Gaussian beams in inhomogeneous media: A review

The paper outlines the most important results of the paraxial complex geometrical optics (CGO) in respect to Gaussian beams diffraction in the smooth inhomogeneous media and discusses interrelations between CGO and other asymptotic methods, which reduce the problem of Gaussian beam diffraction to the solution of ordinary differential equations, namely: (i) Babich’s method, which deals with the abridged parabolic equation and describes diffraction of the Gaussian beams; (ii) complex form of the dynamic ray tracing method, which generalizes paraxial ray approximation on Gaussian beams and (iii) paraxial WKB approximation by Pereverzev, which gives the results, quite close to those of Babich’s method. For Gaussian beams all the methods under consideration lead to the similar ordinary differential equations, which are complex-valued nonlinear Riccati equation and related system of complex-valued linear equations of paraxial ray approximation. It is pointed out that Babich’s method provides diffraction substantiation both for the paraxial CGO and for complex-valued dynamic ray tracing method. It is emphasized also that the latter two methods are conceptually equivalent to each other, operate with the equivalent equations and in fact are twins, though they differ by names. The paper illustrates abilities of the paraxial CGO method by two available analytical solutions: Gaussian beam diffraction in the homogeneous and in the lens-like media, and by the numerical example: Gaussian beam reflection from a plane-layered medium.     

用离子色谱法测定金矿区水样中常规无机离子

利用DX－120离子色谱仪进行阴阳离子的精密度和准确度测定，100mg/L时相对标准偏差范围为1．00％－3．80％，回收经95．83％－105．00％；5mg／L时相对标准偏差范围为1．18％－4．57％，回收率92．40％－103．20％，完全达到实际要求。用该离子色谱仪测定甘肃阳山金矿山水样中常规无机离子，数据表明该区域水质较好，所测离子浓度都未超过饮用水标准。     

Location and quantitative analysis of OH in coesite

 The incorporation of hydrogen (deuterium) into the coesite structure was investigated at pressures from 3.1 to 7.5 GPa and temperatures of 700, 800, and 1100 °C. Hydrogen could only be incorporated into the coesite structure at pressures greater 5.0 GPa and 1100 °C . No correlation between the concentration of trace elements such as Al and B and the hydrogen content was observed based on ion probe analysis (1335 ± 16 H ppm and 17 ± 1 Al ppm at 7.5 GPa, 1100 °C). The FTIR spectra show three relatively intense bands at 3575, 3516, and 3459 cm⁻¹ (ν₁ to ν₃, respectively) and two very weak bands at 3296 and 3210 cm⁻¹ (ν₄ and ν₅, respectively). The band at 3516 cm⁻¹ is strongly asymmetric and can be resolved into two bands, 3528 (ν_2a) and 3508 (ν_2b) cm⁻¹, with nearly identical areas. Polarized infrared absorption spectra of coesite single-crystal slabs, cut parallel to (0 1 0) and (1 0 0), were collected to locate the OH dipoles in the structure and to calibrate the IR spectroscopy for quantitative analysis of OH in coesite (ɛ _{i ,tot}=190 000 ± 30 000 l mol⁻¹ _H2O cm⁻²). The polarized spectra revealed a strong pleochroism of the OH bands. High-pressure FTIR spectra at pressures up to 8 GPa were performed in a diamond-anvil cell to gain further insight into incorporation mechanism of OH in coesite. The peak positions of the ν₁, ν₂, and ν₃ bands decrease linearly with pressure. The mode Grüneisen parameters for ν₁, ν₂, and ν₃ are −0.074, −0.144 and −0.398, respectively. There is a linear increase of the pressure derivatives with band position which follows the trend proposed by Hofmeister et al. (1999). The full widths at half maximum (FWHM) of the ν₁, ν₂, and ν₃ bands increase from 35, 21, and 28 cm⁻¹ in the spectra at ambient conditions to 71, 68, and 105 in the 8 GPa spectra, respectively. On the basis of these results, a model for the incorporation of hydrogen in coesite was developed: the OH defects are introduced into the structure by the substitution Si^4+(Si2)+4O²⁻= ^[4]□^(Si2) + 4OH⁻, which gives rise to four vibrations, ν₁, ν_2a, ν_2b, and ν₃. Because the OH(D)-bearing samples do contain traces of Al and B, the bands ν₄ and ν₅ may be coupled to Al and/or B substitution. Received: 19 December 2000 / Accepted: 23 April 2001     

