A SHAKY ROAD TO SUBNANOMETER BEAMS.
NLC GROUND MOTION, VIBRATION AND STABILIZATION STUDIES1
Andrei Seryi, SLAC, Stanford, USA
Abstract
Ground motion and vibration can be a limiting factor in
the performance of future linear colliders. Investigationsof ground motion have been carried out around the world
for several decades. In this review, results of recent
investigations of ground motion as well as ongoingdevelopments of stabilization methods are presented.

The integrated spectrum over a particular frequency
band gives the corresponding RMS motion. It is easy to
see that the natural ground motion is quite small, as low asa fraction of a nanometer, for frequencies higher thanseveral Hz (see Figure 2).

1 GROUND MOTION STUDIES
Ground motion can conveniently be divided into ‘fast’and ‘slow’ when studying its effect on a linear collider.
Fast motion (f > a few Hz) cannot be adequately correctedby a pulse-to-pulse feedback operating at the repetition
rate of the collider and therefore primarily causes beam
offsets at the IP. Slow motion can be compensated by
feedback and thus results only in beam emittance growth.
Another consideration is that the mechanism that
produces relative displacements is different (discussed
below) for slow and fast motion with a boundary
occurring somewhere in a milli-Hz range.

Figure 2: Ground motion measured in Hiidenvesi caveshowing the amplitude for different frequency bands [5].
The motion in the low frequency bands in Figure 2 ismuch larger, the order of a micrometer, however it isimportant to emphasize that the amplitude shown isabsolute, i.e. it is the motion of a single point with respect
to an inertial reference frame. What is important for alinear collider is the relative motion of two quadrupoles
separated by distances less than the betatron wavelength.

Figure 1: Power spectrum of absolute ground motion
measured in different sites [1,2,3,4,5].
Fast motion is typically represented by a power
spectrum as shown in Figure 1. The power spectrum ofabsolute displacement generally follows a 1/ω4 behavior
on top of which are added the particular signatures fromthe contribution of different sources. For example,
cultural noise (human produced) typically manifests itself
above 1 Hz. Motion from ocean waves causes a peakaround 0.14 Hz.
1

Figure 3: Example of correlation measured in the SLC
tunnel for 100 m separation between probes [4].

Work supported by the U.S. Department of Energy, Contract DE-AC03-76SF00515.

Correlation measurements have shown [1,2,4] thatnatural ground motion consists mostly of elastic waves
with a wavelength given by the phase velocity in the
media. The slowest band of ‘fast’ motion has quite a longwavelength and is therefore highly correlated (see Figure3) and does not cause harmful effects on a linear collider.
In the NLC, the tolerance on jitter in the position ofelements varies significantly. The tolerance for the Final
Doublet (FD) is a fraction of the beam size at the IP,
around 1 nm. Some of the quadrupoles in the beam
delivery system have very tight tolerances as well, on theorder of 5-10 nm. The jitter tolerances for the main linac
quadrupoles are also of the order of 10 nm, since there aremany of them. The relevant frequency range for thesetolerances is determined by the beam-based feedback
which would effectively compensate for motion slower
than about 1/20 of the repetition rate; for the JLC/NLC
design, the frequency band of concern is f > 6 Hz. Moredetailed evaluations of tolerances are given in the next
section.

Figure 4: Integrated spectrum of absolute motion in SLC
sector 10 compared with the motion near the SLD
detector for a variety of situations. The top curves show
motion on the SLD with and without the electronic racks
on. The lower curves show the noise on the pit floor undernominal conditions and when most of the noise sources inthe building were turned off (SLD door opened, most of
on-SLD racks turned off) [6].
From these considerations, one can conclude thatnatural fast ground motion does not represent a limitation
for a linear collider (for present parameters) and the realconcern is cultural noise produced in the vicinity, whether
external or internal to the tunnel or vibrations producedon the accelerator girder itself. An example of culturalnoise is shown in Figure 4 where the noise measured on
the floor of the SLC collider hall and on the SLD detector
is shown in comparison with a quiet location at SLAC.
Most of the noise is produced by very local sources –building ventilation, nearby compressors, etc. – and byvarious equipment mounted on the SLD itself. It is clearthat the NLC detector must be designed carefully with agoal of minimizing vibration. Moreover, all of theconventional facilities support equipment for theaccelerator will have to satisfy vibration criteria.
The fast motion and vibration discussed above is not
the only issue for a linear collider. Ground motion below
0.01 Hz or so, in spite of being very slow, can have arather short wavelength, causing misalignments of thecollider and producing emittance growth. This motion is
not wave-like and can be inelastic. There are two types of
motion – one is diffusive and another is systematic. The
model for the diffusive motion parameterizes the RMS
relative misalignment as an ATL law [2,8]: ∆X2 = ATL
where T is the time since perfect alignment and L is the
distance between points.
The parameter A varies by a few orders of magnitude
when measured in different places and is clearly site andgeology dependent. For example, measurements at the
DESY site gave a value of A = 10-5 µm2/m/s [9] while in atunnel built in rock in Japan, A = 2*10-9 µm2/m/s. The
latter measurements also showed an increase in the valueof A when blasting was used for the tunnel construction[10]. For diffusive motion with a value of A = 5*10-7µm2/m/s, similar to observations at SLAC in the SLC andFFTB tunnels [11,7], the linear collider would requirecontinuous beam based alignment on a time scale of every
30 minutes in order to prevent emittance growth.

