1. 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

2. NLC - The Next Linear Collider Project A.Seryi 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. Scheme of measurements x1x1 x2x2 x3x3 Signals from the quadrant photo detector were combined to determine X and Y relative motion of the tunnel center with respect to its ends.

3. NLC - The Next Linear Collider Project A.Seryi SLAC tunnel drift studies Horizontal and vertical displacement of the SLAC linac tunnel and external atmospheric pressure. Unexpected facts: The tidal component of motion is surprisingly big ~10 micron. Motion has strong correlation with external atmospheric pressure.

4. NLC - The Next Linear Collider Project A.Seryi Tidal motion of the SLAC linac tunnel 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. Subset of data where tidal motion is seen most clearly. Fit of 3 major tidal harmonics

5. NLC - The Next Linear Collider Project A.Seryi Influence of atmospheric pressure Very slow variation of external atmospheric pressure result in tunnel deformation. Explanations: landscape and ground property variations along the linac: - length of landscape change,  - variation of the normal angle to the surface Observed  h=50  m for  P=1000 Pa is consistent with these estimations if  E/E~0.5, h~ ~ 100m,  ~0.5 and E~10 9 Pa. Assumption E~10 9 Pa is consistent with SLAC correlation measurements. Taking v=500m/s (at ~5Hz, I.e. ~100m) and  =2*10 3 kg/m 3, we get E= 10 9 Pa

6. NLC - The Next Linear Collider Project A.Seryi Tunnel motion. Diffusive in time Spectra of tunnel displacements behave as 1/  2 in wide frequency range, as for the ATL law for which P( ,k)=A/(  2 k 2 ) Electronic noise of the measuring system was evaluated with a light diode fixed directly to quadrant photo detector electronic noise Tidal peaks

7. NLC - The Next Linear Collider Project A.Seryi Diffusive in time... Parameter A found in 1999/2000 SLAC measurements. xi2 shows the quality of fit to 1/  2 spectra. fit of the spectra to ATL gives A~ 10 -7 -- 2*10 -6  m 2 /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

8. NLC - The Next Linear Collider Project A.Seryi 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/  2 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 6  m/mbar in Y and 2  m/mbar in X. “A” vs amplitude of atmospheric pressure spectrum aP. Spatial does not depend on f, but given spectra of landscape/ground properties. =>

9. NLC - The Next Linear Collider Project A.Seryi “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 The spectra of ground properties/landscape vary as 1/k 2, the spectra of pressure behave as 1/  2 and together they give 1/(  k) 2 that is (or mimic) diffusive motion For the shallow tunnel, the “A” scales as 1/E 2 or 1/v 4 !!! Look for strong media, (higher Young’s modulus E or shear velocity v)! ? for further studies one of the causes

10. NLC - The Next Linear Collider Project A.Seryi Topography of many natural surfaces exhibits P(k) ~ 1/k 2 behavior of the power spectra (k is spatial frequency, k=2  / )... (Note that definitions in this paper are different from ours. In the paper k is a coefficient and  is the spatial frequency.)