Short-range inverse-square law experiment in space
The objective of ISLES (inverse-square law experiment in space) is to perform a null test of Newton`s law on the ISS with a resolution of one part in 10⁵ at ranges from 100 mm to 1 mm. ISLES will be sensitive enough to detect axions with the strongest allowed coupling and to test the string-theory p...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
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irk-123456789-1288682018-01-15T03:03:01Z Short-range inverse-square law experiment in space Strayer, Donald M. Paik, Ho Jung Moody, M. Vol 3-й Международный семинар по физике низких температур в условиях микрогравитации The objective of ISLES (inverse-square law experiment in space) is to perform a null test of Newton`s law on the ISS with a resolution of one part in 10⁵ at ranges from 100 mm to 1 mm. ISLES will be sensitive enough to detect axions with the strongest allowed coupling and to test the string-theory prediction with R≥ 5 mm. To accomplish these goals on the rather noisy International Space Station, the experiment is set up to provide immunity from the vibrations and other common-mode accelerations. The measures to be applied for reducing the effects of disturbances will be described in this presentation. As designed, the experiment will be cooled to less than 2 K in NASA`s low temperature facility the LTMPF, allowing superconducting magnetic levitation in microgravity to obtain very soft, low-loss suspension of the test masses. The low-damping magnetic levitation, combined with a low-noise SQUID, leads to extremely low intrinsic noise in the detector. To minimize Newtonian errors, ISLES employs a near-null source of gravity, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a distance of 100 mm to 1 mm. The signal is detected by a superconducting differential accelerometer, making a highly sensitive sensor of the gravity force generated by the source mass. 2003 Article Short-range inverse-square law experiment in space / Donald M. Strayer, Ho Jung Paik M. Vol Moody // Физика низких температур. — 2003. — Т. 29, № 6. — С. 637-647. — Бібліогр.: 18 назв. — англ. 0132-6414 PACS: 04.20.-q http://dspace.nbuv.gov.ua/handle/123456789/128868 en Физика низких температур Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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3-й Международный семинар по физике низких температур в условиях микрогравитации 3-й Международный семинар по физике низких температур в условиях микрогравитации |
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3-й Международный семинар по физике низких температур в условиях микрогравитации 3-й Международный семинар по физике низких температур в условиях микрогравитации Strayer, Donald M. Paik, Ho Jung Moody, M. Vol Short-range inverse-square law experiment in space Физика низких температур |
| description |
The objective of ISLES (inverse-square law experiment in space) is to perform a null test of Newton`s law on the ISS with a resolution of one part in 10⁵ at ranges from 100 mm to 1 mm. ISLES will be sensitive enough to detect axions with the strongest allowed coupling and to test the string-theory prediction with R≥ 5 mm. To accomplish these goals on the rather noisy International Space Station, the experiment is set up to provide immunity from the vibrations and other common-mode accelerations. The measures to be applied for reducing the effects of disturbances will be described in this presentation. As designed, the experiment will be cooled to less than 2 K in NASA`s low temperature facility the LTMPF, allowing superconducting magnetic levitation in microgravity to obtain very soft, low-loss suspension of the test masses. The low-damping magnetic levitation, combined with a low-noise SQUID, leads to extremely low intrinsic noise in the detector. To minimize Newtonian errors, ISLES employs a near-null source of gravity, a circular disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the two sides of the source mass at a distance of 100 mm to 1 mm. The signal is detected by a superconducting differential accelerometer, making a highly sensitive sensor of the gravity force generated by the source mass. |
| format |
Article |
| author |
Strayer, Donald M. Paik, Ho Jung Moody, M. Vol |
| author_facet |
Strayer, Donald M. Paik, Ho Jung Moody, M. Vol |
| author_sort |
Strayer, Donald M. |
| title |
Short-range inverse-square law experiment in space |
| title_short |
Short-range inverse-square law experiment in space |
| title_full |
Short-range inverse-square law experiment in space |
| title_fullStr |
Short-range inverse-square law experiment in space |
| title_full_unstemmed |
Short-range inverse-square law experiment in space |
| title_sort |
short-range inverse-square law experiment in space |
| publisher |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| publishDate |
2003 |
| topic_facet |
3-й Международный семинар по физике низких температур в условиях микрогравитации |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/128868 |
| citation_txt |
Short-range inverse-square law experiment in space / Donald M. Strayer, Ho Jung Paik M. Vol Moody // Физика низких температур. — 2003. — Т. 29, № 6. — С. 637-647. — Бібліогр.: 18 назв. — англ. |
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Физика низких температур |
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2025-07-09T10:07:54Z |
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| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6, p. 637–647
Short-range inverse-square law experiment in space
Donald M. Strayer
Jet Propulsion Laboratory, Caltech, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
E-mail: dons@squid.jpl.nasa.gov
Ho Jung Paik and M. Vol Moody
Department of Physics, University of Maryland, College Park, MD 20742, USA
Received December 19, 2002
The objective of ISLES (inverse-square law experiment in space) is to perform a null test of
Newton’s law on the ISS with a resolution of one part in 105 at ranges from 100 �m to 1 mm.
