LIGO is exploring cryogenics as a technique of last resort to reduce the thermal noise of mirrors and suspensions in gravitational wave interferometric detectors. Some of the cryogenic, or cryogenic-related, R&D done at LIGO is reported here. Some ideas being considered to make cryogenics possible may be useful even for room temperature detectors

DeSalvo, Riccardo

Caltech Authors - Main

1
LASER INTERFEROMETER GRAVITATIONAL WAVE OBSERVATORY
- LIGO –
CALIFORNIA INSTITUTE OF TECHNOLOGY
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
Document Type
Conference
Contribution
DCC Number
LIGO-P010032-00-D
Date
30th of October 2001
Path-finding towards a cryogenic interferometer for LIGO
Riccardo DeSalvo
Distribution of this draft: TBD
4th Edoardo Amaldi  conference .on Gravitational Wave
Perth Australia, 8-13th July 2001
California Institute of Technology
LIGO Laboratory - MS 18-34
Pasadena CA 91125
Phone (626) 395-212
Fax (626) 304-9834
E-mail: info@ligo.caltech.edu
Massachusetts Institute of Technology
LIGO Laboratory - MS 16NW-145
Cambridge, MA 01239
Phone (617) 253-4824
Fax (617) 253-7014
E-mail: info@ligo.mit.edu
www: http://www.ligo.caltech.edu/
Path-finding towards a cryogenic interferometer for LIGO
Riccardo DeSalvo
LIGO project, Mail Station 18-34, California Institute of Technology,
Pasadena, CA 91125, USA
Tel ++1 626 395 2968
Fax ++ 626 395 1834
desalvo@ligo.caltech.edu
Abstract
LIGO is exploring cryogenics as the ultimate weapon to reduce the thermal noise of
mirrors and suspensions in Gravitational Wave Interferometric Detector (GWID).  Some
of the cryogenic or cryogenic related R&D made in LIGO are reported here.  Some of the
techniques being considered to make cryogenics possible may become useful even for
room temperature detectors.
Introduction.
In the summer 2000 I was given the homework to explore the technical future of
LIGO, with particular emphasis on cryogenics.
In the course of this study I arrived at some conclusions, some, obvious, at least a
posteriori, some surprising.  The content of this presentation should be regarded as no
more than my very preliminary findings and, in part, my prejudices.
What is almost obvious is that the ultimate GWID will include cryogenics, what is
less obvious is what will it look like.
So far the only serious and coordinated cryogenic GWID development effort is
represented by the LCGT project1 in Japan.
It should be noted though that the modern bar GW detectors2 are cryogenic and their
technology is well developed, but the technical problems involved are intrinsically
different because they do not deal with any significant internal power dissipation.
From the necessity or large advantage of running GWIDs in global coincidence and
from economical and technical considerations, there is an obvious interest that further
development efforts be made under some sort of coordination.
The first, technical, consideration of GWID is that it is almost impossible to run a
cryogenic and a warm interferometer in the same facility (at least not without building a
separate building to physically separate the warm interferometer from the cold one by
several tens of meters).   Failing to do so would cause the cold interferometer to become
the chemical sink for all out-gassing of the warm one and/or would expose it to an
excessive level of thermal radiation.  Therefore the installation of one or more cryogenic
GWID in the LIGO pipes would require jettisoning the yet-to-be-built Advanced LIGO,
an action for which few scientists are prepared at this moment.  As it is difficult to think
of the construction of a third (fourth counting Virgo) large vacuum envelope in the near
future without having first a functionality proof of the cryogenics concept, the natural
choice is to support and assist the existing cryogenic LCGT project.  Then we would
upgrade the LIGO sites to cryogenic GWIDs (or build brand new ones) after a successful
testing of a first large scale interferometer at LCGT.
The second technical consideration is that any cryogenic GDID will be heat
evacuation limited.  Room temperature GWID dissipate the beam deposited power by
simple heat radiation from each test masse.  This heat is a sizeable fraction of the laser
power, which is of the order of the Watt per mirror presently, and will be in the tens of
Watts in some of the advanced interferometers.  The current and advanced interferometer
will run with test masses from a few to several degrees above room temperature.  As
black body radiation falls as T4, an isolated test mass initially cooled near the absolute
zero, would warm up to several tens of degrees Kelvin before finding a radiative
equilibrium.  Consequently any cryogenic detector will be cooled only through heat
transport along its mirror suspension and vibration isolation mechanism.
Once it is accepted that high thermal conductivity and high mechanical Q factors are
needed, it seems a foregone conclusion that any first generation interferometer should use
sapphire both as its test mass3 and for its suspension mechanisms4.  Sapphire though, as
any crystal, has thermal conductivity that peaks at low temperature, but eventually falls
as T3 towards 0oK.  This will automatically set working temperature of the first cryogenic
GWIC at about 30oK, taking advantage of the large (better than metals) sapphire heat
conductivity peak between 20 and 30oK.
Heat conductivity in a metal becomes better than that in a  crystal at still lower
temperatures so that eventually metal flex joints will win5, but the metal quality factors
start becoming substantially worse than that of sapphire.  While, eventually metals will
get a net advantage because of the √T factor.  This happens at temperatures one order of
magnitude below 20oK6.  This mirror working temperature must be achieved with non-
negligible beam power absorbed on the mirrors and requires, for adequate heat
conductivity, cross sections that are prohibitively large for proper mechanical suspension
and isolation.  For these reasons it is my personal prejudice that we should follow the
