Coordinate systems and angles

Between the various fields, perspectives, and the tilt angle, the coordinate system used in the analysis can quickly become quite confusing. It’s important to define it well to begin with. This code assumes the coordinate system described on this page.

General coordinate system

This code uses Cartesian coordinates. The z direction is along the drift axis of the TPC, pointing upstream from the Micromegas. This implies that electrons will drift in a negative z direction as time passes.

The x and y directions are defined by the Micromegas. Take the x direction to be horizontal on the pad plane and y to be vertical.

Caution

It’s important to remember that the Micromegas is rotated when it is installed in the TPC. Therefore, the x and y dimensions of the generated pad plane points are not the same as the horizontal and vertical directions in the lab unless a rotation is applied.

The connector side of the Micromegas has 72-degree rotational symmetry. When the Micromegas is installed in the TPC, it is rotated through 1.5 of these symmetric segments, so the rotation angle for the transformation is –108 degrees.

Using this convention, the beam, fields, and drift have the following alignment:

Quantity	Direction
B field	Along +z
E field	Along +z
Beam	Along -z
Drift	Along -z

Tilting the detector

Tilting the detector presents a special problem since it makes the electric and magnetic fields non-parallel. The easiest way to deal with this is to keep the detector’s coordinate system as above, and tilt the magnetic field vector instead. This is illustrated in the figure below.

The coordinate system when the detector is tilted. Here, \(\tau\) is the tilt angle. From the perspective of the detector’s coordinate system, the magnetic field vector is tilted upward by \(\tau\).

Using this system, the vectors are along these axes:

Quantity	Direction
B field	Components in +y and +z directions
E field	Along +z
Beam	Components in -y and -z directions
Drift	Components in all three directions