Test2d17, 17th 'benchmark test' data file for CPO2D

Ideal parallel plate mirror analyzer.

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 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 CPO2DS.


Here 'planar' symmetry is used, so that the system extends an infinite distance in the +/- y directions.

Theoretically (see for example W Schmitz and W Mehlhorn, J Phys E vol 5, pp 64-68, 1972)

the launch angle should be

alpha0 = 30 degrees

the parameter

K = d*Ue/(a*Us)

should be 2, where e*Ue is the initial energy, Us is the potential difference between the two plates, d is their separation and a is the distance of the launch position below the lower plate. In the present example Ue = 1, Us = 0.5, d = a = 1. Then the distance between the object and image is

z0 = 10.3992.

With these conditions the analyzer has a second order focus, which means that the dependence of the axial crossing position z of a ray that starts with a launch angle alpha can be expressed as

z = z0 + A*(alpha - alpha0)**3 + ...

In other words the term in (alpha-alpha0)**2, which is present for most other types of energy analyzers, has disappeared, which allows this analyzer to be used with a wider range of angles.


The answer to the question in the data file:

stop ray if it crosses a segment?

is 'n' (for 'no'), and so the rays can pass through the sheet of charge at the position of the lower plate, which therefore simulates the behaviour of the 'perfect' parallel plate analyzer (that is, with no fringe-field effects from apertures in the lower plate).


5 rays are started, with values of (alpha-alpha0) of 0, +/- 2.5 and +/- 5.0 degrees.