-lated track,one or two hit-counters in each layer of the TOF hodoscopes,and proper d E/d x inside the upper TOF counters.There is a slight probability that particles in-teract with nuclei in the detector material and only one secondary particle goes into the tracking volume to be identified as a non-interacted event.These events were rejected by requiring proper d E/d x inside the upper TOF counters,because the interaction in the detector is expected to give a large energy deposit in the TOF counter.According to the Monte Carlo simulation with GEANT[10],these events are to be considered only below a few GeV.In order to estimate an efficiency of the non-interacted event selection,Monte Carlo simulations were performed.The probability that each particle can be identified as a non-interacted event was eval-uated by applying the same selection criterion to the Monte Carlo events as was applied to the observed data.The systematic error was estimated by comparing the hit number distribution of the TOF counters.For muons,the simulated data were compared with muon data sample measured on the ground.The systematic error for protons below1GeV was directly determined by the detector beam test using ac-celerator proton beam[11].The resultant efficiency and its error of non-interacted event selection for protons was83.3±2.0%at1.0GeV and77.4±2.5%at 10GeV,and that for helium nuclei was71.6±2.6%at1.0GeV/n and66.0±2.9%at10GeV/n.The efficiency for muons was94.0±0.9%and92.8±0.8% at0.5GeV and10GeV,respectively.The selected non-interacted events were required to pass through thefiducial vol-ume defined in this analysis.Thefiducial volume of the detector was limited to the central region of the JET chamber for a better rigidity measurement.The zenith angle(θz)was limited within cosθz≥0.90to obtain nearly verticalfluxes.For the muon analysis,we used only the particles which passed through the lead plate to es-timate electron contaminations.For the proton and helium analysis,particles were required not to pass through the lead plate so as to keep the interaction probability inside the detector as low as possible.In order to check the track reconstruction efficiency inside the tracking system,the recorded events were scanned randomly.It was confirmed that996out of1,000vi-sually identified tracks which passed through thefiducial volume were successfully reconstructed,thus the track reconstruction efficiency was evaluated to be99.6±0.2%.It was also confirmed that rare interacted events are fully eliminated by the non-interacted event selection.4.2Particle identificationIn order to select singly and doubly charged particles,particles were required to have proper d E/d x as a function of rigidity inside both the upper and lower TOF hodoscopes.The upper TOF d E/d x was already examined in the non-interacted event selection.The distribution of d E/d x inside the lower TOF counter and the selection boundaries are shown in Fig.3.In order to estimate efficiencies of the d E/d x selections for protons and helium nu-clei,we used another data sample selected by independent information of energy loss inside the JET chamber.The estimated efficiency in the d E/d x selection at 1GeV was98.3±0.4%and97.2±0.5%for protons and helium nuclei,respec-tively.The accuracy of the efficiency for protons and helium nuclei was limited by statistics of the sample events.Since muons could not be distinguished from elec-trons by the JET chamber,the d E/d x selection efficiency for muons was estimated by the Monte Carlo simulation to be99.3±1.0%.The error for muons comes from the discrepancy between the observed and simulated d E/d x distribution inside the TOF counters.The d E/d x selection efficiencies were almost constant in the whole energy region discussed here.Particle mass was reconstructed by using the relation of1/β,rigidity and charge, and was required to be consistent with protons,helium nuclei or muons.An appro-priate relation between1/βand rigidity for each particle was required as shown in Fig.4.Since