区域站和基准站气溶胶的分析

文章讨论了秋季（1994年10月）和冬季（1995年1月）在中国西部青海省共和县瓦里关山（36°17′N，100°54′E，海拔3816 m）基准站和中国东北黑龙江省五常县的龙凤山（44°44′N，127°36′E，海拔331 m）及中国东南沿海的浙江省临安县的横畈乡（30°18′N，119°44′E，海拔131 m）两个区域本底站（上述3站均属WMO）所采集的气溶胶样品的质量浓度、可溶性离子浓度的时空分布特征和变化规律。初步得出:气溶胶质量浓度和可溶性离子浓度以临安为最高。其次是龙凤山，而瓦里关山为最低     

743离子交换快速分离—等离子体光谱法同时测定十五个稀土元素

本文研制了适用于地质样品中15个稀土元素分析的快速方法。样品经碱熔沉淀分离和743阳离子交换树脂分离富集将稀土元素制备成溶液用等离子体光谱法(ICP-AES)进行测量。方法检出限为0.002-0.3μg/g,当稀土元素含量为0.5-80,μg/g时,方法相对标准偏差为15％-2％。本方法经过多年的样品分析考验以及不断的改进和完善,证明方法简便快速,分析数据稳定可靠,能很好地满足地质样品中15个稀土分量测定的要求。     

LiBr溶液从低浓度到高浓度的分子动力学模拟

在 L i Br与水的物质量比分别为 1∶ 64、1∶ 32、1∶ 16、1∶ 8、1∶ 4和 1∶ 3的情况下 ,对 L i Br溶液从低温到高温的分子动力学模拟进行了研究。随浓度增加 ,锂离子的水合数量呈减少趋势但同时又从 L i+- Br-接触离子对的数量增加中得到补偿 ,而 L i离子的第一配位壳层的配位数量保持不变。在高浓度 Li Br溶液中 ,Br- O之间的距离有所增加 ,Br-- O的径向分布的形状更趋于非对称 ,从而很好地确定了 Br离子水合壳层 L i+- Br-接触离子对可以在更稀的溶液中产生 ,但随浓度增加而增加。L i+- Br-距离明显短于溶液中 Li离子与 Br离子的离子半径之和 ,也短于 L i Br晶体中两者离子半径之和。高浓度溶液中水分子的结构几乎被破坏 ,水分子间的氢键明显增加 ,但没有消失。对 L i+、Br-和水的扩数系数计算值与实验值进行了比较     

Effect of parallel electric field on electrostatic ion-cyclotron instability in anisotropic plasma in the presence of ion beam and general distribution function—Particle aspect analysis

Dispersion relation, resonant energy transferred, growth rate and marginal instability criteria for the electrostatic ion-cyclotron wave with general loss-cone distribution in low-β anisotropic, homogeneous plasma in the auroral acceleration region are discussed by investigating the trajectories of the charged particles. Effects of the parallel electric field, ion beam velocity, steepness of the loss-cone distribution and temperature anisotropy on resonant energy transferred and growth rate of the instability are discussed. It is found that the effect of the parallel electric field is to stabilize the wave and enhance the transverse acceleration of ions whereas the effect of steepness of loss-cone, ion beam velocity and the temperature anisotropy is to enhance the growth rate and decrease the transverse acceleration of ions. The steepness of the loss-cone also introduces a peak in the growth rate which shifts towards the lower side of the perpendicular wave number with the increasing steepness of the loss-cone.     

