![Figure 6. Spectrum and integral of vertical motion on the floor of the accelerator tunnel (about 35' below ground [4]).](/figures/figure-6-spectrum-and-integral-of-vertical-motion-on-the-ly6vm560.webp)
SLAC-PUB-95-6867
Work supported by Department of Energy contract DE–AC03–76SF00515.
VIBRATION STUDIES OF THE
STANFORD LINEAR ACCELERATOR
†
J. L. Turner, C. Adolphsen, G. B. Bowden, F. J. Decker, S. C. Hartman, S. Matsumoto, G.
Mazaheri, D. McCormick, M. Ross, R. Stege, S. Virostek, M. Woodley
Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309 USA
ABSTRACT
Vibration measurements of the linear accelerator
structures in the SLC linac show a 1 micron rms
vertical motion. This motion reduces to 0.2 micron rms
motion when the cooling water to the accelerator
structures is turned off. The quadrupoles have 250
nanometer rms vertical motion with the accelerator
structure cooling water on and 60 nanometer motion
with it off. These results together with measurements of
the correlations as a function of frequency between the
motions of various components are presented.
I. INTRODUCTION
During the 1994/95 colliding beam run of the SLC,
the measured jitter in the vertical beam position
indicated it had a significant impact on the luminosity
[1]. Diagnosing the sources of jitter became a priority
issue. The possibility of vertical movement of
quadrupole magnets or even accelerator structures
affecting the beam was considered, and efforts toward
modeling and measuring potential sources [2] of beam
jitter in the linac ensued. This paper primarily describes
measurements of quadrupole and accelerator structure
motion in the linac under various conditions and the
conclusions reached.
II. SETUP
The system used for most measurements combined
Mark L4-C geophones, and a SLAC built integrator and
amplifier, with a mobile LabView
®
data acquisition and
analysis system.
The geophone is essentially a mass suspended on a
spring that induces a signal on a coil which is
proportional to velocity of the ground motion for
frequencies above the geophone natural frequency
(~1 Hz). The signal is integrated, amplified, then
digitized at 4 kilohertz on a quad channel board and
analyzed using LabView
®
on a PC. The combined
system as configured for these measurements has good
†
Supported by D.O.E. contract DE-AC03-76SF00515.
resolution from 2 to 100 Hz. Electrical noise in the
geophone measurements was determined to be several
orders of magnitude below the measurement data.
Cross checks of the geophones were made using a
Hewlett Packard HP3560A Dynamic Signal Analyzer
with a PCB Piezotronics model 393B31 accelerometer
and an optical linear encoder (Heidenhain model MT60K)
with 50nm resolution. They agreed at the 10% level.
III. MEASUREMENTS
Vertical motion of accelerator structures was
measured at 1 micron rms, and thought not to be a
problem for SLC beams. Quadrupole vertical motion
was about 250 nanometers rms, enough to be a problem
[2]. Correlation between the motions of two quadrupoles
separated by 12 meters was high in the 8-14 Hz range
(see figure 1) but not elsewhere in the spectrum.
-1
-0.5
0
0.5
1
Normalized Cross
Power Correlation
10 100
Frequency (Hz)
Figure 1. Spectrum of normalized cross power
correlation of vertical motion of two quadrupoles.
Turning off water to the quadrupoles themselves had
little affect, but turning off the water to the adjacent
accelerator structures lowered vibration of the
quadrupoles from about 250 nanometers rms to about 60
nanometers rms (see figure 2). Thus most of the
quadrupole motion is due to the vibrations that are
caused by the cooling water. Much of the motion is at
59 Hz (see figure 2 bottom plot) which can be seen in
the jitter of the beam orbits [3]. The 59 Hz motion is
believed to be due to the accelerator water pump impeller
rotating at 59 Hz. The quadrupole motion in the 8-14 Hz
range, however, was not reduced dramatically with the
water off (see figure 2).
