Spherical Sector Research Articles

Invariants of the spherical sector in conformal mechanics

A direct relation is established between the constants of motion for conformal mechanics and those for its spherical part. In this way, we find the complete set of functionally independent constants of motion for the so-called cuboctahedric Higgs oscillator, which is just the spherical part of the rational A3 Calogero model (describing four Calogero particles after decoupling their center of mass).

The motion of a ball on a grassy lawn

The motion of a ball of constant spherical shape on a grassy lawn represented by a set of deformable rods with one end rigidly attached to a plane, while the other end is free and can contact the ball, is investigated. The contact area on the ball surface is represented by a spherical sector, whose dimensions and location on the ball surface depend on the position of the centre of the ball and its orientation. The projection of the contact area onto the plane is a circle, whose centre and radius vary as the centre of the ball moves. When the rods come into contact with the ball, they experience longitudinal and flexural strains, as well as impact actions on the boundary of the contact area. The translational–rotational motion of a ball on a lawn of rods without friction, as well as motion with viscous friction at the points of contact of the ends of the rods with the ball, is considered.

Ionic debris measurement of three extreme ultraviolet sources

Generation of debris in extreme ultraviolet (EUV) light sources is an inherent and real threat to the lifetime of collection optics. Debris measurement of these sources is useful to enable source suppliers to estimate collector lifetime. At the Center for Plasma Material Interactions (CPMI) at the University of Illinois, an Illinois calibrated spherical sector electrostatic energy analyzer (ICE) was built to measure the ion debris flux in absolute units. In addition to ion flux, the detector is also capable of identifying different ion species present in the plasma utilizing energy-to-charge ratio discrimination. The lifetime of the collector optics is calculated using the measured ion flux. In the current investigation we compare the measurement of ion debris production in three different EUV sources: the Energetiq EQ-10M, the AIXUV-100, and the XTREME XTS 13-35. In the EQ-10M source, three angular measurements are coupled with three variations in operating pressure to measure consequent effects on debris production. These measurements reveal four predominant ion species in the energetic debris analysis: C+, Si+, Xe+, and Xe2+. The amount of debris is reduced as pressure is increased. Various debris mitigation methods are implemented in the AIXUV-100 source and results reveal that four ion species are observed (Ar+, Xe+, Xe2+, and W+), though there does not seem to be a dominant species. The first mitigation technique, backstreaming argon toward the source, reduces the amount of Ar+, Xe2+, and W+, yet increases the amount of Xe+ The increase in Xe+ flux is explained based on charge exchange phenomena. The ICE machine was then attached 1.92 m away from the pinch of XTS 13-35 source, and placed at 25° away from the normal line. The comparison of results reveals that the XTS 13-35 and the EQ-10M sources produced comparable amounts of energetic ion flux per watt of EUV light produced. The AIXUV-100 source generated more ion debris flux per watt of EUV light than the other two sources, though it should be noted that the AIXUV-100 source was capable of producing more than ten times the amount of EUV light power compared to any of the other sources.

Investigation of ions emitted from a tin fuelled laser produced plasma source

In this work ions emitted from a laser produced plasma created from a solid tin target have been analyzed using a spherical sector energy analyzer (ESA). Employing time of fiight analysis, the ESA allows determination of ion energy and charge stage as a function of ion emission angle. Ions of charge Sn+1 - Sn+9 with energy to charge ratios of 0.22 - 3.2keV have been investigated over a range of emission angles from 20 - 80 degrees, relative to the target normal, for three distinct laser pulse energies

高エネルギー電子移動解離が可能なタンデム質量分析装置の開発

A JEOL JMS-HX110 double-focusing mass spectrometer was combined with the collision cell and spherical electric sector of a HITACHI M80-B instrument to perform tandem mass spectrometry experiments. A quadrupole lens doublet was mounted between the mass spectrometer and the collision cell to improve ion transmission into the collision cell. The detection system was also improved to expand the mass range of product ions. These improvements provided reliable spectra of high-energy electron transfer dissociation (HE-ETD) of peptides using an alkali metal target. The present results demonstrated that HE-ETD by a single collision with an alkali metal target could determine the amino acid sequence and phosphorylation site of peptides.