ISLES will be sensitive enough to detect axions with the strongest allowed coupling and to test
the string-theory prediction with R � 5 �m. To accomplish these goals on the rather noisy Interna-
tional Space Station, the experiment is set up to provide immunity from the vibrations and other
common-mode accelerations. The measures to be applied for reducing the effects of disturbances
will be described in this presentation. As designed, the experiment will be cooled to less than 2 K
in NASA’s low temperature facility the LTMPF, allowing superconducting magnetic levitation in
microgravity to obtain very soft, low-loss suspension of the test masses. The low-damping mag-
netic levitation, combined with a low-noise SQUID, leads to extremely low intrinsic noise in the
detector. To minimize Newtonian errors, ISLES employs a near-null source of gravity, a circular
disk of large diameter-to-thickness ratio. Two test masses, also disk-shaped, are suspended on the
two sides of the source mass at a distance of 100 �m to 1 mm. The signal is detected by a supercon-
ducting differential accelerometer, making a highly sensitive sensor of the gravity force generated
by the source mass.
PACS: 04.20.–q
1. Objectives of ISLES
The Newtonian inverse-square law (1/r2 law) of
gravity is a cornerstone of general relativity (GR).
Its validity has been impressively demonstrated by
astronomical observations in the solar system, ex-
ceeding a level of sensitivity for violations of one
part in 108 at 107–109 km. In the wake of interests in
searching for a «fifth force», the past two decades
has seen increased activities on Earth in testing the
1/r2 law on the laboratory and geological scales. The
experimental limit at ranges of 1 cm–10 km now
stands at one part in 103–104. However, due
to difficulties associated with designing sensitive
short-range experiments, the range below 1 mm has
been left largely unexplored [1].
Figure 1 shows the existing limit for tests of the
1/r2 law at ranges below 1 mm and the expected sen-
sitivity of our proposed experiment ISLES for the
International Space Station (ISS), plotted as a func-
tion of range �, where the total potential is written as
© Donald M. Strayer, Ho Jung Paik, and M. Vol Moody, 2003
10
10
10
10
10
10 10 10
�, m
|
|
�
String theory
Hoyle et al. (2001)
Long et al.
Axion
ISLES
2
2 2
2
0
4
4
6
3 355 5 5
Fig. 1. Sensitivity of ISLES and the existing limits.
V r
GM
r
r( ) ( )� � � �1 � �e . (1)
Violations predicted by various theories are also indi-
cated. The expected resolution of ISLES on the ISS is
�� � = 1 10�5 at � = 100 �m–1 mm and �� � = 1 10�2 at
� = 10 �m. At 100 �m, this represents an improve-
ment over the existing limits [2] by over six orders of
magnitude. ISLES reaches four orders of magnitude
beyond the level aimed at by Long et al. [3] in their
ongoing laboratory experiment. The improvement at
ranges less than 100 �m is even greater. As indicated
on Fig. 1, the ISLES experiment is capable of detect-
ing the axion with highest allowed coupling (
=
= 3 10�10), and will test a string theory prediction
with R2 � 5 �m. ISLES is based on the superconduct-
ing gravity gradiometer technology fully developed at
the University of Maryland [4].
However, obtaining the sensitivities displayed in
Fig. 1 for ISLES on the ISS is a nontrivial task. The
vibration environment observed on the ISS, as seen in
the data presently being transmitted down from orbit,
is over 100 times worse than that observed in an
Earth-bound laboratory. The techniques we intend to
apply to reach the sensitivities depicted in Fig. 1 are
the main topics of this paper. Again, we shall be de-
scribing techniques that have been developed earlier
for other experiments at the University of Maryland,
techniques that will be adapted to the ISS for ISLES.
2. Scientific value of short-range 1/r2 law test
Test of general relativity
Existence of a short-range mass-mass interaction
implies a violation of the 1/r2 law, a cornerstone of
GR. Such a force may, or may not, have composition
dependence. Therefore, the 1/r2 law could be vio-
lated even when the equivalence principle (EP) holds
rigorously. So ISLES will complement STEP (satel-
lite test of the equivalence principle) and other EP ex-
periments that aim at testing the EP to high resolution
at ranges near the Earth’s radius or longer,
� � 104 km.
Test of string theories
String theories can be consistently formulated only
in nine spatial dimensions. Because the space we
observe is three-dimensional, the extra dimensions
must be somehow hidden. If there are n compact di-
mensions with radii R1, R2, …, Rn, Gauss’s law im-
plies that the Planck mass MPl is related to a funda-
mental scale M� by
M M R R Rn
nPl
2 � �
�2
1 2... . (2)
In the string theory, as we reduce the distances
probed to shorter than one of the radii Ri, a new di-
mension opens up and changes the r-dependence of
the gravitational force law.