Figure 5: Horizontal and vertical motion of the center ofthe 3 km SLAC tunnel with respect to its ends plottedalong with external atmospheric pressure [7].
X

Recent measurements at SLAC have shown that thevalue of A can depend on changes in atmosphericpressure acting on the ground [7]. Figure 5 shows datataken in the 3 km SLAC tunnel over a period of one
month. There is a clear tidal component seen in thetransverse motion of the tunnel and there is a clear
correlation of the motion with external atmosphericpressure. This correlation was observed over a wide
frequency band (3E-6 – 1E-3 Hz) where the power
spectrum of the tunnel motion behaved as 1/ω2 (the sameas the ATL law) and thus the value of A could be derived.

The spectrum of atmospheric pressure was found tobehave in a similar way (also as 1/ω2) and its amplitude
Ap was surprisingly correlated with A as shown in Fig.6.
The observation that the deformation of the linac tunnel
is correlated with atmospheric pressure variation [7] canbe explained by assuming that the pressure acts on the
ground whose properties vary along the linac. Thisvariation can be due to changes in the Young’s modulus E,changes in the topology of the surface, or changes in thecharacteristic depth of the softer surface layers. It is worth
noting that in this case the atmosphere-driven contribution
to A scales as 1/E2 and therefore depends strongly on
geology which may be partly responsible for the large
variation of A observed in different places.

Figure 6: Parameter A of the ATL law defined fromvertical motion of SLC tunnel plotted against theamplitude Ap of the atmospheric pressure spectrum [7].
Very slow ground motion can also be systematic in timeover periods of months to years. Such motion has been
observed at SLAC, CERN and other places [12]. In somecases such motion can also be described by a simple rule
for its RMS relative misalignment [13]: ∆X2 = AST2L withanother site-specific coefficient AS. At SLAC it appears
that the systematic motion dominates on a time scale
greater than 105 seconds. Studies to investigate this slow
ground motion in more detail are currently in progress atmany different laboratories.

2 MODELING
In order to accurately characterize the influence ofground motion on a linear collider, a comprehensive
mathematical model is required. Such a model would
include understanding of the temporal and spatial
properties of the motion and of the driving mechanisms.
In most cases an adequate representation for such a model
consists of the 2-D power spectrum P(ω,k) based on
measured spectra of absolute motion and correlation.

The ground motion model for the SLAC site [13] uses
measurements of fast motion taken at night in sector 10 of
the SLAC linac [4]. Figure 7 shows the spectrum ofabsolute and relative motion for this model. To evaluate
different levels of cultural noise, we augment this model
to include two other cases with significantly higher andlower noise contributions. The measured spectra and theapproximations used in the models are shown in Figure 1.
The “HERA model” is based on measurements in
DESY [3] and corresponds to a very noisy shallow tunnel
located in a highly populated area where no precautions
were taken to reduce the contribution of various noise
sources in the vicinity or in the tunnel. The “LEP model”
corresponds to a deep tunnel where the noise level is very
close to the natural seismic level, without additional
cultural sources outside or inside of the tunnel. The“SLAC model” represents a shallow tunnel located in amoderately populated area.

Figure 7: Measured (points) and modeling spectrum p(ω)
of absolute motion for the 2 AM SLAC ground motion
model [4,13]. The lower curves show the spectra of
relative motion p(ω,L)/2 for different separation L.
As an example of how such models can be used, acomparison of the performance of the NLC Final Focus
for different ground motion models is shown in Figure 8.
One can see that a site located in a highly populated area
without proper vibration sensitive engineering would
present significant difficulties for a linear collider with theparameters considered. Stabilization of more components
than just the final doublet would be necessary. A site withnoise similar to the “SLAC model” would certainly besuitable, while the “LEP model” would be suitable evenfor much more ambitious beam parameters. These results
should not be considered as an attempt to evaluate any
particular site, or even the models, because for a fully
consistent assessment, various in-tunnel noise sources aswell as vibration compensation methods must be
considered as an integrated system.
The SLAC ground motion model includes all of thefeatures that are presently known, including wave motion,diffusive motion and systematic motion. Figure 9 shows
how these types of motion affect the behavior of RMS
relative misalignment over time. One can see that thiscurve can be divided into three regions: wave dominated,
ATL-dominated and systematic motion dominated.

Figure 8: Integrated spectral contribution to the RMS
equilibrium IP beam offset for the NLC Final Focus withfinal doublets supports at ±8 m for different models ofground motion. Dashed curves correspond to the casewhen the relative motion of the FDs is eliminated [14].