Reduced Stability of the Atlantic Meridional Overturning Circulation due to Wind Stress Feedback during Glacial Times

Abstract A previous study by Mikolajewicz suggested that the wind stress feedback stabilizes the Atlantic thermohaline circulation. This result was obtained under modern climate conditions, for which the presence of the massive continental ice sheets characteristic of glacial times is missing. Here a coupled ocean–atmosphere–sea ice model of intermediate complexity, set up in an idealized spherical sector geometry of the Atlantic basin, is used to show that, under glacial climate conditions, wind stress feedback actually reduces the stability of the meridional overturning circulation (MOC). The analysis reveals that the influence of the wind stress feedback on the glacial MOC response to an external source of freshwater applied at high northern latitudes is controlled by the following two distinct processes: 1) the interactions between the wind field and the sea ice export in the Northern Hemisphere (NH), and 2) the northward Ekman transport in the tropics and upward Ekman pumping in the core of the NH subpolar gyre. The former dominates the response of the coupled system; it delays the recovery of the MOC, and in some cases even stabilizes collapsed MOC states achieved during the hosing period. The latter plays a minor role and mitigates the impact of the former process by reducing the upper-ocean freshening in deep-water formation regions. Hence, the wind stress feedback delays the recovery of the glacial MOC, which is the opposite of what occurs under modern climate conditions. Close to the critical transition threshold beyond which the circulation collapses, the glacial MOC appears to be very sensitive to changes in surface wind stress forcing and exhibits, in the aftermath of the freshwater pulse, a nonlinear dependence upon the wind stress feedback magnitude: a complete and irreversible MOC shutdown occurs only for intermediate wind stress feedback magnitudes. This behavior results from the competitive effects of processes 1 and 2 on the midlatitude upper-ocean salinity during the shutdown phase of the MOC. The mechanisms presented here may be relevant to the large meltwater pulses that punctuated the last glacial period.

Methods for Solving Elliptic PDEs in Spherical Coordinates

A new method for investigating boundary value problems in two dimensions has recently been introduced by one of the authors. The main achievement of this method is that it yields explicit integral (as oppose to series) representations for a variety of boundary value problems. In addition, this method also provides an alternative, apparently simpler, approach for deriving those solution representations that are traditionally constructed by the method of images and of classical integral transforms. Here, we implement this latter approach to boundary value problems formulated in spherical coordinates. In particular, we do the following: (a) We derive the classical Poisson integral formula for the solutions of the Dirichlet problem for the Poisson equation in the interior of a sphere, the analogous formula for the Neumann problem, and the generalizations of these formulae in n dimensions. (b) We derive the solutions of various boundary value problems for the inhomogeneous Helmholtz equation in the interior of a sphere. (c) We solve the Dirichlet problem for the Laplace equation in the interior of a spherical sector.

Lifetime measurements on collector optics from Xe and Sn extreme ultraviolet sources

Next generation lithography to fabricate smaller and faster chips will use extreme ultraviolet (EUV) light sources with emission at 13.5nm. A challenging problem in the development of this technology is the lifetime of collector optics. Mirror surfaces are subjected to harsh debris fluxes of plasma in the form of ions, neutrals, and other radiation, which can damage the surface and degrade reflectivity. This manuscript presents the measurement of debris ion fluxes and energies in absolute units from Xe and Sn EUV sources using a spherical sector ion energy analyzer. Experimentally measured erosion on Xe exposed samples is in good agreement with predicted erosion. This result allows prediction of erosion using measured ion fluxes in experiment. Collector optic lifetime is then calculated for Xe and Sn sources without debris mitigation. Lifetime is predicted as 6h for Xe EUV sources and 34h for Sn EUV sources. This result allows calculation of expected collector optic lifetimes, which can be an important tool in optimizing source operation for high volume manufacturing.

Reduction of Ion Energies From a Multicomponent $Z$ -Pinch Plasma

This paper studies the expanding plasma dynamics of ions produced from a 5J Z-pinch xenon light source used for extreme ultraviolet (EUV) lithography. Fast ion debris produced in such plasmas cause damage to the collector mirror surface. Because of the great degree of erosion and the change in surface roughness properties, the reflectivity of EUV light at 13.5 nm drops drastically. Reducing ion energies and stopping the ion flux are a potential solution toward the success of EUV lithography. Ion energies are measured in kiloelectronvolt range using a spherical sector electrostatic energy analyzer. Preliminary computational work indicates that the observed high energies of ions are probably resulting from Coulomb explosion initiated by pinch instability. Mixed fuel experiments are performed using a mixture of Xe, N <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> , and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . The average energy of the expelled Xe ions is significantly decreased if the mobile lighter gas species are present in the main fuel. The magnitude of the Xe ion signal is reduced as well. This reduction in the quantity of heavy ions and their energy could greatly extend the lifetime of the collector optics used in EUV lithography.

