Download e-book for kindle: Electrostatic Lens Systems by D.W.O. Heddle

By D.W.O. Heddle

This publication permits readers to layout lens structures having valuable features. The textual content covers the fundamental idea of the movement of charged debris in electrostatic fields and describes a number of tools for the calculation of the capability and box distribution for varied electrode geometries. tools, the Bessel functionality growth technique which used to be built by way of the writer and his scholars and the nine-point implementation of the finite distinction procedure, are given distinctive emphasis simply because they're relatively acceptable for implementation through the green person. different tools are mentioned in much less aspect and reference is made to web pages from which demonstration courses for those tools will be got.

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60(8r 2 + 3h2 )V (z, r) = 6(16r 2 + 7h2 )(V (z + h, r) + V (z − h, r)) + (96r 2 + 48rh + 30h2 + 23h3 /r)V (z, r + h) + (96r 2 − 48rh + 30h2 − 23h3 /r)V (z, r − h) + (24r 2 + 12rh + 9h2 + 13h3 /2r)(V (z − h, r + h) + V (z + h, r + h)) + (24r 2 − 12rh + 9h2 − 13h3 /2r)(V (z − h, r − h) + V (z + h, r − h)). 23a) Again, this cannot be applied to points on the axis, but the calculation in terms of the potentials at the five nearest points in the plane is straightforward. , 3660 Waialae Avenue, Suite 304, Honolulu, HI, USA.

If the electrode potentials are V1 and V2 , we can express the axial potential in one of the forms V (z) = 21 (V1 + V2 ) + 21 (V2 − V1 ) (z) = V1 + (V2 − V1 ) (z) where (z) and (z) are functions which range between ∓1 and between 0 and 1 respectively as z → ∓∞. There are various methods of calculating these functions. There is an exact solution for the case of two coaxial cylinders at different potentials, but with no gap between them. This is an unrealistic situation, but it has been used as an aid to the normalization of other expressions.

There are commercial programs available. 6, but they all use the five point method which as we have seen has limitations which may be significant. 1) V (z, r) = (Ak ekz + Bk e−kz )J0 (kr) + V0 . 1, we choose to treat positive and negative values of kz explicitly. 17 shows the geometry of a lens formed by two coaxial cylinders of equal diameter, D, separated by an axial distance, g, and having potentials V1 and V2 . We show the walls of the cylinder to be of finite thickness as we shall later use a result from a finite difference calculation to resolve a problem inherent in this method.

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Electrostatic Lens Systems by D.W.O. Heddle

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