example of the LCGT project, and not try to work substantially below 20oK without, at
the very least, making the intermediate step with sapphire suspensions at 30oK.
It is useful to remember that to reduce the mirror and suspension thermal noise one
can take advantage of several factors.
• The brute force advantage of √T with lower T.
• The increase of mechanical quality factors that ensues from a lower mirror and
suspension temperature.  This advantage is found to differ from sample to sample and
even, in the same sample, from different processing histories.  Taking best advantage of
this factor will require the most R&D efforts.
• Make use of larger beam spot sizes which, averaging over larger mirror surfaces,
bring in a thermal noise advantage varying as 1/r for coating induced thermal noise to
1/√r for bulk dissipation in the mirrors’ bodies.
• Reduce the amount of mechanically stored energy in the suspensions by using
flex joints7 instead of round fibers (for suspension thermal noise only).
It is important to remember that, after lowering the thermal floor of the mirror, one
has to store enough power in the interferometer’s Fabry Perots to reach a matching length
sensitivity.  This generates heat and a heat extraction problem that gets more and more
severe at high frequency, worsening with the square of the frequency of observation.  A
cryogenic GWID is intrinsically easier to design for a low frequency observation band.
Multi Frequency Interferometers?
The heat extraction problem is not the only one when operating a GWID at high
stored beam power.
At a given test mass value the stored beam power level sets both the shot noise slope
on the high frequency side and a radiation pressure fluctuations counter slope at the low
frequency end.  The thermal noise floor lies between these two quantum walls.  The more
one is successful in lowering the mirror and suspension thermal noise, the more the
useful frequency range looks like a narrow cusp.
Almost automatically one gets to the important conclusion that at low thermal noise
conditions, it will be necessary to run two, or maybe even more, GWIDs in parallel, each
with its own stored power level and observable frequency band.  Interestingly this fact
starts being true even at room temperature for advanced interferometers.
Additionally, high frequency- and low frequency- optimized, cryogenic GWID will
look substantially different, probably short and stubby mirror suspensions for high
frequency to optimize large heat extraction, long and skinny suspensions for the latter for
optimizing low-frequency suspension thermal noise behavior.
More on power limitations.
Let’s make a practical example; we consider an interferometer with 1 MW of power
stored in its Fabry-Perots and 1 KW injection power at its inner masses.  We also
consider 1 ppm absorption on the mirror coating and 40 ppm/cm absorption in a 25 cm
thick sapphire substrate (absorption values common in currently readily available
mirrors).  The inner masses would have to dissipate 2 W each while each end mass would
be subjected to only 1 W of losses.  Extracting Watts is already difficult in any cryogenic
system, while extracting it through an absolute minimum of one layer of low thermal
noise suspensions borders the impossible with present techniques.  The first priority must
be to reduce the optical losses and the mirror thermal load.
To efficiently carry out heat one needs large cross sections and short lengths of high
conductivity materials.  To generate efficient mechanical attenuation and low suspension
thermal noise, high mechanical quality factors and little elastically stored oscillation
energy are required.  One presently uses glass fibers or ribbons, which have negligible
thermal conductivity.
One can in principle obtain good thermal conductivity AND preserve high
mechanical quality factors by using crystalline materials, like sapphire, at the temperature
of their peak thermal conductivity.  Metals (except, maybe niobium) do not seem to have
the necessary mechanical quality factors to be employed anywhere near the low thermal
noise test masses.
To better understand the magnitude of the problem it is wise to consider the “success”
of the LCGT test8.  The LCGT team successfully cooled a test mass to 25-30oK through 4
sapphire fibers 250 micron in diameter, 100 mm long.  To do this they paid a price of
roughly 1oK/mW.  They also used aluminum spaghettis to funnel the heat while isolating
the mirror suspensions from most of the cold finger’s chiller vibrations.  While we should
admire the technical prowess of the Japanese team, even allowing for the better
conductivity that might be achieved by improved attachment of the fibers to the mirror, it
is still far from a reasonably working point for a GWID and there is still a very large
amount of R&D necessary for a technical design of a sensible interferometer.  In
particular it is important to realize that the fibers in the Japanese test behaved
substantially below the best measured sapphire thermal conductivity and that it is
therefore necessary to learn how to use sapphire at its best.  The likely answer is the use
of short sapphire flex joints linked to bigger fibers or rods.
The design of a cryogenic interferometer still requires a large amount of R&D
homework to substantially reduce the mirror thermal load and to find a suitable way to
build low thermal noise, high thermal conductivity and high performance vibration
isolation suspensions at cryogenic temperatures.
The LIGO R&D activity.
Although just a fresh startup, LIGO is already very active in all these R&D fields, in
large part due to similar requirements driving the Advanced LIGO R&D.
I will resume these activities in the following paragraphs.
• Mirror coating power absorption.
Advanced LIGO is also hampered by power losses and excess substrate thermal noise
in its mirrors.  An aggressive R&D program has started.
This large effort will be made in collaboration with Virgo and private companies to
reduce the power absorbed in the mirror coating from the current ~ppm to 0.1 ppm or less
