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 gains prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, photo technology and electronic picture processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in these kind of domain names. This monograph summarizes the authors' wisdom and event obtained 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 large number of general-purpose and problem-oriented courses, asymptotic research according to perturbation conception is still probably the most powerful instruments to penetrate deeply into the essence of the matter in query.
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Additional resources for Selected Problems of Computational Charged Particle Optics
In the first whereas in the second example, the domain Oxy is a circle of unit-radius, p ﬃﬃﬃ one it represents a square with the side length 2. In both cases, the ðsÞ is assumed constant: ’ ðsÞ ¼ ’ 0. boundary potential ’ Let us see the total charge QS induced on the boundary. The first example allows a simple exact solution since the charge density s(s) is constant on the circumference. Eq. 41) degenerates into the simplest algebraic equation QS À 2p 2ðp ln 0 ð1 þ cos fÞ2 þ sin2 f 0; df ¼ ’ D20 ð1:43Þ 0 =lnD20 .
1016/S1076-5670(08)00802-1 # 2009 Elsevier Inc. All rights reserved. 39 40 Surface Charge Singularities Near Irregular Surface Points previously known singular function C and the smooth function s0 . From a mathematical viewpoint, such substitution returns the solution to the class of Ho¨lder functions but modifies the kernel of the integral equation. It is very important that the modified kernel still preserves the logarithmic singularity; therefore, according to the Voronin-Tsetsoho theorem, the transformed first-kind Fredholm equation with respect to s0 proves to be well-conditioned.
The 7-point finite-difference operator for 3D Laplace operator reads D’ % ’iÀ1; j; k þ ’iþ1; j; k þ ’i; jÀ1; k þ ’i; jþ1; k þ ’i; j; kÀ1 þ ’i; j; kþ1 À 6’i; j; k h2 : ð1:62Þ 30 Integral Equations Method in Electrostatics The 5-point operator DðplÞ ’ % ’iÀ1; j þ ’iþ1; j þ ’i; jÀ1 þ ’i; jþ1 À 4’i; j h2 : ð1:63Þ can be applied in the planar case. The situation is somewhat complicated in the axisymmetric case because the axisymmetric Laplace operator DðaxÞ ’ ¼ Dzr ’ þ ’r =r degenerates on the symmetry axis.
Selected Problems of Computational Charged Particle Optics by Dmitry Greenfield