Derivation of a modified paraxial formalism for two-dimensional trajectories in electron and ion sources of non-simple geometries

A modified paraxial formalism has been developed which describes two-dimensional charged particle beam dynamics in electron and ion sources with pointed or needle-type geometries. A Hamiltonian formalism, and a more exact treatment of energy conservation is used to derive the modified paraxial equation for two-dimensional trajectories in systems with axially symmetric prolate-spheroidal beams. Calculations have been done for a gallium field emission liquid metal ion source modeled by a hyperboloid of revolution and planar extractor. Two important conclusions emerge from these calculations: i) The dominant effect of space-charge, for source geometries with small radii of curvature, occurs in the region close to the apex (<0.05 n) and ii) beam divergence has a strong dependence on geometry. This latter effect is a consequence of large two-dimensional field gradients near the apex of sources with needle-type or pointed geometry.This work was supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-8108829     

Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Reply to comment on “variational formulation for the equilibrium condition of a conducting fluid in an electric field”

In this comment we respond to the several criticisms of the paper by Sujatha et al. raised by Kingham and Bell. In particular, we demonstrate that, contrary to their assertion, Taylor's solution for the electrostatic fields can never satisfy the boundary conditions for the actual experimental configurations involving field emission liquid metal ion sources and other experiments on electrostatically stressed conducting fluids. It is further argued that a careful analysis of Taylor's experimental procedure and observations suggests that although the observed static structures have a macroscopic axial-symmetry they have not the idealized conical shapes of prescribed angle. Furthermore, the formation of the Taylor cone structure is shown to be inconsistent with the principle of energy minimization.It is concluded that none of the criticism raised by Kingham and Bell invalidate any of the analysis or conclusions presented in the paper by Sujatha et al.This work has been supported in part by the Division of Materials Research, National Science Foundation, Grant No. DMR-81008829     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

An approximate treatment of scattering based on the delta boundary operator

The development of a scheme to treat two-dimensional electromagneticscattering by electrically large, perfectly conducting bodiesis described. It incorporates the effects of surface curvatureand non-local phenomena and has the potential to provide thebasis for a general technique yielding more accurate predictionsthan the widely used physical optics method.     

A review of the theoretical and experimental analyses of electron spin polarization in ferromagnetic transition metals: I. Field emission,photoemission, magneto-optic Kerr effect and tunneling

Until recently studies of solid surfaces have used exclusively photons, atoms, ions, and unpolarized electrons as experimental probes. However, in the last few years polarized electron beams have been used to investigate the electronic and atomic properties of the bulk and surfaces of solids. This has resulted in the development and application of a number of different experimental techniques sensitive to the electron spin polarization (ESP). The experimental results have often been less than definitive and frequently conflicting. For example, the observation of ESP from the ferromagnetic metals by photoemission, field emission, and tunneling experiments lead to contradictory conclusions concerning the validity of the Stoner-Wohl-farth-Slater (SWS) band theory of ferromagnetism. Additional complication of this problem has been introduced by recent magneto-optical Kerr-effect measurements which tend to support the ESP predicted by SWS theory.In this review we present a critical analysis of these experiments and their theoretical interpretation. It is shown that the results of these experiments do not necessarily contradict each other nor any of the current one-electron theories of itinerant ferromagnetism. It is further shown how, based on the use of over-simplified models to describe the physical processes involved in the experiments, the opposite conclusion can be reached. Based on the analyses in this paper, improvements in the theoretical models are suggested. We also discuss, from a theoretical point of view, the relative advantages and the limitations of the different experimental techniques using ESP to probe the electronic and magnetic structures of solids and surfaces.A fundamental objective of this and the following paper is to help develop a theory of spinpolarized electron emission and tunneling phenomena which will provide the basis for a systematic ESP spectroscopy of surfaces, interfaces, and thin films. This has prompted a reexamination of the ferromagnetism of 3d-transition metals and of their surfaces. The present work leads to some observations concerning the current interpretation of itinerant ferromagnetism and possible refinements of the SWS theory to produce better agreement with the ESP sensitive experiments.     

The multiple-image interactions and the mean-barrier approximation in MOM and MVM tunneling junctions

The effect of the multiple image interactions on theI–V characteristics and the reliability of the mean barrier approximation in calculating the current in MOM and MVM tunneling junctions are critically examined. It is demonstrated that the continued use of the uncorrected form of Simmons' original multiple-image force interaction in the analysis of tunneling junctions can lead to serious errors in both the current and the dynamic resistance. An extensive numerical analysis of planar junctions including the image potential suggests that the basic mean barrier approximation formulated by Simmons is essentially a thick barrier approximation. It also is shown that the conventional mean barrier approximation is a relatively poor approximation for the tunneling barriers of interest, and that it is not possible to establish a reliable a priori estimate of its range of validity.This research was supported in part by the NATO Research Grants Program, Grant No. 1902, Scientific Affairs Division, Brussels, Belgium     

Examination of the electronic energy band model for one-dimensional disordered thin films

The nature of the electronic states in a disordered one-dimensional finite system subject to traveling wave boundary conditions is examined. A method is developed whereby these states can be characterized as either “localized” or extended. The concept of localization of states is modified so as to be applicable to amorphous thin films. The extent to which the disorder modifies the band structure of the ordered system is investigated as a function of disorder and the nature of the electronic states is related to the elastic tunneling transmission coefficient for a model metal-semiconductor-metal heterojunction. The results seem to corroborate the Mott-CFO model.