the1/βdistribution is well described by Gaussian and a half-width of the1/βselection band was set at3.89σ,the efficiency is very close to unity (99.99%for pure Gaussian).4.3Contamination estimation4.3.1ProtonsProtons were clearly identified without any contamination below1.7GV by the mass selection,as shown in Fig.4.Above1.7GV,however,light particles such as positrons and muons contaminate proton’s1/β-band,and above4GV deuterons (D’s)start to contaminate it.To distinguish protons from muons and positrons above1.7GV,we required that light output of the aerogel Cherenkov counter should be smaller than the threshold. This requirement rejected96.5%of muons and positrons while keeping the effi-ciency for protons as high as99.5%.The aerogel Cherenkov cut was applied below 3.7GV,above which Cherenkov output for protons begins to increase rapidly. Contamination of muons in proton candidates after the aerogel Cherenkov cut wasestimated and subtracted by using calculated muonfluxes[20],which was nor-malized to the observedfluxes below1.0GeV where positive muons were clearly separated from protons.The positron contamination was calculated from the nor-malized positive muonfluxes and observed e/µratios.The resultant positive muon and positron contamination in the proton candidates was less than0.8%and4.1% below and above3.7GV,respectively,at26.4g/cm2where observed(µ+e)/p ratio is largest during the experiment.The error in this subtraction was estimated from the ambiguity in the normalization of the muon spectra to be less than0.2%and 0.8%below and above3.7GV,respectively.Since the geomagnetic cut-off rigidity is4.2GV,most of deuterons contaminating proton candidates above4GV are considered to be primary cosmic-ray particles. The primary D/p ratio was estimated by our previous measurement carried out in1998–2000at Lynn Lake,Manitoba,Canada,where the cut-off rigidity is as low as0.5GV.The D/p ratio was found to be2%at3GV.No subtraction was made for deuteron contamination because there is no reliable measurement of the deuteronflux above4GV.Therefore,above4GV hydrogen nuclei selected which included a small amount of deuterons.The D/p ratio at higher energy is expected to decrease[12]due to the decrease in escape path lengths of primary cosmic-ray nuclei[13]and the deuteron component is as small as the statistical error of the protonflux.4.3.2Helium nucleiHelium nuclei were clearly identified by using both upper and lower TOF d E/d x as shown in ndau tail in proton’s d E/d x might contaminate the helium d E/d x band,however this contamination from protons was as small as3×10−4.It was estimated by using another sample of proton data selected by d E/d x in the JET chamber.No background subtraction was made for helium.Obtained heliumfluxes include both3He and4He.4.3.3MuonsElectrons and pions could contaminate muon candidates.To estimate electron con-tamination,we used the d E/d x information inside the lower TOF counters covered with the lead plate.We calculated lower TOF d E/d x distribution for muons and electrons using the Monte Carlo simulation.The most adequate e/µratio was es-timated by changing weights both for muons and electrons so as to reproduce the observed d E/d x distribution.The simulated distributions well-agreed with the ob-served data as shown in Fig.5.The electron contamination was about10%of muon candidates at0.5GV,and less than1%above1GV.Since in the lower energy re-gion,the difference between the d E/d x distributions for electrons and muons are small,rejection power of d E/d x selection are lower.The error was estimated duringthefitting procedure to be about5%at0.5GV and0.1%at8.0GV.Accuracy of the electron subtraction was limited by poor statistics of electron events.For the pion contamination we made no subtraction,thus the observed muonfluxes include pions.According to a theoretical calculation[14],theπ/µratio at a residual atmo-sphere of3g/cm2through10g/cm2was less than3%at1GV and less than10% at10GV.Between1.6and2.6GV,protons contamination in the positive muon