Download Selected Problems of Computational Charged Particle Optics by Dmitry Greenfield PDF
By Dmitry Greenfield
Advances in Imaging and Electron Physics merges long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. This sequence positive factors prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, photograph technology and electronic photograph processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in these kinds of domain names. This monograph summarizes the authors' wisdom and adventure bought over a long time of their paintings on computational charged particle optics. Its major message is that even during this period of strong pcs with a mess of general-purpose and problem-oriented courses, asymptotic research in keeping with perturbation idea is still probably the most powerful instruments to penetrate deeply into the essence of the matter in query.
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X; yÞ appears as x ¼ xðsÞ þ y0 ðsÞh; y ¼ yðsÞ À x0 ðsÞh: s y h x FIGURE 17 The near-surface curvilinear coordinates system (s, h). ð1:54Þ 28 Integral Equations Method in Electrostatics The curvilinear coordinate system (s,h) is orthogonal, and the square of the infinitesimal length element is dl2 ¼ ð1 þ k0 ðsÞhÞ2 ds2 þ dh2 ; ð1:55Þ where k0 ðsÞ ¼ y00 ðsÞx0 ðsÞ À x00 ðsÞy0 ðsÞ is the local curvature coefficient. The Laplace operator transformed to the curvilinear coordinates (s, h) reads as 0 D¼ @2 1 @2 k0 @ k0 h @ À ; þ þ @h2 ð1 þ k0 hÞ2 @s2 1 þ k0 h @h ð1 þ k0 hÞ3 @s ð1:56Þ 0 where k0 ðsÞ ¼ y000 ðsÞx0 ðsÞ À ðsÞy0 ðsÞ.
9 may help to trace a large number of trajectories and determine both the transparency coefficient and the scattering function of a grid cell. Our aim here is to show that taking into account some features specific to the problem in question may advance the calculations. The mathematical model of a fine-structure grid represents an infinite periodical array of cells. The direct use of the classic 3D BEM immediately restricts the case to only a few adjacent grid cells involved in the calculation and complimented with two additional finite-size electrodes generating the electric field on both sides of the grid.
2 15 0. 0. 4 25 0. 6 35 0. 40 0. 8 45 0. 0 FIGURE 28 The singularity index versus the reduced permittivity ratios in the case of three dielectric wedges, the faces of which intersect at right angles. As above, no exact solution to this equation exists for all possible values of the apex angle b. Therefore, here we restrict ourselves to the numerical results shown in Figure 29 and investigate some limiting cases. As in the case above, the singularity index lies in the range 0 g < 1=2. The asymptotic behavior may be easily analyzed in the limits of high permittivity (e >> 1) and small apex angle (b << 1).