in future.  In the next future several tens of coating runs will be manufactured with
varying coating parameters, techniques, evaporators and materials and measured with the
aim to reduce the absorbed power by at least an order of magnitude and minimize the
mechanical losses in the coatings.  The most promising of these samples will be available
for calorimetric tests in cryogenic environment.
• Sapphire substrate absorption.
Mono-crystalline sapphire crystals of the dimensions required by a GWID (40 Kg or
more) are currently not available.  Advanced LIGO also has base-lined sapphire as the
substrate material for its mirror despite the fact that its relatively high power absorption
in bulk sapphire (40 to 80 ppm/cm) introduces more thermal load than fused silica.  To
solve this problem LIGO is running two separate sapphire R&D programs in
collaboration with 2 industrial partners, Crystal Systems in the USA and SIOM in P.R. of
China.
The results of these developments will be available for cryogenic tests and for any
cryogenic GWID design.
These “parasitic” contributions are at present coming “for free”; at the end of the
Advanced LIGO R&D they will have to be carried forward to finalize the results for
cryogenic use.
Other efforts are made in LIGO specifically for cryogenics interferometers.
• Sapphire to sapphire bonds.
The construction of a sapphire suspension will be quite intricate and will require
bonding of sapphire to sapphire.  There are several promising candidates being presently
tested to bond quartz to sapphire and sapphire to sapphire.  Tests of sapphire to sapphire
silicate bonds are being made in Caltech9 in collaboration with ICRR.
• Flex joint development.
It is my prejudice that, because of fiber’s unfavorable aspect ratio, we will not be able
to build a good cryogenic GWID cooled through fibers.
Following the example of the U.W.A. group10 11, we would like to focus on membrane
flex joints.   Unlike them, though, we focus on crystalline flex joints.  For this reason at
Caltech we started, in collaboration with Universita’ di Pisa, a development for sapphire
machining using numerically controlled ultrasound grinders12.
In ultrasound machining a “soft” metallic tool is energized by a powerful
piezoelectric vibrator while a slurry of fine grit flows around it.  The tool is hovered just
above the material to be machined.  The grit, energized by the ultrasounds, grinds any
hard material without applying macroscopic efforts or vibrations.  A first sapphire flex
joint obtained with a coarse machining grit is shown in figure 1.
This first flex joint is slightly less than 400 micron thick over a width of 3 mm and a
length of about a mm.  After the coarse cut shown in figure we plan to reduce the still
rough surface with a progression of passes with finer and finer grits.  As ultra sound
machining uses the same grits employed in mirror polishing, we expect to eventually
obtain thin flex joints and good surface finishes.
The results achieved with different samples and techniques will be measured at
Caltech.  The best samples will be provided to ICRR for more in depth testing.
We hope with the ultrasound technique to achieve finer membranes than in
conventional grinding techniques.  We also plan to try treatment of superficial cracks and
dislocations (that may limit the quality factors or hamper the thermal conductivity).  We
will use thermal treatments and/or ablation to apply a final molecular level polishing13.
Using these and other techniques we hope to engineer very short flex joints with large
aspect ratios to support the payload and carry the heat while reducing the elastic stored
energy and depress the suspension thermal noise.
Suspension thermal noise can be pushed back, beyond the gravity gradient noise
limit, by simply decreasing the suspension resonant frequency.  This might be done using
longer suspension struts.  Longer suspensions will only go so far because of the limited
overhead space and because longer struts can be achieved only at the cost of increasing
their thermal resistance.  Alternative geometries, like for example the folded pendulum14,
may allow arbitrarily low resonant frequencies with short struts.  A possible folded
pendulum mirror suspension geometry is shown in figure 2.  Numerical Control
Ultrasound milling may allow the design of intricate shapes of struts and counterweights
to achieve sufficiently low suspension thermal noise while maintaining high thermal
conductivities.
• Heat extraction techniques.
The sapphire flex joints will provide low thermal noise suspensions with large
thermal conductivities.  A couple of stages recessed from the test mass, it may be
possible to build conventional thermal bridges towards a cold finger.  Alternatively one
could use, closer to the mirror, more exotic systems like the LASSOR optical chilling.
Richard Epstein at LANL15 seems confident that this technique, presently developed for
liquid nitrogen temperatures, can be extended at the 20oK level.
Conclusions
LIGO is starting to contribute to the development of Cryogenic GWID.
The long path towards a cryogenic LIGO passes through collaboration with the other
GW experiments and R&D efforts.
One of the most surprising ideas coming from exploring the cryogenic problems is
the realization that, considering the low thermal noise floor promised by Advanced
LIGO, it may be advantageous already at room temperature to build two separate
interferometers, one dedicated to low and one to high frequency detection ranges. This
may well be the first payoff from LIGO R&D effort in cryogenics.
Figure 1:  Feasibility test flex joint obtained by Ultra Sound machining.  The insert
shows the surface roughness obtained with coarse grits.  Finer grits are expected to give
better finishes.  Polishing to optical levels will be necessary to make low noise flex joints.
Figure 2:  Folded pendulum suspension geometry study.  Geometries like this are
designed to push the suspension thermal noise to frequencies lower than the gravity
gradient wall limit.
References
                                                
