Input data for a 3D flat circular disc

A flat circular disc that has a hole at the centre (that is, an annulus, with an inner radius that is non-zero).

The radial direction can be subdivided evenly or unevenly. The uneven distribution gives a higher density of segments near the inner edge, so that all the triangular segments have approximately the same shape (in particular, this avoids some of the triangles becoming long and thin). The fields at an inner sharp edge are usually very strong and so the charge densities there are very high, so it is usually advisable to use the 'uneven distribution' option and/or to make up the disc in about 3 parts, with the highest density of segments on the inner part.

The uneven distribution is therefore recommended unless the outer edge of the disc is a critical region (in which case it would probably be better to use a separate annulus to model the outer edge).

The inner radius must not be less than the outer radius divided by 10. If a smaller inner radius is required then another disc can be put inside the hole. If there is no inner hole (that is, if an inner radius of 0 is required) then the complete type of disc can be used (but this cannot be stretched or clipped, although selected segments can be removed). The most awkward situation is when a complete, stretched disc is required. The options are then:

(1) Use a series of discs inside discs.

(2) Fill the hole with triangles (preferably of the end disc type -the last type in the list) and manually stretch the triangles.

(3) Use the users equations option. Then there is much greater flexibility in defining discs, for example:

shap3d36 Elliptical electrode, by users equations.

shap3d37 Elliptical hole in circular electrode, by users equations.

shap3d39 Square hole in round disc, by users equations.

shap3d40 Round hole in a square disc, by users equations.

shap3d42 A small hole in a circular disc, by users equations.

shap3d49 5 holes in circular disc, by users equations.

The user specifies:

(1) The first radius and the x,y,z coordinates of the centre (where the first radius can be the inner or outer radius, and where the inner radius is zero for a complete disc without a hole at the centre).

(2) The second radius and the x,y,z coordinates of any other point on the axis of the disc, to give the orientation of the disc.

(3) The numbers nv1,nv2 that label the voltages that are applied to the disc (the values of the voltages will be entered later)

-nv1 and nv2 are the same if disc is an equipotential

-they are different if a potential gradient is required in the z direction.

(4) If nv1 and nv2 are different, then the user specifies the values of z at which these 2 voltages are applied.

(5) Either:

(a) The numbers n1 and n2 of divisions along the radius and around the axis respectively, giving 4*n1*n2 triangles for disc with a hole at centre. The numbers n1 and n2 might be changed by the program.

Or (the usual recommended choice):

(b) The total number N of segments and 0. The 0 will trigger the program to partition N into n1 along the radius and n2 around the axis, in such a way that all the trapeziums formed by pairs of triangles are as nearly square as possible. The final number of triangles will be 4*n1*n2, which might be slightly different from N (so if greater control is required, use n1 and n2).

For important advice on subdividing please look at section 3.4 of the Users Guide or the general advice on segmentation.

(6) An even or uneven (the recommended choice) distribution of subdivisions radially.

The numbers n1 and n2 (or N) apply to the minimum sector, before reflections in any planes of symmetry. (When the axis of the disc is the z axis and the x=0, y=0 and x=y symmetry planes have not been called and N is small the program might make n2 = 8 to give 8-fold symmetry about the z axis, in case other parts of the system have this symmetry.)

There is no need to worry about any planes of reflection symmetry when entering the above information -you can enter a whole disc. The program will test for consistency with those planes and will remove the unnecessary parts (and this will be done before the subdivision into the more basic shapes). The total number of segments starts at the number given by the user but is then doubled for each reflection.

For technical reasons, stretching and clipping are not possible with this type of disc, although selected segments can be removed.

All types of electrodes can be scaled and/or shifted and/or reflected and/or rotated.

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 radial direction is divided evenly unless there is a 'u' in the 7th position of the line that starts with 'dis', eg a line such as:

'disc, uneven radial distribution'

Typical data for a circular disc, taken from test3d02.dat, are:

disc, uneven radial dist

0.90 0. 0. 1.0 1st radius, centre of disc

1.10 0. 0. 3.0 2nd radius, any other point on axis

3 3 numbers of 2 applied voltages (can be same)

1 4 total number of subdivisions and 0, or divisions along radius and around axis

The data required are:

(1) 1st radius and x,y,z coordinates of centre.

(2) 2nd radius and x,y,z coordinates of any other point on axis.

(3) Numbers nv1,nv2 that label voltages that are applied to the disc.

(4) If nv1 and nv2 are different, then enter values of z at which these 2 voltages are applied.

(5) Either:

(a) The numbers n1 and n2 of divisions along the radius and around the axis respectively, giving 4*n1*n2 triangles.

Or

(b) The total number N of segments and 0. The 0 will trigger the program to partition N into n1 along the radius and n2 around the axis, in such a way that all the trapeziums formed by pairs of triangles are as nearly square as possible. The final number of triangles will be 4*n1*n2, which might be slightly different from N (so if greater control is required, use n1 and n2).

For important advice on subdividing please look at section 3.4 of the Users Guide or the general advice on segmentation.