The solution of the inverse problem of gravitational potential using a set of measurements of different field elements

A numerical solution of the inverse problem of the gravitational field at a single point is obtained using six field elements for a point, a spherical cap, a differential spherical sector and a vertical segment. In the system of six equations obtained, the unknowns are the mass of the body, the depth of its center, and the second, third, and fourth degree moments. The accuracy of the solution of this system is ten times higher than when using three field elements.

Multi-point sandwich forming of a spherical sector with tool-shape compensation

The need for a cost-effective means of rapid, small-batch quality parts manufacture is greater than ever in the sheet metal industry. A new reconfigurable multi-point forming process, multi-point sandwich forming (MPSF), has been conceived and investigated as a possibly useful method to fulfill this need. This process is different from to conventional multi-point forming, in that a re-usable die sheet is used, a large distance between pins exists in the reconfigurable die and the upper die is made of polyurethane. In the work described in this paper, the performance of a multi-pin die with pins in circular array and an adjustable blank holder is investigated. This die is suitable to form work-pieces with rotational symmetry. Also, a die shape optimization design method using inverse displacement compensation is presented. Experimental and simulation results from forming a spherical shell sector, with a diameter of 380 mm show this method is feasible and effective. The results also show the blank holder can reduce/eliminate dimples that sometimes arise in the work-piece and the deformation of the interpolator during the forming process can induce a shape error in the formed work-piece.

Location and volume of the active site of chymotrypsin

The active site of chymotrypsin molecule (approximated by a sphere with radius of 20 A) was taken as the largest cavity on the enzyme surface. The volume inside the approximating sphere is sufficient for placement of 95% of non-hydrogen atoms of the enzyme. The active site cavity is localized in a spherical sector with solid angle of 80 degrees whose axis passes through the CB-atom of the Ser195 residue. The volume of the active site cavity is about 2700 A(3) (8% of the volume of the approximating sphere) as computed by the Monte-Carlo method from known X-ray data. The size and shape of the active site cavity is sufficient for entrance of significantly large fragments (more than 60 non-hydrogen atoms) of the substrate molecule. At the active site cavity bottom, there is a narrow compartment adjacent to an oxy-anion hollow and accessible to water but not to substrate molecules. The water molecules inside this narrow compartment can take part in heat exchange with the external medium during different steps of the enzymatic process.

Characterization of collector optic material samples exposed to a discharge-produced plasma extreme ultraviolet light source

Extreme ultraviolet (EUV) light sources with efficient emission at 13.5 nm are needed for next-generation lithography. A critical consideration in the development of such a source is the lifetime of collector optics. These experiments expose optics to a large flux of energetic particles coming from the expansion of the pulsed-plasma EUV source to investigate mirror damage due to erosion, layer mixing, and ion implantation. The debris ion spectra are analyzed using a spherical sector energy analyzer (ESA) showing ion energies of 2 to 13 keV, including Xe+-Xe+4, Ar+, W+, Mo+, Fe+, Ni+, and Si+. Microanalysis is performed on samples exposed to 10 million pulses, including atomic force microscopy (AFM), showing increased roughness for most exposed samples. Notably, a Mo-Au Gibbsean segregated alloy showed surface smoothing over this time frame, suggesting that the segregation worked in situ. TRIM predictions for ion implantation are consistent with ion debris measurements from the ESA. Finally, time exposures of samples from 2, 20, and 40 million pulses show an initial roughening with smoothing of the exposed samples at longer time frames. Constant erosion is demonstrated with the SEM. These analyses give an experimental account of the effects of the ion debris field on optic samples exposed to the EUV source.