candidates and its error were estimated byfitting the1/βdistribution with a double-Gaussian function as shown in Fig6.The estimated ratio of proton contamination in muon candidates was less than3.3±1.3%.4.4CorrectionsIn order to determine the proton,helium and muon spectra,ionization energy loss inside the detector material,live-time and geometrical acceptance need to be esti-mated.The energy of each particle at the top of the instrument was calculated by sum-ming up the ionization energy losses inside the instrument with tracing back the event trajectory.The total live data-taking time was measured exactly to be40,601 seconds by counting1MHz clock pulses with a scaler system gated by a“ready”status that control thefirst level trigger.The geometrical acceptance defined for this analysis was calculated as a function of rigidity by using simulation technique[15]. In the high rigidity region where a track of the particle is nearly straight,the geo-metrical acceptance is0.097m2sr for protons and helium nuclei,and0.030m2sr for muons.The acceptance for muons is about1/3of that for protons and helium nuclei,because we required muons to pass through the lead plate while protons and helium nuclei were required not to pass through the lead plate.The simple cylindri-cal shape and the uniform magneticfield make it simple and reliable to determine the precise geometrical acceptance.The error which arose from uncertainty of the detector alignment was estimated to be1%.5Results and discussionsThe proton and heliumfluxes in energy ranges of0.5–10GeV/n and muonflux in 0.5GeV/c–10GeV/c,at small atmospheric depths of4.5g/cm2through28g/cm2, have been obtained from the BESS-2001balloonflight.The results are summarized in Table1.The statistical errors were calculated as68.7%confidence interval based on Feldman and Cousins’s“unified approach”[16].The overall errors including both statistic and systematic errors are less than8%,10%and20%for protons,helium nuclei and muons,respectively.The obtained proton and helium spectra are shown in Fig.7.Around at3.4GeV for protons and1.4GeV/n for helium nuclei, a geomagnetic cut-off effect is clearly observed in their spectra.The proton spec-trum measured by the AMS experiment in1998[17]at the similar geomagnetic latitude(0.7<ΘM<0.8,whereΘM is the corrected geomagnetic latitude[18])is also shown in Fig.7.The AMS measured proton spectra in space(at an altitude of380km),which are free from atmospheric secondary particles7.In the BESS results the atmospheric secondary spectra for protons below2.5GeV are observed. Fig.8shows the observed proton and heliumfluxes as a function of the atmospheric depth.Below2.5GeV the protonfluxes clearly increase as the atmospheric depth increases.It is because the secondary protons are produced in the atmosphere.In the primaryfluxes above the geomagnetic cut-off,thefluxes attenuate as the at-mospheric depth increases.In this energy region,the production of the secondary protons is much smaller than interaction loss of the primary protons.This is be-cause theflux of parent particles of secondary protons is much smaller due to the steep spectrum of primary cosmic rays.Figs.9and10show the observed muon spectra together with theoretical predic-tions.The predictions were made with the hadronic interaction model,DPMJET-III[19],which was used for the evaluation of atmospheric neutrinofluxes[20]. The obtained protonfluxes were used to reproduce the primary cosmic-rayfluxes in the calculation.Fig.11shows the observed muonfluxes as a function of atmo-spheric depth together with the calculatedfluxes.The calculatedfluxes show good agreement with the observed data.Further detailed study of the hadronic interaction models will be discussed elsewhere.6ConclusionWe made precise measurements of cosmic-ray spectra of protons,helium nuclei and muons at small atmospheric depths of4.5through28g/cm2,during a slow descending period of12.4hours,in the BESS-2001balloonflight at Ft.Sumner, New Mexico,USA.We obtained the proton and heliumfluxes with