Test3d02, 2nd 'benchmark test' data file for CPO3D

Idealised cylindrical deflection analyzer

This deals with the â€˜perfectâ€™ cylindrical deflection

analyzer, and is the analogue of test3d01.dat.

(This is a system with cylindrical symmetry, and so can be solved even more quickly and accurately with CPO2D, using the data in test2d02.dat).

Detailed description:

The number of segments used in the present example is small enough for the example to be run with the 'demo' version of CPO3D. Higher accuracy could of course be obtained with more segments, using the standard or full versions of CPO3D.

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.

This simulation is analogous to that in the first benchmark test, so please consult the notes at the end of file test3d01.dat for further information.

The cylinders are of radius 0.75 and 1.25, and of depth 2.0 (the middle 0.5 of which is more finely divided than the rest). The top and bottom are closed off by an annular plate at the mean potential. The potentials of the cylinders are such that the potential at r = 1 should be 1 and the field should be 2 (see detailed equations on CDA). The calculated values along two different radial vectors appear on the screen, and are consistent with the requested inaccuracy of 0.001.

A 'test plane' is put at the exit plane of the analyzer. At this plane the final distance of the median ray from the centre of curvature should be 1. The calculated value (see the output file tmp3a.dat) is 1.0001 and the final energy is 0.99894 (giving errors of 0.01% and 0.11%, which are consistent with the requested ray inaccuracy, 0.1%, and the number of segments before reflections, 80). The errors can be made smaller (the first one becomes 0.01%) by using the 't' option (for 'total' energy, but this option has not been included in the lines of the given data file because of ease of misuse). In this option the user would input the value 1.0 for the initial potential, and then the program would make the necessary adjustment to the potential everywhere in the system, so that the total energy (a constant of motion) would be exactly 0eV.

Using the 'mesh' method of ray tracing, with a mesh spacing of 0.05, gives approximately the same accuracy in approximately the same time. Further rays that are close to this first one would however be calculated very quickly (try this by repeating the data line a few times above for the first ray).

The computing times for the charges and ray are approximately 6 and 5 seconds respectively.