1 Kazuaki Kuroda, et al., Large-scale Cryogenic Gravitational wave Telescope, Proposal,
ICRR, University of Tokyo, 3-2-1, Midoricho, Tanashi, Tokyo 188-8502, Japan.
2 Several presentation in this conference
3 T. Uchiyama, et al., “Mechanical quality factor of a cryogenic sapphire test mass for
gravitational wave detectors”, Phys. Lett. A, 261 (1999), page 5,11
4 T. Uchiyama, et al., “Mechanical quality factor of a sapphire fiber at cryogenic
temperatures”, Phys. Lett. A, 273 (2000), page 310,315
5 L. Ju, et al., “The quality factor of Niobium flex joints”, Phys Lett. A 254 (1999), p.
239-244
6 private communication, Adalberto Giazotto, Virgo project, Pisa.
7 Ju Li, et al. "Low Loss Niobium Flexure Suspension Systems", this conference.
8 T. Uchiyama, et al., “Cryogenic cooling of a sapphire mirror suspension for
interferometric gravitational wave detectors”, Phys. Lett. A, 242 (1998), page 211,214
9 tests made by Helena Armandula in Caltech.
10 M. Baker, et al., “The Q-factor of flexure membranes”, Meas. Sci. Technol., 12,
(2001), p.  1666-1671
11 D.G. Blair, et al., “Ultrahigh Q pendulum suspensions for gravitational wave
detectors”, Rev. Sci. Instr., 64 (7), 1993, p. 1899-1904
12 R&D run by Alessandro Bertolini in Pisa and Caltech.
13 see for example the web site at Epion.com
14 D. Blair, et al., “Performance of an ultra low-frequency folded pendulum”, Phys. Lett.
A 193 (1994), p. 223-226
15 Richard Epstein, Los Alamos National Laboratory, private communication,
http://nis-www.lanl.gov/projects/lassor/cooling.html.


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Path-finding towards a cryogenic interferometer for LIGO

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Path-finding towards a cryogenic interferometer for LIGO

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