10
-9
10
-7
10
-5
10
-3
Power Spectrum (µm
2
/Hz)
10
-1
10 100
Q701 Water On
Frequency (Hz)
Q701 Water Off
0
0.05
0.1
0.15
0.2
0.25
Integrated Spectrum (µm)
0.3
10 100
Frequency (Hz)
Q701 Water On
Q701 Water Off
Figure 2. Quadrupole motion spectrum (top) and
integrated spectrum (bottom) with accelerator cooling
water on and off.
Not all quadrupoles exhibit the same behavior.
Figure 3 shows some examples of the integrated
spectrum. Note that the fraction of 8-14 Hz motion and
59 Hz motion differs. Oscillations at 28-30 Hz dominate
the spectrum of quadrupoles that have upright supports
(the so called matching quadrupoles, see Q901 in figure
3) even with the water off. These quadrupoles also have
a spike at 59 Hz that disappears when the accelerator
water is turned off.
0
0.05
0.1
0.15
0.2
0.25
Integrated Spectrum (µm)
0.3
Q501
Q601
Q801
Q901
Q701
Frequency (Hz)
10 100
Figure 3. Integrated vertical motion of five quadrupoles
with the accelerator water on.
Much of the quadrupole motion is related to the
design of its support. The centroid of the quadrupole is
offset along the beam direction (Z) which allows the
quadrupole to vibrate in an arc in the ZY plane (see
figure 4). Clamping the quadrupoles to the adjacent
structure reduced the 10-14 Hz motion significantly.
Figure 4. Side view of standard quadrupole with arrows
showing direction of movement.
Quadrupoles in different sectors are affected by
different accelerator water circuits. Those sampled in
sector 12 did not show as large a 59 Hz problem as seen
in sectors 14 and 15.
To study the difference, the pipe vibration near the
pump was measured in sector 14. The 59 Hz motion
was observed. Also, a pressure transducer was used to
measure the time variation of the pressure at sector 12
and 14. The pump rotates at 59 Hz, and pump impellers
have five vanes which create a large contribution at 295
Hz. Figure 5 shows the integrated spectra of the pressure
variations.
10
-11
10
-9
10
-7
10
-5
Integrated Spectrum (psi)
10 100
Sector 14
Sector 12
Frequency (Hz)
Figure 5. Integrated water pressure variations from two
accelerator water systems.
10
-9
10
-7
10
-5
0.001
Power Spectrum (µm
2
/Hz)
10 100
Accelerator Floor
Frequency (Hz)
0
0.002
0.004
0.006
0.008
0.01
Integrated Spectrum (µm)
10 100
Accelerator Floor
Frequency (Hz)
Figure 6. Spectrum and integral of vertical motion on
the floor of the accelerator tunnel (about 35' below
ground [4]).
Finally, measurements of the accelerator floor
motion were made. Figure 6 shows an example.
Integrated values (>2 Hz) between 9 and 35 nanometers
were observed on different days.
IV. SUMMARY AND CONCLUSIONS
The largest contributor to quadrupole vertical
vibration in the SLC is due to the motion of the
accelerator cooling water. Much of this motion is at 59
Hz. The 59 Hz is transmitted from the pump by
modulating the water pressure. Pump impeller quality
may be the cause.
Compounding the problem is a ~10 Hz resonant
quadrupole support structure. Its effect was reduced by
adding wedge supports. Other types of quadrupoles need
similar fixes.
V. REFERENCES
[1] P. Emma, "The Stanford Linear Collider,"
Contribution WAG01, 1995 PAC
[2] C. Adolphsen and T. Slaton, "Beam Trajectory
Jitter in the SLC Linac," Contribution WAB08, 1995
PAC
[3] M. G. Minty et al, "Optimization of Feedback
Performance at the Stanford Linear Collider",
Contribution RPB03,1995 PAC
[4] R. B. Neal, "The Stanford Two-Mile Accel-
erator," W. A. Benjamin, Inc. 1968