Choice of cylindrical (that is, axial) or planar symmetry.


See also note on symmetries and reflections


CPO2D can be used for systems of electrodes that have either cylindrical (that is, axial) or planar symmetry.


Cylindrical symmetry denotes that the system of electrodes is rotationally symmetric about an axis, the z axis, and that the only other relevant coordinate is the distance r from the z axis. The potential does not depend on the azimuthal angle phi.

In principle r is always positive, but the plots in CPO2D show the plane that passes through the z axis -so this plane has phi = 0º above the axis and 180º below. The vertical coordinate for the rays is then essentially r*cos(phi), which is positive above the axis and negative below. So in this projection rays can cross the axis. More exactly, each ray represents a cut through a sheet of that is symmetric around the axis. After all the rays have been traced the plots show 2 cuts for each sheet, at phi = 0º and 180º, above and below the axis.


Planar symmetry denotes a system in which the electrodes extend to plus and minus infinity in the y direction, so that the only relevant coordinates are then x and z. The potential does not depend on y. (Technical note: In planar symmetry the program cannot make the length Y in the y direction infinitely large, so it is made 1000 times larger than the maximum extent of the electrodes in either of the other two directions. This has essentially no effect on the calculated potentials and fields inside the system of electrodes, nor on the calculated charge per unit length in the y direction. It does however affect the potentials and fields outside the electrodes, at distances of the order of Y/10 or more in the xz plane. Note that in principle if Y is infinitely large the external potential would never fall to zero, a situation that the program cannot simulate.)


CPO2D systems with axial symmetry can also be used for non-meridional rays (that is, rays that have non-zero angular momentum about the axis and so cannot pass through the axis). Similarly for CPO2D systems with planar symmetry can also be used for non-xz-plane rays (that is, rays that do not have zero velocity in the y direction).



For users who are editing or constructing an 'input data file' without the use of the data-builder -that is, pre-processor:

But Manual editing is certainly not recommended -it is a relic from the time when the databuilder was not available All users are strongly encouraged to use the databuilder, which always gives the correct formats and which has many options for which the formats are not described or easily deduced.


The choice is made in the first line after the caption, where either 'c' or 'p' should be put, for cylindrical or planar symmetry respectively.