통신해양기상위성 통신 탑재체의 우주 방사선 환경 모사 및 영향 추정

통신해양기상위성의 통신 탑재체가 겪게 될 우주 방사선 환경을 포획된 입자, 태양 양성자 그리고 우주선으로 구분하여 각각 NASA AP8/AE8 모델, JPL91 모델, 그리고 NRL CREME 모델을 사용하여 전산 모사 하였다. 이러한 우주 방사선 환경이 위성 내 통신 탑재체에 미치는 영향을 추정하기 위해 총 이온화 방사선 효과의 분석에 필요한 Dose-Depth 곡선 및 단일사건효과 발생률 계산에 필요한 LET 스펙트럼 구하였다. 통신 탑재체 내의 각 장치별 차폐 효과 차이를 고려한 총 이온화 방사선 효과의 예측을 위해서 기계 구조 모델을 만든 후 구형 분할 방법을 적용하였다. 이를 통해 통신 탑재체 내 각 장치의 위치별 총 이온화 방사선 효과를 예상하였으며 동일한 외부 방사선 환경에 대해서 차폐 효과에 따라 최고 8배까지 방사선 효과가 다르게 나타났다. Space radiation environment for COMS is simulated by NASA AP8/AE8, JPL91 and NRL CREME models, respectively for trapped particle, solar proton and cosmic-ray. The radiation effects on electronic devices in communication payload are also estimated by using simulation results. Dose-depth curve and LET spectrum are calculated for estimating total ionizing dose(TID) effect and single event effect(SEE) respectively. Spherical sector method is applied to dose estimation at each position in the units of communication payload to consider shielding effect of platform and housing. Total ionizing dose at each position varies by 8 times through shielding effect under the same external space radiation environment.

Measured electron IMFPs for SiC

AbstractSilicon carbide (SiC) is a wideband semiconductor that is very promising for many applications in optoelectronics and microelectronics. Since information on the electron transport processes in SiC is scarce, its systematic study is highly desirable. The aim of this work is to determine experimentally by elastic peak electron spectroscopy (EPES), for the first time, the inelastic mean free paths (IMFPs) in bulk SiC with different structural properties (polycrystalline and monocrystalline materials) and surface concentrations of its constituents. The relative EPES measurements were carried out in the electron energy range 0.2–2.0 keV with two different analyzers (double‐pass cylindrical mirror analyzer (DCMA), spherical sector analyzer (SSA)) and the use of Ni standard. The measured IMFPs were uncorrected for surface excitations and compared with those calculated from the TPP‐2M and G‐1 predictive formulae using Fano plots. Good agreement was found between the measured and the calculated electron IMFPs in SiC exhibiting different structural properties. Copyright © 2006 John Wiley &amp; Sons, Ltd.

Ion debris characterization from a z-pinch extreme ultraviolet light source

An XTREME Technologies XTS 13-35 extreme ultraviolet (EUV) light source creates a xenon z pinch that generates 13.5nm light. Due to the near x-ray nature of light at this wavelength, extremely smooth metal mirrors for photon collection must be employed. These are exposed to the source debris. Dissolution of the z-pinch gas column results in high-energy ion and neutral release throughout the chamber that can have adverse effects on mirror surfaces. The XTREME commercial EUV emission diagnostic chamber was designed to maximize diagnostic access to the light and particulate emissions from the z pinch. The principal investigation is characterization of the debris field and the erosive effects on optics present. Light emission from the z pinch is followed by ejection of multiply charged ions and fast neutral particles that make up an erosive flux to chamber surfaces. Attenuation of this erosive flux to optical surfaces is attempted by inclusion of a debris mitigation tool consisting of foil traps and neutral buffer gas flow. Characterization of the z-pinch ejecta is performed with a spherical sector energy analyzer (ESA) that diagnoses fast ion species by energy-to-charge ratio using ion time-of-flight (ITOF) analysis. This is used to evaluate the debris tool’s ability to divert direct fast ions from impact on optic surfaces. The ITOF-ESA is used to characterize both the energy and angular distribution of the direct fast ions. Xe+ up to Xe+4 ions have been characterized along with Ar+ (the buffer gas used), W+, Mo+, Si+, Fe+, and Ni+. Energy spectra for these species from 0.5 up to 13keV are defined at 20° and 30° from the pinch centerline in the chamber. Results show a drop in ion flux with angular increase. The dominant species is Xe+ which peaks around 8keV. Ion flux measured against buffer gas flow rate suggests that the direct fast ion population is significantly attenuated through increases in buffer gas flow rate. This does not address momentum transfer from scattered ions or fast neutral particles. These results are discussed in the context of other investigations on the effects of total particle flux to normal incidence mirror samples exposed for 1×107 pulses. The samples (Si∕Mo multilayer with Ru capping layer, Au, C, Mo, Pd, Ru, and Si) were exposed to the source plasma with 75% argon flow rate in the debris mitigation tool and surface metrology was performed using x-ray photoelectron spectroscopy, atomic force microscopy, x-ray reflectivity, and scanning electron microscopy to analyze erosion effects on mirrors. These results are compared to the measured direct ion debris field.

