xmpl3d01, 1st 'example' data file for CPO3D

A practical hemispherical deflection analyzer (HDA).


The analyzer consists of two hemispheres of radii 0.75 and 1.25, with 4 hoops being used to correct for the end effects.


(This simulation has cylindrical symmetry and so can be solved more quickly and accurately with CPO2D).

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.


The 'clipping' option has been used to remove the parts of the spheres that lie beyond the plane that contains the entrance and exit positions and hoops, and also to remove unnecessary parts of the hoops, which leaves some ragged edges. (Alternatively hemispheres can be defined that have their end planes in the plane of the hoops, and then they can be clipped to remove the unwanted parts perpendicular to this plane, all of which is illustrated in shap3d05.dat). The number of subdivisions for the 2 hemispheres have been chosen to be approximately proportional to their radii, as recommended.


The median ray should have kinetic energy = 1eV, potential energy = -1eV, and therefore a total energy of 0eV, but the correction of the end effects is not perfect and so the calculated initial potential will not be exactly 1.0. Therefore the 't' option (for 'total energy') has been used for the energy, and the initial potential has been specified as 1.0. The calculated initial potential will then be adjusted to make it 1.0, and all other potentials will be given the same adjustment, so that the total energy (a constant of motion) will then be exactly 0eV. But beware, it is easy to misuse the 't' option and so obtain misleading results -therefore it is important to look at the information box or the output data file to make sure that the initial kinetic energy has the required value.


The value of y at the exit plane (x=0, which has been specified as a 'test plane') would be 1.0 with perfect fringe-field correction (and a perfect computation!), but in this example is 0.99854 (see the output data file 'temp1a.dat'). The final value of the kinetic energy is determined by the final potential, which is also affected by fringe field effects.


The computing time for the boundary charges is 6 sec, using a 66MHz 486 PC, and for each ray is approximately 16 sec.