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

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**Extra info for Selected Problems of Computational Charged Particle Optics**

**Example text**

5 120Њ b 150Њ 180Њ The singularity index when a dielectric wedge touches a regular conductive The exact solution to Eq. 28) is known only for a few particular cases. As an example, we quote here, after some simplifying transformations, the singularity index expression 2 jw1 À w2 j g ¼ 1 À l0 ¼ arcsin pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ p 2 1 À w 1 w2 ð2:29Þ found by Veselov and Platonov (1985) for three dielectric wedges, the faces of which intersect at right angles as shown in Figure 28. Here w1 ; w2 designate the reduced permittivity ratios e1 À e3 e2 À e3 w1 ¼ ; w2 ¼ ð2:30Þ e1 þ e3 e2 þ e3 taking values in the interval ðÀ1; 1Þ.

23) depends only on the ratio e1 =e2 , with no loss of generality we may put e1 ¼ e > 1 and e2 ¼ 1. This assumption corresponds to the case of one dielectric wedge with the apex angle b, and the rest of the space within the angle 2p À a À b empty (vacuum). It is also convenient to introduce the normalized variables bÃ ¼ b=ð2p À aÞ, x ¼ 2 À ð2 À a=pÞl and rewrite Eq. 23) in the form sin½pð2 À xÞ þ eÀ1 sin½pð2 À xÞð1 À 2bÃ Þ ¼ 0: eþ1 ð2:24Þ The value bÃ 2 ½0; 1 is the fraction of the space between the conductive faces occupied by dielectric.

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).