Proceedings o f the 22nd Linear Accelerator Meeting in Japan

Com parison of Tunneling M ethods for JLC
C h risto p h M ontag
KEKHigh E nergy A ccelerator R esearch O rg an izatio n
1-1 O ho, T su k u b a-sh i, Ibaraki-ken 305

Abstract
Due to the very low vertical beam emittances required for future Linear Colliders to achieve high luminosities
orsome 1034cm—2sec一1, these machines will be extremely sensitive to ground motion, leading to vibration ofthe focusing magnets. Therefore, ground motion has to be studied in detail. For JLC, two different tunnelingmethods are being discussed. To compare both methods regarding the coherence properties of motion of thetunnel floor, seismic measurements have to be performed in several sample tunnels, designed for purposes otherthan accelerator installation. The obtained data can then be used as input data for simulation algorithms
to study beam dynamics under the influence of ground motion. Recent results of these investigations will bepresented.

1Introduction

To achieve high luminosities of some 1034 cm一2sec—\
all Linear Collider schemes currently under study re­quire very low emittance beams. To avoid luminos­
ity degradation due to beam offset at the interaction
point (IP), ground motion induced jitter of the focus­
ing elements has to be kept within tight tolerances.
Allowing for a luminosity loss of 3%, the toleraole
beam motion ay of two Gaussian beams with rms
beam size crbeam can be derived usingC =;£ o *0.97£° . eXP( - 2士).

⑴

Assuming uncorrelated motion of the N q quadrupoles in the main linac and a periodic FODO latticewith /3-function scaling as (3 cca / E y the rms vibra­tion tolerance aq can be estimated as [1, 2]^*-20.25 • I^end • /^e]n dNq⑶

Here eend and /3end denote the geometric emittance atthe end of the main linac and the average ^-functionof the last FODO cell, respectively, (i is the phaseadvance per FODO cell. In the case of JLC, theresulting vibration tolerance is about 10 nm [3]. It
should be noted here that this formula holds only

for the quadrupoles m the main lmac, while in thefinal focus system the tolerances are tighter by a fac­
tor of about 5 to 10 [4, 5], but there they cannot be
expressed by eq. (2) .
Due to the extreme sensitivity of linear collider beam
motion to ground vibrations, much effort has beenspent during recent years in order to determine spec­
tra and correlation properties of ground motion [6 ,7, 8]. Since the properties of ground motion were
found to be very site-depending due to different geo­
logical conditions at the various locations (see fig. 1),
it turned out that a careful choice of the future linear
collider site is necessary.
Since it is expected that various tunneling methods
will lead to different properties of the resulting tunnel
floor regarding correlation of vibrations [3], seismic
measurements in various tunnels built for purposes
other than accelerator installation are under consid­
eration. The obtained results will then be used as
input data for simulation codes in order to investi­
gate the beam jitter amplitudes resulting from vibra­tion of magnets mounted on the floor of the futureaccelerator tunnel.

2Tunneling methodsBasically, two different tunneling methods are underconsideration for the construction of the JLC tunnel.
In the New Austrian Tunneling Method (NATM),the tunnel is excavated by blasting the surroundingrock and stabilizing it using shotcrete. Additionally,systematic rock bolting can be used to further sta-

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Taking signals x(t),y(t) from both instruments si­
multaneously, the correlation j(u) can be calculated
from the Fourier spectra asHere,X(u)Y*{u}x(t) . exp(-iujt) dtlimT -^ o oT-ly(t) • exo(iujt) dt

1nFigure 1 : Comparison of ground motion power spec­
tra measured at KEK (Tsukuba, japan), SSC (Waxahachie, Texas, USA), VEPP-3 (Novosibirsk, Rus­sia), UNK (Protvino, Russia) and HERA (DESY,Germany) [6]

⑶

7( 山）

⑷

is the mutual power spectrum of x(t) and y(t), re­spectively. X(uj)X*(uj) and Y( uj)Y (u) are similarly
defined. As usual the asterisk denotes complex con­jugate, while the average has to be taken over differ­ent spectra. As an example, figure 2 shows coherenGe
properties of ground motion obtained at DES^.
D e n o tin g t h e r a t i o o f c o r r e la t e d t o u n G o rre la te d

To determine the correlation properties of groundmotion, two identical seismometers have to be used.

