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A Vibrating Wire System For Quadrupole Fiducialization
LCLS-TN-05-11
A Vibrating Wire System For Quadrupole Fiducialization
Zachary Wolf
SLAC
May 6, 2005
Abstract
A vibrating wire system is being developed to ducialize the quadrupoles between
undulator segments in the LCLS. This note provides a detailed analysis of the system.
1
Introduction
1
The LCLS will have quadrupoles between the undulator segments to keep the electron
beam focused. If the quadrupoles are not centered on the beam axis, the beam will receive
transverse kicks, causing it to deviate from the undulator axis. Beam based alignment will
be used to move the quadrupoles onto a straight line, but an initial, conventional alignment
must place the quadrupole centers on a straight line to 100 m
2
. In the ducialization step
of the initial alignment, the position of the center of the quadrupole is measured relative
to tooling balls on the outside of the quadrupole.
The alignment crews then use the
tooling balls to place the magnet in the tunnel. The required error on the location of the
quadrupole center relative to the tooling balls must be less than 25
m
3
.
In this note, we analyze a system under construction for the quadrupole ducialization.
The system uses the vibrating wire technique to position a wire onto the quadrupole mag-
netic axis. The wire position is then related to tooling balls using wire position detectors.
The tooling balls on the wire position detectors are nally related to tooling balls on the
quadrupole to perform the ducialization. The total 25
m ducialization error must be
divided between these three steps. The wire must be positioned onto the quadrupole mag-
netic axis to within 10
m, the wire position must be measured relative to tooling balls on
the wire position detectors to within 15 m, and tooling balls on the wire position detectors
must be related to tooling balls on the quadrupole to within 10 m
4
. The techniques used
in these three steps will be discussed.
The note begins by discussing various quadrupole ducialization techniques used in the
past and discusses why the vibrating wire technique is our method of choice. We then give
an overview of the measurement system showing how the vibrating wire is positioned onto
1
Work supported in part by the DOE Contract DE-AC02-76SF00515.
This work was performed in
support of the LCLS project at SLAC.
2
LCLS parameter database http://www-ssrl.slac.stanford.edu/htbin/rdbweb/LCLS_params_DB_public.
3
H. D. Nuhn et al., "General Undulator System Requirements", LCLS Physics Requirements Document
1.4-001.
4
ibid.
1 the quadrupole axis, how the wire position detectors locate the wire relative to tooling balls
without touching the wire, and how the tooling ball positions are all measured. The novel
feature of this system is the vibrating wire which we discuss in depth. We analyze the wire
dynamics and calculate the expected sensitivity of the system. The note should be an aid
in debugging the system by providing calculations to compare measurements to.
2
Comparison Of Quadrupole Fiducialization Techniques
A number of techniques have been used in the past to ducialize quadrupoles. The rotating
coil technique and several di¤erent stretched wire techniques are discussed here.
A very common quadrupole ducialization technique uses a rotating coil. If the quadru-
pole center is not on the axis of rotation of the coil, a dipole component in the quadrupole
eld is measured
5
. If either the quadrupole is moved onto the coil axis until the measured
dipole component is zero, or the measured dipole component is used in a calculation to
determine the center position relative to the coil, then the quadrupole tooling balls can be
related to the coil rotation axis to ducialize the quadrupole. This technique has very high
sensitivity and quadrupole motions of a fraction of a micron can be resolved
6
. It is fairly
di¢ cult, however, to determine the axis of rotation of the coil to a few microns in a global
coordinate system.
This axis information is required for LCLS ducialization, however,
making the technique di¢ cult at best for our use.
Because of the di¢ culty in locating the axis of a rotating coil at the micron level, many
groups have used a single stretched wire for ducialization which can be located at the
micron level. The HERA quadrupoles were ducialized with a moving wire technique
7
in
which a stretched wire was translated in the quadrupole and the voltage induced in the wire
was integrated to give the ux change in the circuit. By performing precision motions of the
wire, the position of the magnetic center of the quadrupole was determined. The magnetic
center position was then related to tooling balls on the magnet for ducialization.