Sheath effects on DEMETER ion drift measurements

The “Instrument d’Analyse du Plasma” on DEMETER includes an ion drift meter used to measure the direction of the incoming ram plasma ( [Berthelier et al., 2006a] and [Berthelier et al., 2006b]). Given the velocity of the satellite, and expected flow velocities of plasma along DEMETER's orbit, it is estimated that at mid latitudes, the direction of incident plasma as measured by IAP should be within approximately 2° of the ram direction. Yet, significantly larger angular deviations are measured routinely. An important assumption made in the interpretation of onboard instruments, such as IAP, is that neither the spacecraft nor the instrument significantly perturb the plasma that is being measured. In view of the large observed angular deviations, this paper examines the possible effect of the electrostatic sheath surrounding IAP. This is done with the 3D PIC simulation code PTetra. The model uses a full 3D particle in cell code with unstructured tetrahedral mesh capable of accurately representing the satellite geometry. The mesh is also adaptive so as to provide a fine spatial resolution in the vicinity of the particle sensor where it is needed, and a coarse resolution in regions where plasma parameters vary over a longer scale length. Calculation results show that while particle deflection associated with the electrostatic sheath near IAP can account for appreciable angular deflections for representative ionospheric plasmas, they are typically smaller than the ones observed. Additionally, the model is unable to reproduce the latitudinal dependence of the observed large deflection angles. It is concluded that sheath effects may cause appreciable distortions on the IAP type of ion flow meter instruments, and on other particle sensors in general. The larger observed deviations and their latitudinal dependence, however, must be attributable to other physical processes not accounted for in the model.     

The construction and development of SHRIMP I: An historical outline

In 1973 Bill Compston advocated the building of an ion microprobe at the Research School of Earth Sciences (RSES) at the Australian National University (ANU). The commercial ion probes available at this time were too small to have sufficient sensitivity for trace element analysis and too low in mass resolution to avoid molecular interferences. The project commenced in 1974 with the appointment of a former ANU PhD student Steve Clement who had expertise in beam transport theory. To achieve high sensitivity and high mass resolution, beam transport theory indicated that a much larger magnet than in any commercially available mass spectrometer would be required. Clement chose an ion optical design, by Professor Matsuda of Osaka University in 1974, which had the required combination of high mass resolution and high transmission. Clement's job was to produce the detailed scientific designs and machine drawings for the new instrument as well as testing the completed instrument. Clement coined the term SHRIMP-Sensitive High Resolution Ion MicroProbe. By the end of 1977 nearly all the components had been manufactured and the big electromagnet had been successfully tested. In the following year the secondary mass analyzer was assembled and tested using a thermal ionization source and showed great promise with flat-topped peaks at 5000 resolution and 50% transmission with 50 V energy spread. At this stage the machine had far exceeded the specifications for the available commercial ion probes. Continued development during 1981 to the point where the original design specifications were fully realized was time consuming since learning how to use the entirely novel instrument was no simple task; no one else had an instrument like SHRIMP. The application of the instrument to zircon U–Pb geochronology established the necessary operating conditions for measuring Pb isotopic compositions and the elemental ratios Pb/U and U/Zr from 20 μm diameter spots on single zircon grains. Application of this in the early 1980s started a revolution in Precambrian geology by the ability to produce rapidly accurate and precise age determinations on structurally complex zircon samples.     

Reverse time migration with Gaussian beams using optimized ray tracing systems in transversely isotropic media

Prestack depth migration is a key technology for imaging complex reservoirs in media with strong lateral velocity variations. Prestack migrations are broadly separated into ray-based and wave-equation-based methods. Because of its efficiency and flexibility, ray-based Kirchhoff migration is popular in the industry. However, it has difficulties in dealing with the multi-arrivals, caustics and shadow zones. On the other hand, wave-equation-based methods produce images superior to that of the ray-based methods, but they are expensive numerically, especially methods based on two-way propagators in imaging large regions. Therefore, reverse time migration algorithms with Gaussian beams have recently been proposed to reduce the cost, as they combine the high computational efficiency of Gaussian beam migration and the high accuracy of reverse time migration. However, this method was based on the assumption that the subsurface is isotropic. As the acquired azimuth and maximum offsets increase, taking into account the influence of anisotropy on seismic migration is becoming more and more crucial. Using anisotropic ray tracing systems in terms of phase velocity, we proposed an anisotropic reverse time migration using the Gaussian beams method. We consider the influence of anisotropy on the propagation direction and calculate the amplitude of Gaussian beams with optimized correlation coefficients in dynamic ray tracing, which simplifies the calculations and improves the applicability of the proposed method. Numerical tests on anisotropic models demonstrate the efficiency and accuracy of the proposed method, which can be used to image complex structures in the presence of anisotropy in the overburden.