Transcript SLAC tunnel motion and analysis Andrei Seryi SLAC

NLC - The Next Linear Collider Project
SLAC tunnel motion and
analysis
Andrei Seryi
SLAC
Originally given at The 22nd Advanced ICFA Beam Dynamics Workshop
on Ground Motion in Future Accelerators
November 6-9, 2000, SLAC
http://www-project.slac.stanford.edu/lc/wkshp/GM2000/
Reported briefly to the Advanced Seismic Sensor Workshop,
Lake Tahoe, March 24-26, 2004
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Recent SLAC tunnel drift studies
• Goal: to perform systematic
studies of slow tunnel
motions
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Measurements were done from
December 8, 1999 to January 7,
2000.
These measurements were
possible due to PEP- II shutdown.
The linac alignment system
working in the single Fresnel lens
mode allowed submicron
resolution.
First measurements of this kind
were done in November 1995 by
C.Adolphsen, G.Bowden and
G.Mazaheri for a period of about
48hrs.
x3
x2
x1
Scheme of measurements
Signals from the quadrant photo detector
were combined to determine X and Y
relative motion of the tunnel center
with respect to its ends.
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SLAC tunnel drift studies
Unexpected facts:
• The tidal component
of motion is
surprisingly
big ~10 micron.
• Motion has strong
correlation with
external atmospheric
pressure.
Horizontal and vertical displacement of the SLAC linac tunnel
and external atmospheric pressure.
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Tidal motion of the SLAC linac tunnel
Subset of data where
tidal motion is seen
most clearly.
Fit of 3 major
tidal harmonics
• Observed tidal motion is ~100 times larger than expected.
(N.B. the system is not sensitive to change of slope due to tides, but only to change of the
curvature)
• Higher amplitudes are caused by enhancement of tides due to ocean loading in
vicinity (~500km) of the shoreline.
•
Tidal motion is slow, it has long wavelength and is not a problem for linear
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collider.
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Influence of atmospheric pressure
Very slow variation of external atmospheric pressure
result in tunnel deformation. Explanations: landscape
and ground property variations along the linac:
h 
P h E
E E
Observed h=50mm for P=1000 Pa is consistent with
these estimations if E/E~0.5, h~  ~ 100m, a~0.5 and E~109 Pa.
Assumption E~109 Pa is consistent with SLAC correlation measurements.
h 
P
α
E
 - length of landscape change,
a - variation of the normal angle
to the surface
v
E
2 ρ (1   )
Taking v=500m/s
(at ~5Hz, I.e. l~100m)
and r=2*103 kg/m3,
we get E= 109 Pa
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Tunnel motion. Diffusive in time
• Spectra of tunnel
displacements behave
as 1/w2 in wide
frequency range, as
for the ATL law
for which
P(w,k)=A/(w2 k2)
Electronic noise of the measuring
system was evaluated with a light
diode fixed directly to quadrant
photo detector
Tidal peaks
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Diffusive in time...
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Parameter A found in 1999/2000 SLAC measurements.
fit of the spectra to
ATL gives A~ 10-7 -2*10-6 mm2/m/s
“A“ is higher for
vertical plane.
The value “A” varies
in time. Why?
The “A” value is
consistent with FFTB
measurements with
stretched wire over 30 m
distance
xi2 shows the quality of fit to 1/w2 spectra.
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Atmospheric pressure again
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Correlation X or Y and atmospheric pressure is
significant from 10-6 up to about 0.003 Hz.
Spectra of pressure also behave as ~ aP/w2
The amplitude of “A“ correlates with amplitude
of pressure spectrum aP.
The ratio (X/P) almost does not depend on
frequency in 10-6 -0.003 Hz and is about
6mm/mbar in Y and 2mm/mbar in X.
=>
“A” vs amplitude of atmospheric pressure spectrum aP.
Spatial l does not depend on f, but
given spectra of landscape/ground
properties.
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“A” versus Young’s modulus
Spatial variation of ground and/or landscape + variation of atmospheric
pressure is a major cause of diffusive-like motion of the SLAC linac tunnel
one of the
causes
The spectra of ground properties/landscape vary as 1/k2 , the spectra of
pressure behave as 1/w2 and together they give 1/(w k)2 that is (or mimic)
diffusive motion
For the shallow tunnel, the “A” scales as 1/E2 or 1/v4 !!!
? for further studies
Look for strong media, (higher Young’s modulus E or shear velocity v)!
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Topography of many natural surfaces exhibits P(k) ~ 1/k2 behavior
of the power spectra (k is spatial frequency, k=2p/l)
...
...
(Note that definitions in this paper are different
from ours. In the paper k is a coefficient
and w is the spatial frequency.)
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