# 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 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 .

## 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

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 |