C.Montag, J.Rossbach
Next generation Linear
Colliders require very low emittance beams in order to achieve sufficiently
high luminosities. Due to the extremely small beam sizes of some
ten nanometers height at the IP, these machines are very sensitive to ground
motion leading to uncorrelated quadrupole jitter. As measurements performed
at several laboratories indicate, the required vertical jitter tolerances of
To achieve sufficiently high luminosities of some
AN ACTIVE MECHANICAL STABILIZATION SYSTEM FOR LINEAR
COLLIDER QUADRUPOLES TO COMPENSATE FAST GROUNDMOTION
DESY
Notkestrasse 85
D-22607 Hamburg
GermanyAbstract
rms for frequencies above 
cannot be guaranteed in an active accelerator environment.
Therefore,
an active stabilization system based on geophones and piezo actuators has
been developed as part of the DESY S-band Linear Collider Test Facility.
This system damps magnet motion in the frequency band 
by
up to 
resulting in remaining jitter rms values of some
even in a very noisy environment.
Recent results of the system's performance
with different sensor types
will be presented.
Introduction
, future linear colliders
make use of extremely tiny beam spot sizes at the interaction point
(IP) of some 
height and some 
width.
To provide head-on
collisions of the two opponing linac beams, beam trajectories have to be
controlled by some means in order to fight ground motion induced beam jitter.
The required tolerances for uncorrelated vertical quadrupole vibrations can be
estimated as [1,2]
vertically and
horizontally.
Since ground motion measurements (fig.1) at DESY [3]
indicate that vertical ground motion amplitudes have to be expected in the
vicinity of the required tolerance limit, an active stabilization system
for the linac quadrupoles has been developed to fight beam jitter at its
source.
Figure 1: Integrated power spectrum of vertical ground
motion obtained in HERA hall west.
For compensation purposes, the spectrum of ground motion can be divided into
two frequency bands, each of them requiring different compensation schemes.
While for low frequency distortions beam-based methods are applicable, this
method fails in the high frequency region beyond 
and leads to
reasonable damping only below approximately 
[4].
Therefore, high frequency beam jitter has to be compensated independently of
the beam.
The simplest possible solution consists of a passive vibration absorber
with resonance frequency 
well below the lowest frequency to be
compensated. Though such a system would be capable of damping high frequency
vibrations by a factor 
it would, on the other hand, be very
sensitive to any excitation acting on the magnet itself, like cooling water
pressure fluctuations etc.
To achieve significant damping of frequencies beyond 
a
resonance frequency of 
is necessary. Together with a magnet
mass of 
this leads to a very small spring constant of the
passive absorber being 
Therefore, even a
static force as small as 
would lead to a magnet
displacement of 
These considerations led to the development of an active stabilization system
with a vibration sensor on top of each magnet and some means of actuator to
move the magnet in order to keep it at rest.
As can be easily shown, application of an active feedback system to a
low frequency passive vibration absorber would lead to a modification of the
system's spring constant only within the limited bandwidth of the vibration
sensor, while for very low as well as very high frequencies the system would
show the same behaviour as a purely passive one [5].
Therefore, piezo actuators
with high resonance frequencies have been chosen.
At present state, geophone type vibration sensors made by KEBE Scientific
Instruments are used to measure magnet motion. The internal noise of these
sensors has been determined to 
for frequencies
higher than 
[6],
which is well below the desired remaining magnet
jitter.
For simplicity reasons, the mechanical design was chosen such that the magnet
is tilted by a single piezo actuator around its horizontal transverse
axis, as schematically shown in figure 2.
Figure 2: Schematic view of the active stabilization
system.
The complete active stabilization system is shown in figure 3.
Figure 3: Active stabilization system, consisting of a KEBE
geophone on top of the magnet and a piezo actuator below it to tilt the
quadrupole around its horizontal transverse axis. A match-box in front
indicates the size.
The active stabilization systm has been set up in DESY hall 2, an
experimental hall close to the DESY synchrotrons. Due to the vicinity
of two accelerators, several transformers and other technical equipment,
this can be considered as a typical example for an operating Linear Collider
environment. Therefore, the results obtained there should be similar to
those to be expected in the future accelerator.
To determine the system's performance, a second identical sensor was placed
on the floor just below the magnet. The signals of both the feedback sensor
and this second one were sampled simultaneously at 
The
transfer function of the active stabilization was calculated as the square
root of the ratio of the two corresponding power spectra 
and
The resulting transfer function is shown in figure 4,
together with the theoretically expected curve..
Figure 4: Mesured feedback gain (thick line) in the frequency
band from 0 to 
calculated from the square root of the
ratio of the power spectra measured on top of the magnet and on the ground,
respectively. The smooth thinner curve shows the theoretical transfer
function.
Additionally, the rms values 
and 
of the displacement
in the frequency band 
to infinity were calculated as
The result is shown in figure 5.
Figure 5: Measured rms values of ground (solid) and magnet
motion (dashed0 with the feedback system switched on in the frequency band
to infinity as function of the lower frequency 
ranging
from 0 to 
To improve the system's performance, the application of broadband seismometers
made by Guralp Systems Ltd.is under study. These sensors provide flat
velocity response in the frequency band from 0.1 to 
Therefore, an increased feedback gain around is expected.
Figure 6 shows a comparison of the theoretical transfer functions
of the existing system with KEBE geophones and the device under construction
with these new seismometers.
Figure 6: Comparison of theoretically calculated transfer
functions of the present system with KEBE geophone (dashed)
and the new design with Guralp broadband seismometer (solid).
measured in
HERA hall West, the expected rms value 
can be calculated as
Figure 7 shows the corresponding rms values of ground and magnet motion using the transfer functions of the two systems.
Figure 7: Theoretical rms values for the present system
with KEBE geophone (dashed) and the new design with Guralp broadband
seismometer (dotted), calculated from the ground motion spectrum measured in
HERA hall West and the transfer functions shown in fig.6.
The solid line represents the ground motion rms value.
As has been experimentally demonstrated, active stabilizatio of mechanical
quadrupole vibrations is possible down to some rms for
frequencies beyond which is well below the required tolerance
for the SBLC main linac. With new broadband seismometers used as feedback
sensors, even the much tighter tolerances in the final focus system might be
met, at least under the presupposition of a less noisy environment due to
the absence of accelerating structures, modulators, klystrons etc.
[1] T.O.Raubenheimer, The Generation and Acceleration of Low
Emittance Beams for Future Linear Colliders, SLAC report 387, 1991
J.Rossbach, Tolerance on Uncorrelated Motion of
Quadrupoles for Linear Colliders, DESY M-VM 93-01
V.Shiltsev, B.Baklakov, P.Lebedev, C.Montag,
J.Rossbach, Measurements of Ground Vibrations and Orbit Motion at HERA,
DESY HERA 95-06
M.G.Minty, C.Adolphsen, L.J.Hendrickson, R.Sass,
T.Slaton, M.Woodley, Feedback Performance at the Stanford Linear Collider,
SLAC preprint; see also M.Ross, SLC Linac Vibration Study, Sixth
International Workshop on Linear Colliders LC95, KEK Proceedings 95-5
C.Montag, Active Stabilization of Mechanical Quadrupole
Vibrations for Linear Colliders, DESY 96-053, accepted for publication by
Nucl.Instr.Meth.A
C.Montag, M.Lomperski, J.Rossbach, Studies of
Measurement and Compensation Techniques of Magnet Motion for Linear Colliders,
Proc.EPAC 94