By D.W.O. Heddle
This e-book allows readers to layout lens platforms having important features. The textual content covers the elemental concept of the movement of charged debris in electrostatic fields and describes numerous tools for the calculation of the capability and box distribution for varied electrode geometries. equipment, the Bessel functionality growth technique which was once constructed via the writer and his scholars and the nine-point implementation of the finite distinction procedure, are given particular emphasis simply because they're really acceptable for implementation by way of the green person. different tools are mentioned in much less element and reference is made to web pages from which demonstration courses for those equipment can be received.
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This ebook allows readers to layout lens structures having worthy features. The textual content covers the fundamental concept of the movement of charged debris in electrostatic fields and describes a number of equipment for the calculation of the capability and box distribution for varied electrode geometries. tools, the Bessel functionality growth procedure which used to be constructed by means of the writer and his scholars and the nine-point implementation of the finite distinction procedure, are given targeted emphasis simply because they're quite acceptable for implementation by means of the green consumer.
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Extra info for Electrostatic Lens Systems
The basis for this is that each time we calculate the potential at some point, we move it towards its final value, but by only a small amount, and indeed by an amount which is progressively smaller. Over-relaxation involves replacing the potential at a point not by the simple mean of that at its four neighbours but, recognizing that next time around it will be changed even more, we make a bigger change immediately. We write V (x, y) = g (V (x − 1, y) + V (x + 1, y) + V (x, y − 1) + V (x, y + 1)) 4 − (g − 1)V (x, y)† where V (x, y)† is the value of V (x, y) from the preceding iteration and g is called the acceleration parameter.
In particular, the potential of the electrode itself must be reproduced by the charge distribution. 11) where Vk is the potential at a position rk due to charges qj = σj dSj at positions rj on each of n electrodes. In the present context of round lenses with axial symmetry, the problem reduces to the summation of the potentials at a point due to rings of charge on all the electrodes. 3 in which the potential at the ring of radius ri due to the charge on the ring of radius rj is to be found. 11) is l = [ri2 + rj2 − 2ri rj cos(αi − αj ) + (zi − zj )2 ]1/2 .
The maximum safe value of g depends on the size of the array and also on its shape. This example has only 2401 free points and would be regarded as a rather small array. 97. The Pascal program RELAX51 used for this calculation is shown, in outline, on the following page, and a compiled version, with certain refinements, is included on the program disk. 2 Estimates of g. 9 is based on these expressions. 7 be needed. 0001 do BEGIN average; c:=c+1; END; readln; UNTIL g=0; END. 9 Estimates of the acceleration parameter, g, for arrays of Y (R) × X(Z) points.