Shap3d29.dat, 29th 'shape' file for CPO3D

To illustrate the hexagonal option.

The ‘hexagonal’ option is accessed from the screen /databuilder/symmetries/.

This option forces hexagonal (also called 6-fold or sextupole) symmetry of the potentials and fields around the z axis.

Here there are 6 discs with circular holes, in the xy plane. The geometry is similar to that of shap3d14.

Hexapole antisymmetry has been selected, so the symmetry of the potential field around the z axis is +-+-+-.

This antisymmetry can be seen in the contour plots and also in the data in the ray output file.

If this option is de-selected the data in the ray output file shows slight deviations from the correct anti-symmetry.

If 2 of the 4 discs are removed, leaving those centred at (x,y) = (0,1) and (0,-1), then the potentials inside the discs are correct even at the positions of the missing discs. This type of procedure could be useful for reducing the number of segments in some simulations.

This technique is also described in shap3d14.

Technical note:

In this option the program rotates the point at which a field is required to a point in the ‘primary sector’, which is the sector that has an angular range from -30 to +30 degrees with respect to the y axis. It is assumed that the axis of the system is the z axis and that the xz plane (that is, the y = 0 plane) is a plane of voltage symmetry. The program calculates the field (or potential) at this point and then rotates the field back to the original direction (taking account of any changes in sign of the fields and potentials).