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Frequency,

Hz

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Measurements0>

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30U9J9 :Sbilize the tunnel if necessary. In the next step, thetunnel is water-proofed, and then arch lining is ap­
plied by a travelling form. Finally, the tunnel floor isbuilt using concrete. This method results in a semi­
circular cross section of the tunnel•
The second method utilizes a large drilling machine
to bore the tunnel and is therefore referred to as
Tunneling Boring Method (TBM). Again, shotcreteis used to stabilize the tunnel against water leaks.
After water-prooting, the tunnel walls are suppliedwith the lining consisting of concrete segments. Incontrast to NATM, TBM results in a circular crosssection of the tunnel, which might be less suitable
for accelerator installation.
Both tunneling methods will have some effect on thesolid rock mass surrounding the tunnel, since they
will introduce little cracks there. These destructions
are expected to be significantly larger for the NATM
tunneling method due to the blasting, than for TBM,
resulting in worse correlation properties of groundmotion. It was experimentally confirmed that thepower spectrum densities of relative motion of two
points in such tunnels are significantly larger by afactor of about 5 [7]. On the other hand, careful lin­
ing may overcome these deficiencies. For example,
the concrete tunnel floor for both methods may beconnected to the undistorted rock using bolts of suf­
ficient length, therefore overcoming the problem ofcracks in the surface layer.

Frequency,

Figure 2 : Coherence spectra of vertical ground mo­tion at three different distances of b m,15 m and
30 m, measured in HERA hall West [6]ground motion power spectrum densities as 5, themodulus トレ)丨 of the correlation, which is usuallyreferred to as the coherence, can be expressed as(5)= \[T ^ h y

議Therefore, the coherence 17 (0;) | can be interpreted asa measure of the ratio of correlated to uncorrelated
ground motion.
While the ground motion power spectrum
in asingle point can be roughly approximated as
p {u o)A [um^^nrfsec)】
P { u)~フ，（6 )the power spectrumL) of uncorrelated motion of
two points at a distance L was experimentally foundto be(7)with A and B being proportionality constants.
In the time domain, the latter corresponds to a vari­ance a" of the motion of the two points after a timeinterval T as
び2 =•l ,(8)and is therefore referred to as the ATL rule [9].

4Simulation of beam jitter

To investigate the effects of ground motion on beam
properties in linear colliders, two complementary
simulation algorithms have been developed [10].
Both codes can be adapted to any measured power
spectra and correlation properties of grond motion.
While one of them, based on digital filtering of white
noise random signals, is very useful in determining
the effect of the magnitude of the AT L constant Aon the beam, the second one employs inverse Fouriertransforms to get the time signals of motion of eachmagnet from the power spectra. This latter codeis therefore appropriate to determine the effect ofground motion waves travelling at some angle 6 tothe linac, therefore leading to potentially very longeffective wavelengths.
As an example, figure 3 shows the resulting rms beamjitter at the end of the main linac of the S-band Lin­ear Collider SBLC being designed at DESY.

References[1] J. Rossbach, Tolerance on Uncorrelated Mo­
tion of Quadrupoles for Linear Colliders, DESY
M/VM 93-01[2] T. 0. Raubenheimer, The Generation and Ac­
celeration of Low Emittance Flat Beams for Fu­
ture Linear Colliders, SLAC report 387, 1991

Figure 3: Resulting rms beam jitter at the end of theSBLC main linac as a function of the proportional­
ity constant A in the ATL rule [10]. The solid line
represents the rms jitter amplitude resulting frompure ground motion, while the dashed line shows
the corresponding value with active stabilization ofquadrupoles [11].
[3] JLC Design Study, KEK, Tsukuba, 1997
[4] K. Oide, Final Focus System for the JLC, KEK
preprint 89-190[5] O. Napoly, CLIC Final Focus System: Up­
graded Version with increased Bandwidth andError Analysis, CEA/DAPNIA/SEA 94 10[6] V. Shiltsev, B. Baklakov, P. Lebedev, C. Montag, J. Rossbach, Measurements of Ground Vi­
brations and Orbit Motion at HERA, DESY
HERA 95-06[7] Shigeru Takeda, N. Yamamoto, K. Oide,Ground Motion Studies for Large Future Lin­ear Colliders, Proc. PAC 97[81 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, Vibration Studies of
the Stanford Linear Accelerator, SLAC-PUB95-6867[9] B. Baklakov, P. Lebedev, V. Parkhomchuck,
A. Sery, A. Sleptsov, V. Shiltsev, Investigation ofSeismic Vibrations for Linear Collider VLEPP,Sov.Phys. ZhTF., vol.63, No.10，1993 (in Rus­sian)[10] C.Montag，Active Stabilization of Mechanical
Quadrupole Vibrations in a Linear Collider Test
Facility, DESY 97-030[11] C.Montag, Active stabilization of mechani­
cal quadrupole vibrations for linear collid­
ers, Nucl. Instr. and Meth. in Phys. Res. A 378(1996) 369-375