&CELL: methods: coordinate_system

Cartesian

In Garfield, the default coordinate system is a Cartesian system of (x,y,z) coordinates, all of which are expressed in units of cm.

Such a system is used for chambers constructed from wires and planes unless one of the following conditions is met:

the chamber is declared to have a PERIODICITY in phi;
the chamber contains a PLANE at constant r or phi;
the chamber contains a TUBE.

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, tetrahedral or rectangular coordinates, as appropriate.

Polar

Chambers that have either a PERIODICITY in \φ or a PLANE at constant r or \φ, but no TUBE are described in polar coordinates:

r: distance from the origin, in cm;
\φ: angle with respect to the positive x-axis, in degrees;
z: distance from the (x,y) plane, in cm.

Polar coordinates are internally dealt with by the conformal mapping:

(x,y) = exp(\&rho;,\&phi;)
z     = \&zeta;

thanks to which the potential functions and drift-line integration procedures for Cartesian coordinates can be used. Most of the commands accept polar coordinates for input and translate the the output to polar coordinates. Procedures as a rule don't do this. A set of procedures is therefore provided for these transformations: CARTESIAN_TO_POLAR, CARTESIAN_TO_INTERNAL, INTERNAL_TO_CARTESIAN, INTERNAL_TO_POLAR, POLAR_TO_CARTESIAN and POLAR_TO_INTERNAL.

Tube

Tube coordinates are used in chambers that contain a TUBE, which can have PERIODICITY in \φ but in which there is no PLANE. Tube coordinates are never used with field maps.

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 mapped with a local Schwarz-Christoffel expansion.

Go to the top level, to &CELL, to methods, to coordinate_system, to the topic index, to the table of contents, or to the full text.

Formatted on 21/01/18 at 16:55.