31st 2D example, conical lens with apertures transverse to the axis of the lens.

The lens is situated between cones of semi-angle 45 degrees. The lens is an einzel lens composed of 3 apertures that are transverse to  the axis of the lens (ie the apertures are at right angles to the surfaces of the cones). (For another type of conical aperture lens see xmpl2d41.dat.  Yet another type would be the analogue of an axial lens composed of cylinders,

ie a conical lens in which the lens elements are cut sections of cones.)

The lens is used to focus a 'parallel' beam to a point on the axis of  the cones.  The median ray is initially directed towards a point on the axis  at z = 20, which is also the required focal point of the lens.

The lens elements are 3 apertures.  The first and third are at ground potential (V = 1).  When the inner and outer parts of the middle element are at the same potential there is lens action but the system also deflects the median ray.  To counteract this deflection, so that the beam can be brought to a focus at z = 20 the inner and outer parts are given different potentials, V3 and V4.

The 'automatic focusing' option is used to find the values of V3 and V4 that give the best focus at z = 20.

The focusing power and the deflection are determined primarily by the mean  voltage V5 = (V3 + V4)/2 and the difference V6 = V4 - V3 respectively. Therefore the 'related voltages' option has been used to define V3 and V4 in terms of V5 and V6, and then V5 and V6 are varied, to give a faster optimisation.

The resulting voltages given in the output information are:

Voltage number   5         2.606462

Voltage number   6         0.026141

The minimum value of the rms size of focus is:

size of focus=  1.017E-02 =best so far

This value is within 10 percent of that obtained with xmpl2d41.dat.

The values of z at the focus are given by the second column of the output

information:

 -1.08501e-08 20.0147 -0.683914 0.729563 1.0004 0 4.76329e-05 -6.32412e-06 19.993 -0.691006 0.722849 1.0004 0 4.75906e-05 -1.97013e-07 19.9869 -0.697617 0.716471 1.00039 0 4.75727e-05 -5.5449e-09 19.9907 -0.703896 0.710303 1.00039 0 4.75717e-05 -4.46344e-08 19.9994 -0.709981 0.704221 1.00038 0 4.75813e-05 -7.5397e-09 20.0081 -0.716002 0.698098 1.00038 0 4.75957e-05 -9.844e-08 20.0122 -0.722085 0.691804 1.00039 0 4.76094e-05 -1.28749e-08 20.0071 -0.728357 0.685198 1.0004 0 4.76171e-05 -3.57989e-09 19.9881 -0.734949 0.678123 1.00041 0 4.76136e-05

To see these ouputs quickly, copy the present data file to another file and remove the automatic focusing option.

Examples of papers that concern toroidal analyzers and conical lenses:

T J Reddish et al, Rev Sci Instrum 68, 2685 (1997)

A Danjo et al, Rev Sci Instrum 70, 1970 (1999)