32nd 2D example, conical lens with apertures transverse to the axis of the cones.

The lens is situated between cones of semi-angle 45 degrees.

The lens is an einzel lens composed plates that are transverse to the axis of  the cones.

(For another type of conical aperture lens see xmpl2d40.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 a set of 8 plates that are perpendicular to the axis of the cones.  Four of the plates are outside the beam while the other four are inside.  There are some practical advantages in this arrangement.

The entrance and exit plates are all at ground potential (V = 1).  The other 4 plates are given the different potentials V3, V4, V5 and V6.

The 'automatic focusing' option is used to find the values of V3 to V6 that give the best focus at z = 20.

The resulting voltages given in the output information are:

Voltage number   3         2.070014

Voltage number   4         2.267342

Voltage number   5         2.038888

Voltage number   6         2.320902

The minimum value of the rms size of focus is:

size of focus=  1.124E-02

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:

 -4.88139e-08 20.0056 -0.689526 0.724261 1.00039 0 4.766e-05 -1.92862e-08 19.9911 -0.696356 0.717696 1.00039 0 4.76281e-05 -5.7936e-09 19.9896 -0.70277 0.711418 1.00038 0 4.76173e-05 -4.01541e-07 19.9958 -0.70891 0.705299 1.00038 0 4.76207e-05 -1.13387e-08 20.0047 -0.714909 0.699218 1.00037 0 4.76322e-05 -2.37727e-08 20.0118 -0.720893 0.693047 1.00037 0 4.76462e-05 -1.03433e-08 20.0125 -0.726986 0.686652 1.00038 0 4.76575e-05 -1.75429e-08 20.0022 -0.733319 0.679885 1.00039 0 4.76609e-05 -2.3797e-09 19.9759 -0.740026 0.672578 1.0004 0 4.76509e-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)