Download Electrostatic Lens Systems by D.W.O. Heddle PDF

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By D.W.O. Heddle

This e-book permits readers to layout lens structures having precious features. The textual content covers the fundamental conception of the movement of charged debris in electrostatic fields and describes numerous tools for the calculation of the aptitude and box distribution for numerous electrode geometries. equipment, the Bessel functionality growth process which used to be constructed via the writer and his scholars and the nine-point implementation of the finite distinction procedure, are given distinctive emphasis simply because they're quite acceptable for implementation via the green person. different tools are mentioned in much less element and reference is made to web content from which demonstration courses for those tools can be received.

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Considerable reductions 40 Electrostatic Lens Systems can be made by recognizing planes of symmetry in the problem. 10 shows the electrodes of two aperture lenses, one with two apertures and the other with three. The origin of coordinates is at the centre of the lens. 5 along the line from a to b. It is easy to test the validity of this last condition by applying it at a large radial distance and examining the change in potential distribution between the aperture plates as a function of radial position: it is usually very good provided that (D3 − D1 )/A is greater than about two.

80 when | V | fell below 10−12 . 5 × 10−16 . 11. The progress of the convergence of the axial potential is shown for the nine point case. There is little point in continuing the convergence test beyond z = 9D because the potential is distorted by the zero potential ‘end cap’ at z = 10D. 16. This compares the axial potential found after adequate convergence of both calculations. 80. V9 (z) − V5 (z) V9 (z) where the notation should be transparent. We know that the five point method does not converge to the correct potential and we shall see later that the nine point method does converge correctly in a certain sense, so the differences shown in this figure indicate the scale of the error in the five point method as applied to a lens geometry.

11 The dependence of | V | on the iteration number for the array of RELAX51 calculated using the five point method using single and double precision arithmetic and with two values of the acceleration parameter, g. effect of the discrete nature of the process and will also depend on the acceleration parameter. It is useful to examine their behaviour as it may be a guide to the completion of the iterative process. It would be impracticable to examine the changes at every point for a large array, typical of lens systems, but we shall see later that all the lens parameters of general interest can be deduced from the axial potential and changes in this can be an adequate guide.

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