Experimental test chamber design for optics exposure testing and debris characterization of a xenon discharge produced plasma source for extreme ultraviolet lithography

A commercial EUV light source is currently used in the MS-13 EUV Micro Exposure Tool (MET) produced by Exitech Ltd. The source uses a xenon z-pinch discharge to produce 13.5 nm light intended for use in extreme ultraviolet lithography (EUVL). During operation, an erosive flux of particles is ejected from the pinch plasma, contributing to limitations in the lifetime of nearby collector optics. A diagnostic chamber is presented that permits characterization of the debris fields present, exposure of optical samples, and evaluation of debris mitigation techniques. Available diagnostics include a Faraday cup, a spherical sector energy analyzer (ESA), and a EUV photodiode. This paper details the chamber design and initial results of source characterization. Faraday cup analysis shows that the maximum theoretical ion energy is 53 keV, ESA measurements show the presence of Xe +, Xe 2+, Ar +, W +, and Mo + ions, and microanalysis of exposed mirror samples is used to show the erosive effects of plasma exposure.

Interfacial factors affecting polymeric diphenylmethane diisocyanate/wood bond strength

AbstractPolymeric diphenylmethane diisocyanate (pMDI) has been used for making wood board composites for over 30 years, although its growth in application has been limited mainly by the perception that it is a high‐cost alternative to formaldehyde‐based adhesives. Increased use of pMDI adhesive in making wood composites will require optimization of the process variables involved. One such factor is the unresolved question of the interfacial aspects most responsible for building strong wood composites. Some argue that adhesive surface coverage is primarily responsible for board strength; others assert that penetration of the pMDI into the wood matrix is a primary characteristic of strong boards. This article will provide evidence that the interfacial aspect most important in building board strength is surface coverage of the wood particles or fibers. Experiments controlling the depth of pMDI penetration into wood matrices and then measuring their adherend strength were performed. We also calculated the potential efficiencies to be obtained from maximizing the surface coverage and minimizing the matrix penetration using a spherical sector model. Neither high nor low pMDI viscosity offered a significant advantage in surface covering pine or oak, although it is speculated that minimizing the droplet size of pMDI in the resination step could lead to substantial efficiency improvements in adhesive coverage. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 449–455, 2005

The performance of implicit ocean models on B- and C-grids

Fully-implicit primitive equation ocean models are useful to study the sensitivity of steady ocean flows to parameters, to determine bifurcations of these flows associated with instabilities and to use relatively large time steps in transient flow computations. This paper addresses a problem related to the origin of wiggles occurring in fully-implicit C-grid models. The situation considered is the computation of three-dimensional thermally-driven steady flows in a midlatitude spherical sector. We determine the reason why in a coarse resolution C-grid implicit model, the values of the lateral friction coefficients are restricted to far higher values than for the same B-grid model. The analysis also reveals why the B-grid discretization is superior for the computation of this type of flows.

Downstream Ion Energy Distributions in a Hollow Cathode Ring Cusp Discharge

The presence of energetic ions produced by a hollow cathodes operating at high-emission currents (>10 A) has been documented in the literature. As part of an ongoing effort to uncover the underlying physics of the formation of these ions, ion efflux from a high-current hollow cathode operating in an ion thruster discharge chamber was investigated. With use of a spherical sector electrostatic energy analyzer located downstream of the discharge cathode, the ion energy distribution over a 0-60-eV energy range was measured. The sensitivity of the ion energy distribution function to zenith angle was also assessed at three different positions: 0, 15, and 25 deg. The measurements suggest that the majority of the ion current at the measuring point falls into the analyzer with an energy approximately equal to the discharge voltage. The ion distribution, however, was found to be quite broad. The high-energy tail of the distribution function tended to grow with increasing discharge current. Sensitivity of the profiles to flow rate at fixed discharge current was also investigated. A simple model is presented that provides a potential mechanism for the production of ions with energies above the discharge voltage.