35th benchmark test for CPO3D

 Field near the tip of a cone.


Obtained from test2d19.dat, using the conversion program conv2to3.exe and setting the number of radial subdivisions to 4 and 'saving' in CPO3D.

 Then the test for 'aspect ratios' has to be effectively disabled  by entering -1000 in \databuilder\ printing level...\allowed reading error...\Maximum aspect ratio

 The lines asking for output data on the fields are added separately.


 It can be seen that the program has automatically concentrated  the segments at the tip.  Using the right-click zoom option we can zoom into the tip and see that the length of the last segments is  only 2.6E-8.


 Results obtained:

   r       z        potential             ex             ez         

                  prog     exact      prog  exact    prog   exact

  0.000   0.000  1.00000  1.00000    0.000  0.000    3.4E5  inf

  0.000   0.002  0.88319  0.88368    0.000  0.000    20.09  20.13

  0.000   0.004  0.85166  0.85213    0.000  0.000    12.80  12.80 

  0.002   0.000  0.91805  0.91854    14.00  14.10    23.45  23.39

  0.004   0.000  0.89602  0.89645    8.960  8.962    14.91  14.87


  The accuracy is similar to that obtained in test2d19.

 If we disable the 'uneven distribution' option on the editing sheet for the cone then the segments are evenly spaced axially and the  results are much less accurate.  For example the 3rd line of the above table becomes

   r       z        potential             ex             ez         

                  prog     exact      prog  exact    prog   exact

   0.000   0.004  0.89920  0.85213    0.000  0.000     8.91  12.80  


 This can of course easily be improved by using a succession of conical surfaces with the smallest at the tip.


 It is usually possible to achieve an automatic concentration of  segments where the charge densities are highest by using the  iterative subdivision (adaptive segmentation)  option.  In the present case however the segments near the tip have such a small area that the charges on them are not significantly higher than the charges on other segments (and  iterative subdivision uses the charges, not the charge densities).

But the iterative subdivision option would be expected to be suitable for realistic rounded tips.