SLAC tunnel motion and analysis

1
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/GM20
  00/
• 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
• 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 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

Observed Dh50mm for DP1000 Pa is consistent
with these estimations if DE/E0.5, h l 100m,
a0.5 and E109 Pa. Assumption E109 Pa is
consistent with SLAC correlation measurements.
Taking v500m/s (at 5Hz, I.e. l100m) and
r2103 kg/m3, we get E 109 Pa
l - length of landscape change, a - variation of
the normal angle to the surface
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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)

Tidal peaks
electronic noise
Electronic noise of the measuring system was
evaluated with a light diode fixed directly to
quadrant photo detector
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Diffusive in time...

• fit of the spectra to ATL gives A 10-7 -- 210-6
  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

Parameter A found in 1999/2000 SLAC
measurements. xi2 shows the quality of fit to
1/w2 spectra.
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Atmospheric pressure again

• 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.
gt
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A versus Youngs 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 The spectra of ground properties/landscap
e 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 !!!
Look for strong media, (higher Youngs modulus
E or shear velocity v)!
one of the causes
? for further studies
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Topography of many natural surfaces exhibits P(k)
1/k2 behavior of the power spectra (k is
spatial frequency, k2p/l)
...
...
(Note that definitions in this paper are
different from ours. In the paper k is a
coefficient and w is the spatial frequency.)