Selected Problems of Computational Charged Particle Optics by Dmitry Greenfield

Selected Problems of Computational Charged Particle Optics by Dmitry Greenfield

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, picture technological know-how and electronic snapshot processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in a majority of these domain names. This monograph summarizes the authors' wisdom and event received over decades of their paintings on computational charged particle optics. Its major message is that even during this period of robust desktops with a mess of general-purpose and problem-oriented courses, asymptotic research in keeping with perturbation thought continues to be probably the most potent instruments to penetrate deeply into the essence of the matter in query.

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Thus, we have the right to set the boundary condition y j *0 j *1 j0 j1 j *0 FIGURE 18 j *1 j *2 j2 j *2 j *3 j *4 j3 j4 j *3 x j *4 The 5-point finite-difference operator for the axisymmetric Laplace problem. Integral Equations Method in Electrostatics 31 not strictly on the electrodes themselves but at the mesh nodes located close to the electrodes as shown in Figure 19. This implies that the electrodes appear to be ‘‘isolated’’ from the rest volume by the set of the near-boundary nodes at which the potential is already known and which, therefore, should be excluded from the iterative solution of the Laplace equation.

N; y1 ¼ 0; yNþ1 ¼ 2p À a). 10) to the linear system of two first-order differential equations q1 e1 r q e2 x a q2 FIGURE 25 e3 Homogeneous dielectrics adjoining a conductive wedge. 44 Surface Charge Singularities Near Irregular Surface Points Y0 ¼ l Z; Z0 ¼ ÀleðyÞY; eðyÞ ð2:15Þ (index m is omitted), the right-hand side of which does not contain the eðyÞ derivatives. 12) takes the form ek Y0 ðyk À 0Þ ¼ ekþ1 Y0 ðyk þ 0Þ ð2:16Þ which immediately follows from the continuity of the function ZðyÞ. 15) and therefore can be presented as the matrix exponent  )  (   cosðlDyk Þ  0  eÀ1 eÀ1 k  k sinðlDyk Þ     Mk;kþ1 ðlÞ ¼ exp lDyk   ¼   Àe sinðlDy Þ  Àe 0  cosðlDy Þ k k k k ðDyk ¼ ykþ1 À yk Þ: ð2:18Þ Following Manticˇ, Paris, and Berger (2003), let us construct the transfer matrix      P1;N ðlÞ R1;N ðlÞ  M1;N ðlÞ ¼   ¼ MNÀ1;N ðlÞ .

The singularity index g is maximal if the dielectric wedge is located symmetrically with respect to the conductive wedge and occupies exactly one half of the outside space. The minimal transition time in our quick-action problem is À1=2 T 0 ¼ 4 arctanðemax Þ and, correspondingly, ! 7) up to 1 with emax increasing from 1 to infinity. The case of pure dielectric vertex can be studied similarly; the only difference is that the periodicity condition Zð0Þ ¼ Zð2pÞ should also be imposed. It is noteworthy that any arbitrary rotation of the dielectric media as a whole does not affect the singularity index.

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