overall errors of8%and10%,respectively,in an energy region of0.5–10GeV/n.The muon fluxes were obtained with an overall error of20%in a momentum region of0.5–10GeV/c.The results provide fundamental information to investigate hadronic interactions of cosmic rays with atmospheric nuclei.The measured muon spectra showed good agreement with the calculations by using the DPMJET-III hadronic interaction model.The understanding of the interactions will improve the accuracy of calculation of atmospheric neutrinofluxes.AcknowledgementsWe would like to thank NASA and the National Scientific Balloon Facility(NSBF) for their professional and skillful work in carrying out the BESSflights.We are indebted to M.Honda and T.Kajita of ICRR,the University of Tokyo for their kindest cooperation for Monte Carlo simulations and theoretical interpretations.We would like to thank ISAS and KEK for their continuous support and encouragement for the BESS experiment.The analysis was performed with the computing facilities at ICEPP,the University of Tokyo.This experiment was supported by Grants-in-Aid(12047206and12047227)from the Ministry of Education,Culture,Sport, Science and Technology,MEXT.References[1]Y.Fukuda et al.,Phys.Rev.Lett.81(1998)1562.[2]S.Orito,in:Proc.ASTROMAG Workshop,KEK Report KEK87-19,eds.J.Nishimura,K.Nakamura,and A.Yamamoto(KEK,Ibaraki,1987)p.111.[3] A.Yamamoto et al.,Adv.Space Res.14(1994)75.[4]Y.Asaoka et al.,Nucl.Instr.and Meth.A416(1998)236.[5]Y.Ajima et al.,Nucl.Instr.and Meth.A443(2000)71.[6]Y.Shikaze et al.,Nucl.Instr.and Meth.A455(2000)596.[7]T.Sanuki,et al.,Astrophys.J.545,(2000),1135.[8]M.Motoki,et al.,Astropart.Phys.19,(2003),113.[9]T.Sanuki,et al.,Phys.Let.B,541,(2002),234.[10]R.Brun,et al.,GEANT3.21,CERN Program Library Long Write up W5013.[11]Y.Asaoka,et al.,Nucl.Instr.and Meth.A,489,(2001),170.[12]E.S.Seo,et al.,Proc.25th ICRC,Durban,3,1997,337.[13]I.J.Engelmann,et al.,A&A,1996,233.[14]S.A.Stephens,Proc.17th ICRC,Paris,4,1981,282.[15]J.D.Sullivan,Nucl.Instr.and Meth.95(1971)5.[16]G.J.Feldman and R.D.Cousins,et al.,Phys.Rev.D,57,(1998),3873.[17]M.Aguilar,et al.,Phys.Rep.366(2002)331.[18]A.Brekke,Physics of the Upper Polar Atmosphere,Willey,New York,1997,127-145.[19]S.Roeseler,et al.,SLAC-PUB-8740,hep-ph/0012252,unpublished.[20]M.Honda,et al.,Proc.27th ICRC,Hamburg,2001,162.and private communication.Fig.1.Cross sectional view of the BESS detector.010203040Local time(hour)A l t i t u d e (k m )-60-40-200T e m p e r a t u r e (°C )102030Altitude(km)A t m . d e p t h (g /c m 2)Fig.2.Altitude during the BESS-2001balloon flight experiment(top).Temperature and residual atmosphere as a function of altitude(bottom).11110Rigidity(GV)Fig.3.Distribution of d E /d x inside the lower TOF counters.Solid lines show selection boundaries for protons and helium nuclei.Dashed lines show those for muons.110R(GV)Fig.4.Distribution of 1/βfor Z =1particles.Solid lines show the selection boundaries for protons.Dashed lines show those for muons.12101101010e v e n tsFig.5.Observed and simulated distribution of d E /d x inside the lower TOF counters for the events in which track passed through the lead plate.Dashed line shows the selection bound-ary for 0501001502002503003504001/βe v e n t sFig.6.An estimation of proton contamination by the TOF information.Hatched area shows an estimated proton contamination.1310102110E kinetic (GeV/n)F l u x (m -2s r -1s e c -1(G e V /n )-1)-1110110E kinetic (GeV/n)Fig.7.The observed proton and helium spectra.The error bars include statistical error only.In the proton spectra,atmospheric secondary components are clearly observed below 2.5GeV in the BESS results.141010Atm. depth (g/cm 22)F l u x (m -2s r -1s e c -1(G e V /n )-1)110Atm. depth (g/cm 22)Fig.8.The observed proton and helium fluxes as a function of atmospheric depth.1510-1110102Atm. depth (g/cm 2)F l u x (m -2s r -1s e c -1(G e V /c )-1)-1110102Atm. depth (g/cm 2)Fig.11.The observed negative and positive muon fluxes.The solid lines show theoretical predictions calculated by using DPMJET-III.17。
