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&CELL: methods: coordinate_system


Cartesian

In Garfield, the fundamental coordinate system is Cartesian.

Potentials for chambers made of wires and planes are computed using a variety of potential_functions.

Cartesian coordinates are also used for field maps, even if the map is of the axially symmetric (r,z) type. The potentials for field maps are polynomially interpolated in triangular, tetrahedric or rectangular coordinates, as appropriate.


Polar

Polar coordinates are dealt with by the conformal mapping:
(x,y) = exp(rho,phi)

Most of the commands translate the internal coordinates to polar coordinates, but procedures as a rule don't do this. A set of procedures has been provided for these transformations: CARTESIAN_TO_POLAR, CARTESIAN_TO_INTERNAL, INTERNAL_TO_CARTESIAN, INTERNAL_TO_POLAR, POLAR_TO_CARTESIAN and POLAR_TO_INTERNAL.


Tube

The tube coordinates are special in the sense that the wire locations are listed in Cartesian coordinates, while the tube is an object with a polar shape. Garfield internally uses Cartesian coordinates for cells of this type.

Potentials in round tubes are computed using the conformal mapping:

    z - z0
z = -----------
    1 - z0bar z
which maps z0 to 0 and which maps the unit circle onto itself.

Potentials in polygonal tubes are computed by mapping the centre of the tube to a round tube, while the edges are


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Formatted on 0103-05-16 at 14:04.