Machine:Coordinate System and Conventions

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Machine Coordinate System

The stored electrons in Sirius will be circulating in clockwise direction (as seen from the top). The motion of an electron is described in terms of coordinates related to the machine ideal orbit. Any position is specified in an orthogonal, right-handed coordinate system that follows the ideal particle traveling along the ideal path. is the coordinate along the ideal orbit and points in the direction of the particle velocity, that is tangent to the ideal orbit. The transverse coordinates and measure the horizontal and vertical deviations from the ideal orbit, with pointing to the outside of the ring and pointing upward. See Figure 1. The vectorial cross product holds.

The direction of for different kinds of magnets in the Sirius coordinate system are shown in Figure 2, where the term 'focusing' refers, by convention, to the plane of the orbit. The direction of the electron velocity is given by .

Figure 1: Coordinate system for Sirius. Top view.

Figure 2: direction for different kinds of magnets for electrons circulating clockwise. points to the outside of the storage ring.

BPM Coordinate System

Figure 3: 45 degree Rotated BPM Coordinate System
Figure 4: Cross BPM Coordinate System

The Beam Position Monitors Coordinate System is as shown on Figure 3. The antennas A, B, C and D are displayed, along with the beam direction (going outside of the figure). For further information, see DIG:Beam Position Calculation.

Direction Origin +
x-axis Horizontal, perpendicular to beam prolongation Centre of beam To the left, outward the storage ring
y-axis Vertical, perpendicular to beam prolongation Centre of beam Upwards

Beamline Coordinate System

Figure 5: Beamline coordinate system and rotation around axis.

Direction Origin + Rotation around the axis
z-axis along beam propagation source point in the beam direction roll
x-axis horizontal, perpendicular to beam prolongation center of beam to the left, outward, opposite to storage ring pitch (equal to Bragg rotation)
y-axis vertical, perpendicular to beam prolongation floor of experimental hall upwards yaw