# I.R. Coordinate System Axes Conventions

Martin Nordby

11 April 96

## 1. Abstract

This note describes the various coordinate systems used in the PEP-II Interaction Region, and specifies the IR Reference Frame as the standard coordinate system, and the conventional “aisle-side” view as the default view for PEP-II I.R. mechanical layouts and drawings. This standard is consistent with that already being used in the PEP-II HER and LER.

## 2. Interaction Region Coordinate Systems

There are five coordinate systems commonly used in the PEP-II IR. Dimensions, views, and references are made to all of the five, so below is an explanation of them:

2.1 PEP-II Coordinate System

This system is identical to the coordinate system used for PEP [1], but offset vertically downward by 498 mm [2]. The center of this coordinate system is the center of the PEP-II Rings, at the same elevation as the plane of the HER.

PEP-II Coordinate System

Origin: Center of the PEP-II rings. Elevation above mean sea level = 65.986 m

+X: Direction from the PEP-II ring center through the center of IR-12 (nominally north).

+Y: Up, parallel to gravity vector through the ring center.

+Z: Direction from the PEP-II ring center through the symmetry point (mid-arc) in Arc 3 (nominally east).

2.2 PEP Control Line

The original PEP machine had a straight trajectory through each interaction region, and the beam orbit was described with respect to a straight line running parallel to it. This PEP Control Line was nominally parallel to the tunnel walls, and orthogonal to the IR-2 Hall walls. Its origin was the PEP interaction point for that IR. For IR-2, the PEP Control Line Coordinate System is defined as:

PEP Control Line

+Z: Rotated by -60 degrees from the PEP (and PEP-II) Coordinate System Z-axis.

+Y: Up.

+X: Radially outward from the center of the PEP ring.

Origin:

Radial distance from the PEP Ring center: 338.883313 m

Vertical offset from the PEP-II Coordinate System: +498 mm

2.3 IR Reference Frame

The interaction point for PEP-II is located radially outward from the PEP Control Line. However, neither beamline runs parallel to the old PEP beams nor, for that matter, straight at all, until far back in the tunnel. Thus, a convenient, physically intuitive coordinate system can be defined independent of the beam trajectories, but parallel to the old PEP Control Line, running through the new PEP-II Interaction Point.

IR Reference Frame

+Z: Parallel to the PEP Control Line, in the direction of the High Energy Beam (HEB).

+Y: Up.

+X: Radially outward from the center of the PEP-II rings.

Roll: Plane perpendicular to gravity through the I.P.

Pitch: Plane perpendicular to gravity through the I.P.

Yaw:

0 mrads with respect to the PEP Control Line

-60 degrees with respect to the PEP-II Coordinate System.

Origin:

Position of the PEP-II Interaction Point.

With respect to PEP-II Coordinate System [3]: (169.529761 m, 0 m, 293.634159 m)

Radial distance from the PEP-II Coordinate System origin: 339.05952 m

Radial distance from the PEP Control Line: +176.21 mm

Vertical offset from the PEP Control Line: -498 mm

2.4 Collision Axis Coordinate System

This coordinate system has been used for accelerator physics studies as a convenient reference for beam orbit simulations, lacking any other nominal reference frame. The collision axis is defined as the line along which the beams travel as they collide head-on at the interaction point.

Collision Axis Coordinate System

+Z: Colinear with, and in the direction of, the HEB trajectory at the interaction point.

+Y: Up.

+X: Perpendicular to +Z and +Y to complete a right-handed coordinate system. This is pointing nominally outward from the center of PEP-II.

Roll: Plane perpendicular to gravity through the I.P.

Pitch: Plane perpendicular to gravity through the I.P.

Yaw:

-16.354 mrads with respect to the IR Reference Frame.

-1.063552 rads with respect to the PEP-II Coordinate System [4].

2.5 Detector Coordinate System

Defined by the BaBar Detector as orthogonal to the detector elements and solenoid field.

Detector Coordinate System

+Z: Parallel to the Detector solenoid field, in the direction of the HEB.

+Y: Up.

+X: Perpendicular to +Z and +Y to complete a right-handed coordinate system. This is pointing nominally outward from the center of PEP-II.

Roll: Plane perpendicular to gravity through the I.P.

Pitch: Plane perpendicular to gravity through the I.P.

Yaw:

+20.000 mrads with respect to the Collision axis[5].

+3.646 mrads with respect to the IR Reference Frame.

## 3. Default or Standard Coordinate System

Because of its physically intuitive orientation, the IR Reference Frame Coordinate System is the default, or standardly-used system for all PEP-II IR mechanical components and layouts. Thus, all dimensions on a drawing, and all model geometry in a CAD file, should be oriented, and should measure with respect to the IR Reference Frame, unless specifically called out otherwise. See the pictures on page 4 and 5, which show the relation between the IR Coordinate System and the others.

For completeness, whenever possible, the coordinate system used should be identified, and a labeled coordinate triad shown. Dimensions can be identified by their coordinate system using these names:

IR Coordinate System: IR X, IR Y, IR Z

Detector Coordinate System: det X, det Y, det Z

## 4. Standard Views

In keeping with the intuitive nature of the IR Coordinate System, the standard view for PEP-II IR drawings and layouts should be what is seen from the entrance to the IR-2 hall, or from the aisle side of the machine. This is consistent with the practice for all other beamlines at SLAC, and minimizes the potential for confusion during installation and servicing.

Below are views of the IR Coordinate System triad from the four standard views.

[1] W. Davies-White, et al. B-Factory Coordinate System, Asymmetric B-Factory Collider Note ABC-31, 8 Mar 91.

[2] T. Fieguth, D. Kharakh, M. Pietryka. Correcting PEP-II Elevations, General distribution memo, 10 Jan 95.

[3] Lattice file 1 ler15.mad Revision: 1.39 (Date: 1996/01/19 00:49:39). Based on MAD Version: 8.2/13 Run: 01/18/96 16.49.50. Located on the PEP-II Server disk, URL: ftp://pepii-server.slac.stanford.edu/Lattice/ler/latest_lattice/l960118/ ler.survey_summary

[4] Lattice file 1ler15.mad Revision 1.39, op cit.

[5] Mike Sullivan, APIARY 8.6 (B3\$86E) run of MAGBENDS. Located on the WWW at URL: http://www.slac.stanford.edu/accel/pepii/near-ir/home.html