This
technique worked very well for the measurement of the HERA quadrupoles. The magnets
involved, however, were superconducting quadrupoles several meters long. In spite of the
size and eld strength of the magnets, the measured signals in the single, slowly moving
wire were very small and special care had to be taken so that thermal emfs did not cause
many microns of error. Because the LCLS quadrupoles are much weaker than the HERA
quadrupoles, this technique appeared extremely challenging and we did not pursue it.
Another elegant way to ducialize quadrupoles involves the pulsed wire technique
8 ;9
. A
small diameter Cu-Be wire is stretched through the quadrupole and a short pulse of current
is sent through the wire. If the wire is in a magnetic eld, it will experience a force which
causes the wire to move.
The magnet can be moved until the wire is stationary after
5
A. K. Jain, "Basic Theory Of Magnets", Proc. CERN Accelerator School on Measurement and Align-
ment of Accelerator and Detector Magnets, Anacapri, April, 1997, CERN 98-05 (1998) 1-26.
6
C. Rago et al., "High Reliability Prototype Quadrupole For The Next Linear Collider", SLAC-PUB-8990
(2002).
7
H. Brueck et al., "Methods For Magnetic Measurement Of The Superconducting HERA Magnets",
Kerntech 56 (1991) 248-256.
8
R. Warren, C. Elliot, "New System for Wiggler Fabrication and Testing", LA-UR 87-2981 (1987).
9
C. Fortgang, "Taut Wire Alignment Of Multiple Permanent Magnet Quadrupoles", LA-UR-89-2696
(1989).
2 the current pulse, and then the quadrupole is centered on the wire. The tooling balls on
the magnet are located relative to the wire to ducialize the magnet.
We set up such a
system in the SLAC magnetic measurements lab and we could very easily detect by eye on
an oscilloscope motion of as little as 5
m of a prototype LCLS quadrupole. The method
was fairly insensitive, however, to pitch and yaw of the quadrupole.
Without pitch and
yaw information, the measurement leads to a line through the quadrupole on which the
integrated transverse eld is zero.
This line is not unique, as an innite number of lines
have zero integrated transverse eld. The next time the magnet is ducialized, a di¤erent
line might be found.
This is of no consequence to the electron beam, but it would be
benecial for alignment to get a unique, reproducible result.
A technique used at SLAC for the SLC nal focus quadrupoles involved a vibrating
wire
10
. The wire was mechanically vibrated with audio speakers. The magnet was moved
until the voltage induced in the wire at the frequency of wire vibration went to zero. The
quadrupole was then centered on the wire.
This technique was very sensitive to magnet
motion. It was di¢ cult, however, to determine a line representing the axis of the moving
wire. The technique led to a line for which the transverse eld integral was zero, but the
line was not unique and could be pitched and yawed relative to the quadrupole as discussed
above.
Our method of choice for the LCLS quadrupoles is another vibrating wire technique
11 ;12
.
In concept, it is similar to the pulsed wire technique.
Instead of a large current pulse in
the wire, however, an AC current is used. The alternating current frequency is set to the
natural frequency of vibration of the wire. When the magnet is centered on the wire, the
transverse magnetic eld along the wire is zero and the wire does not experience a force and
does not move. When the quadrupole is moved, however, the current in the magnetic eld
produces an alternating force at the natural frequency of vibration of the wire. Since the
wire vibrates at its resonant frequency, the technique is extremely sensitive. In addition,
the pitch and yaw of the magnet can be determined, as will be shown, resulting in a unique
ducialization. In this note, the vibrating wire technique is described in detail.
The note continues with an overview of the measurement system. Practical aspects such
as how the wire is located are discussed. Then the equations of motion for the stretched
wire with an alternating applied force are derived and solved. E¤ects such as gravity and
vibration damping are included. A model vibrating wire system is discussed and values of
parameters such as wire diameter and length are inserted into the general equations so that
estimates of the performance of the system can be made.
3
Overview of the Quadrupole Fiducialization System
The components of the vibrating wire quadrupole ducialization system are shown in gure
1. A wire is tensioned between xed end points and through the quadrupole being ducial-
ized. The quadrupole is on a mover which positions the magnetic axis of the quadrupole
1 0
G. Fischer et al., "Precision Fiducialization of Transport Components", SLAC-PUB-5764 (1992).
1 1
A. Temnykh, "Vibrating Wire Field-Measuring Technique", NIM A399 (1997) 185-194.
1 2
A. Temnykh, "The Use of Vibra