Machine:Coordinate System and Conventions

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 $\text{[math]}$ that follows the ideal particle traveling along the ideal path. $\text{[math]}$ is the coordinate along the ideal orbit and $\text{[math]}$ points in the direction of the particle velocity, that is tangent to the ideal orbit. The transverse coordinates $\text{[math]}$ and $\text{[math]}$ measure the horizontal and vertical deviations from the ideal orbit, with $\text{[math]}$ pointing to the outside of the ring and $\text{[math]}$ pointing upward. See Figure 1. The vectorial cross product $\text{[math]}$ holds.

The direction of $\text{[math]}$ 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 $\text{[math]}$ .

Figure 1: Coordinate system for Sirius. Top view.

Figure 2:

\text{[math]}

direction for different kinds of magnets for electrons circulating clockwise.

\text{[math]}

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

Machine:Coordinate System and Conventions