There are two major characteristics in GM frequency(f) in quiet sites. Generally at f < 0.1Hz, diffusive motion is dominant, while "elastic" waves are dominant at f>0.1Hz.
The diffusive motion has been formulated by the ATL rule, which tells that RMS of relative displacementidelta_y2) is proportional to distance between two points(L) and elapsed time(T); delta_y2=ATL, where A is a site-dependent constant of 10-16 ~ 10-21m/sec. Its power spectra is expressed by A/(omega k)2(1-cos(kB/(A omega2)), where omega=2 pi f, B is another constant. At omega < (B/AL)1/2, delta_y2 becomes ATL. An example is a tilt measurement between two points separating by 50m by National Astronomical Observatory Mizusawa at Esashi ,Japan, The measured period is 15 years from June 1979 to April 1994. Results show a random walk which is clearly different from oscillation. A is (0.33 +/- 0.05)x10-18m/sec. Another example is a HELA observation by one BPM at HERA-e, rms electron orbit motion(L(FODO)=23.5m) and rms proton orbit motion(L(FODO)=47m), whose A was estimated to be (4+/-2) x 10-18m/sec. HERA tunnel is 6km long under the city.
In general waves consists of ocean swell at ~0.2Hz, crustal resonances at ~3Hz and cultural noises at 1 ~ 100Hz as well as earth quakes at 3~10 Hz. The wave is approximated to be plane wave, i.e. two dimensional wave. Its direction is assumed to be uniformly distributed on a plane. So, along the LINAC, k-dependence is expressed by 2/SQRT(k2cut - k2), k = 0~kcut, where kcut = omega/velocity. The correlation is simply expressed by cos kL, where L is a distance between two points along the LINAC.
There are measured power spectra at high energy laboratories; UNK, LEP/CERN, HERA/DESY, SLC/SLAC and ATF/KEK etc. . Recently the ILC-TRC luminosity working group made three GM models (A,B,C) to represent the LEP, SLAC and HERA as the most quietAquiet and noisy (urban area) sites, respectively. The models have the ATL rules and three waves in two dimensional power spectra of omega and k (wave number). Phase velocities of the ground motion are 3,000m/sec at the A model and 450+1,900exp(-f/2) m/sec at the B and C models.
In future, we would like to make a model at KEK-site (deep underground) to evaluate a Luminosity stabilization.
(2) FEATHER: Status Report (N.Delerue, KEK)
(transparencies, 4 pages, pdf ,1.4MB )
Nicolas briefly reported the beam test with GPIB communication. Since there were many timeout experiences, the performance shall be investigated in more details. The designs of movable kicker and BPM have been completed and the fabrication has been ordered to company. It will take three months to fabricate them. He is writing a report for the design.
(3)Beam scattering at LINAC (T.Yamamura, Univ. of Tokyo)
Yamamura explained his plan for simulation. He proposed to use GEANT4 for this purpose. However, it is pointed out that the best way to simulate the scattering at LINAC must be to use SAD. Synchrotron radiations of "real" emission of photons with finite angles have recently been installed in the SAD. So, he can use such a scheme. He is encouraged to communicate with Oide-san ( one of SAD authors at KEK).