3 STABILIZATION METHODSFor the NLC, the ground motion and vibration issues
have been systematically addressed by proper design,
careful consideration of sites and geology, and by
development of appropriate stabilization methods.
An important issue for the NLC design is the location.
An ideal site should have little external cultural noise,
now or in the future. Solid rock is the preferredsurrounding media since fast motion will be better
correlated and slow motion will be reduced. In real life
the proximity to an existing major laboratory would also
be a great advantage. This proximity would notnecessarily mean compromising the other requirements
since a deep tunnel version of the NLC could have goodgeology and low noise and still be located near an existinglab. This is true for all of the deep tunnel NLC locations
that have been considered in both Illinois and California.
Of course a good site alone is not sufficient, the noise
generated by the linear collider equipment itself and by
conventional facilities equipment must be appropriately
controlled and minimized (by design and by further
passive or active damping). This would allow thetolerances to be met without any additional active
stabilization or correction techniques for all of the
focusing and accelerating elements of the linear collider
with the only exception being the final doublet.
Though the NLC detector must be designed tominimize vibrations, it is unlikely that the tolerances forthe final quadrupoles mounted on the detector could be

met without additional active measures. Several methods
are being developed to provide the necessary relative
stability for the final doublet, among them position
stabilization via feedback and correction of the magnetic
center position with dipole coils via feedforward. Bothmethods would rely on either inertial measurements of the
motion by seismometers or on optical interferometricmeasurements of their position with respect to each otheror to stable ground under the detector (“Optical anchor”).

Figure 9: RMS relative motion versus time for two points
separated by 30 m for the 2 AM SLAC site ground motion
model [13].
The “Optical anchor” developed first at SLAC [15] andnow being expanded at UBC [21] has demonstrated aresolution of about 0.2 nm [15] which would be more thansufficient for measuring the position of the FD.

Figure 10: Integrated spectrum measured on the floor(ch0) and on top of a 1500 kg PEP-II quadrupole (ch1)stabilized with the use of three STACIS vibration
insulation stands [18,20].
An attempt to stabilize the position of a quadrupole wasmade at DESY as part of the S-Band linear collider
project [16]. In this case a single seismometer and a single
piezo-mover were used to stabilize the effective positionof the quadrupole center. A reduction of RMS motion by

a factor of 3 was achieved (from 100 nm to about 30 nm
for frequencies higher than a few Hz).
Another attempt at inertial stabilization was performed
at SLAC using three commercial STACIS insulation
stands now produced by TMC [17] to stabilize theposition of a 1500 kg PEP-II quadrupole [18,20]. In thiscase the floor motion was reduced by about a factor of 20(from 40 nm to 2 nm for f > 2 Hz). However, additionalslow noise of the order of 200 nm was introduced (seeFigure 10) and the performance in the horizontal plane
was not as satisfactory.

Figure 11: Simulated performance of the fast intra-bunch
feedback showing the capture transient for an initialbeam-beam offset of about three sigma. The upper plotshows the position of the beams at the IP. The lower plotshows the position of the outgoing beam at the BPM(blue), the analog response of the BPM processor (green),
and the kicker drive signal, in arbitrary units (red).
Essentially full luminosity is restored in 42 ns [24].
These first examples of inertial stabilization (or inertial
sensing for feedforward) do not satisfy the requirements
for NLC. In a real collider, the system must detect andappropriately minimize motion of two extended andseparated FDs without excessively disturbing thecorrelation with the rest of machine. In addition, thesystem must work in an external magnetic field and it
must be compact and reliable. R&D to address theseissues will continue at SLAC and in other laboratories[21,22,23].
In addition to the beam independent methods of IR
stabilization, beam based methods are also being
developed, in particular a fast correction within the bunchtrain. The intra-train feedback will use a position monitor(BPM) near the IP to detect the offset of the first bunchesof the train. The signal is the beam-beam deflection due tothe relative offset of the beams and fast kickers are thenused to correct the rest of the bunch train. Recent
preliminary evaluation indicates that such system istechnically feasible with available components and could
provide efficient capture of beams with several sigma

offset [24]. This would significantly reduce therequirements on incoming beam jitter and on stabilizationof the FD. Further R&D will concentrate on a technicaldemonstration of this system.

CONCLUSION
Ground motion and vibration are important issues forany future linear collider and they have been extensively
studied and modelled at different laboratories around theworld. In this paper, we have outlined our present
understanding of the ground motion and vibration
problem and described the models used to evaluate theeffects. We have also discussed the ongoing efforts onstabilization techniques that are being pursued by the
NLC group.
The review presented is certainly just a brief snapshotof this very actively developing field. To get a broader
picture of the issues, including discussion of similar
problems in circular accelerators as well as in nonaccelerator experiments, the reader is referred to theproceedings of the recent ICFA Workshop on Ground
Motion held at SLAC in November 2000 [19].
This paper summarizes results obtained by many
people from laboratories throughout the world. The author
would like to acknowledge all of their contributions.

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