Xmpl2d56, 56th 'example' data file for CPO2D
2-aperture lens with curved electrodes.
Prepared for paper 68 in the publications list, Optimization of the shapes of electrodes of electrostatic lenses, by F H Read, Microscopy and Microanalysis 21 Suppl S4, 276-279 (2015)
See the paper for more detailed information.
The use of the curved surface gives a large improvement in the spherical aberration, compared with traditional designs with flat apertures.
See also xmpl2d57, for 3D tube lenses.
The data lines that define the first curved surface are:
users equns n
r 0.5 2.1 name of variable number 1 and its limits
a 1 name of parameter number 1 and its fixed value
s 3.06 name of parameter number 2 and its fixed value
R 2.1 name of parameter number 3 and its fixed value
0 name of parameter number 4 and its fixed value
r
R*a-sqrt((R*a)^2-a*r^2+1.e-6)-s
1 1 numbers of 2 applied voltages (can be same, for equipotential electrode)
200 102 number of subdivisions, type of subdivision
In fact this equation is that of an elliptical curve, but with a = 1 it becomes circular.
So the ‘users equation’ could have been written more simply as:
z = R – sqrt(R^2 – r^2) – s (but elliptical shapes were being explored).
Rewriting again,
(z – (R – s))^2 + r^2 = R^2,
which is a circle of radius R centred at z = R - s.
We have s = 3.06, R = 2.1, r = 0.5 to 2.1 in 200 steps, so z goes from -3.00 to 0.96.
One further point: the ‘type of subdivision’ is 102 to give concentration of segments
at both ends.
See xmpl2d57, for quantitative data on the 2 types of lenses.