By D.W.O. Heddle
Electrostatic Lens platforms: moment version permits readers to layout lens platforms for focusing beams of charged debris that experience invaluable features. The booklet covers the elemental thought 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. It emphasizes the Bessel functionality growth strategy, built through the writer and his scholars, and the nine-point implementation of the finite distinction procedure. Demonstration courses of different tools are available through the internet sites supplied. A bankruptcy on aberrations provides formulae that allow the coefficients to be made up our minds through an extension to the ray tracing methods, demonstrating optimal stipulations for lens operation.
The booklet is followed by means of a disk that gives a set of laptop courses (LENSYS for MS-DOS) meant for functional use within the layout and research of structures utilizing around lenses with apertures or cylindrical parts. those courses are of price even to skilled staff within the box who could be fairly accustomed to a lot of the fabric within the textual content.
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Additional resources for Electrostatic Lens Systems, 2nd edition
Example text
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.
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 . 3 Diagram to indicate the coordinates appropriate to the calculation of the potential of a point due to a ring of charge. The absolute values of the angles are arbitrary because of the axial symmetry so, for convenience, let αi = π which allows us to simplify this expression as l = [(ri + rj )2 − 4ri rj sin2 (αj /2) + (zi − zj )2 ]1/2 = [(ri + rj )2 + (zi − zj )2 ] 1 − 4ri rj sin2 (αj /2 (ri + rj )2 + (zi − zj )2 1/2 .
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. 7, but with 51 points on a side. 5. 8(b) shows, on linear scales, the sum potential for a number of values of g. 90 this condition is reached after 95 cycles. Notice that the final value is reached, in this case, from above. 90. The maximum safe value of g depends on the size of the array and also on its shape.
