xmpl2d05, 5th 'example' data file for CPO2D

A 'beam' of rays focussed by a double-cylinder lens.

This file is identical to the 1st example file, xmpl2d01.dat, except that a 'beam' of rays is specified. There are 4 rays in the beam, all starting from a point object at z=-4 and directed towards a 'pupil' (that is, an angle-defining aperture) of radius 0.2 at z=-2.

The number of segments used in the present example is small enough for the example to be run with the ‘demo’ version of CPO2D. Higher accuracy could of course be obtained with more segments, using the standard or full versions of CPO2D.

Detailed description:

The following data were obtained when the memory and speed of PC's was much more limited than at present, so the available number of segments was small and the requested inaccuracies were fairly high to give a quick demonstration.

The 'uniform beam' option is used, so that each ray represents the same area of the pupil, and since the system has cylindrical symmetry this implies that the initial launch angles are spaced non-uniformly.

Other differences are that lens properties and other information are not requested, and that the 'mesh' method of ray tracing is used (although in this example the number of rays is not large enough for this method to be faster than the 'direct' method).

Other options for defining the beam are also available. These options are intended for the creation of beams that travel in the z direction, and they might fail for beams at large angles to this direction.

Here are some examples of the available options. In each case the lines that are given would replace the analogous lines in the file above.

(1) A beam that is defined by a 'window' (that is, a size-defining aperture) and a 'pupil' (that is, an angle-defining aperture), both of non-zero radius, and that has a uniform density per unit area:

beam -definition of rays

uniform distribution

-0.1 -4.0 0.1 -4.0 r,z (or x,z) of 2 ends of the 'window '

-0.1 -2.0 0.1 -2.0 r,z (or x,z) of 2 ends of the 'pupil'

3 6 1.0 0.0 n's for window and pupil, eV, mA

(2) A beam that has some of the rays coming from the edge of the window and passing through the edge of the pupil, and the other rays distributed uniformly over the radii:

beam -definition of rays

end and middle

-0.1 -4.0 0.1 -4.0 r,z (or x,z) of 2 ends of the 'window '

-0.1 -2.0 0.1 -2.0 r,z (or x,z) of 2 ends of the 'pupil'

3 6 1.0 0.0 n's for window and pupil, eV, mA

(3) A beam in which the positions of the beam in the window and pupil are random, but distributed approximately uniformly per unit area. A 'c' has been put in the 10th space in the line that has 'random' at the beginning, and this is followed by a controlling number, so that the random sequence will always be the same if the controlling number is unchanged (see the relevant note for other forms of randomness):

beam -definition of rays -

random c 2.0

-0.1 -4.0 0.1 -4.0 r,z (or x,z) of 2 ends of the 'window '

-0.1 -2.0 0.1 -2.0 r,z (or x,z) of 2 ends of the 'pupil'

18 1.0 0.0 total number of rays, eV, mA -

(4) A uniform parallel beam (here the pupil has been put at infinity):

beam -definition of rays

uniform distribution

-0.1 -4.0 0.1 -4.0 r,z (or x,z) of 2 ends of the 'window '

-0.1 2.E6 0.1 2.E6 r,z (or x,z) of 2 ends of the 'pupil'

3 1 1.0 0.0 n's for window and pupil, eV, mA

(In the ‘demo’ version of the program the maximum number of ray points is easily exceeded. To obtain all the ray information it might be necessary to use longer step lengths.)