One theoretically well-motivated value for M� is
1 TeV, which solves the gauge hierarchy problem,
namely, gravity is so weak compared to the other
forces. For two large dimensions of similar size, one
obtains R1 � R2 � 1 mm [5]. Cosmological and astro-
physical constraints give a bound M�> 100 TeV [6,7],
while the most stringent bound, M� > 1700 TeV, co-
mes from the evolution of neutron stars [8]. This most
stringent bound corresponds to R1 � R2 < 40 nm.
While this range is beyond the reach of ISLES, there
are cosmological assumptions going into these bounds,
and a null result from ISLES would supply indepen-
dent confirmation of the model being tested.
Search for the axion
The standard model of particle physics successfully
accounts for all existing particle data; however, it has
one serious blemish: the strong CP problem. Strong
interactions are such that parity (P), time reversal
(T), and charge conjugation (C) symmetries are auto-
matically conserved in perturbation theory. However,
non-perturbative effects induce violations of P and CP
(parameterized by a dimensionless angle
), but no
such violations have been observed in strong interac-
tions. An attractive resolution of this problem is de-
velop in [9]. One ramification of their theory is the
existence of a new light-mass boson, the axion
[10,11]. The axion mediates a short-range mass-mass
interaction. The experimental upper bound
3 10–10
corresponds to a violation of the 1/r2 law at the level
of �� � � 10–4 at � = 1 mm, a force strength that is
within reach for ISLES as depicted in Fig. 1.
The axion could also solve the major open question
in astrophysics: the composition of dark matter. Ga-
lactic rotation curves and inflation theory require that
there should be more mass in the universe than is ob-
served. Although neutrino mass, MACHOs (MAssive
Compact Halo Objects), and many hypothetical parti-
cles have been offered as explanations, the solution re-
mains elusive. The axion is one of the strongest candi-
dates for the cold dark matter [12].
3. Principle of the experiment
Newtonian null source
To maximize the masses that can be brought to dis-
tances of 100 �m from each other, flat disk geometry is
used for both the source and test masses, as is done by
Long et al. [3]. An infinite plane slab is a Newtonian
null source in that the gravity force it exerts on a
638 Fizika Nizkikh Temperatur, 2003, v. 29, No. 6
Donald M. Strayer, Ho Jung Paik, and M. Vol Moody
nearby mass does not depend on the distance between
the mass and the slab. We approximate such a null
source by using a circular disk of sufficiently large di-
ameter. Figure 2 shows the configuration of the source
and test masses with associated coils and capacitor
plates.
Levitated test masses
Two disk-shaped superconducting test masses are
suspended on the two sides of the source mass using
magnetic forces and are coupled magnetically to form
a differential accelerometer. The motions induced in
the test masses are detected by sensing coils (LS1 and
LS2) in Fig. 2.
On Earth it is difficult to suspend two flat disks on
opposite sides of the source mass at such proximity
without significantly modifying the geometry and
stiffening the differential mode, thus degrading the
resolution of the experiment. In microgravity on the
ISS, each test mass can be suspended by applying only
minute forces from a pancake coil (LS1 or LS2) and
from a small ring coil (LR1 or LR2) coupled to a nar-
row slanted rim of the test mass.
Second harmonic detection
As the source mass is driven at frequency fS along
the symmetry axis, the first-order Newtonian fields
arising from the finite diameter of the source mass are
canceled upon differential measurement, leaving only
a second-order error at 2fS. By symmetry, the Yukawa
signal also appears at 2fS. The second harmonic detec-
tion, combined with the common-mode rejection ratio
(CMRR) of the detector, reduces source-detector vi-
bration coupling by over 300 dB.
Expected signal
The design allows a source displacement of � 50 �m.
The differential acceleration signals expected from the
Newtonian force (with correction to 10%) and the
Yukawa force with �� � = 10�5 and � = 100 �m are plot-
ted in Fig. 3 as a function of the source mass position.
The rms amplitude of the Yukawa signal corresponding
to a � 50-�m displacement is 12 10 11 2. . � m s The rms
amplitude of the Newtonian error term arising from the
finite diameter of the source mass is 10 10 16. � m s2 be-
fore compensation. While these force amplitudes at 2fS
are similar, the Newtonian error will be computed and
removed to less than 10% as depicted in Fig. 3, which is
straightforward.
Need for low gravity
Sensitive experiments searching for weak forces in-
variably require soft suspension for the measurement
degree of freedom, for which superconducting mag-
netic levitation offers great promise. Levitation in
Earth’s gravity, on the other hand, requires a large
magnetic field that tends to couple to the measure-
ment axis through metrology errors, and thus stiffens
the mode. The large value of magnetic field also makes
the suspension more dissipative. Fields close to the
critical field Hc of the superconductor must be used to
levitate the masses on Earth. As well, surface
Short-range inverse-square law experiment in space
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6 639
Fig. 2. Configuration of the source and test masses.
120
80
40
0
–40 –20 0 20 40
Source mass position, m�
Yukawa
(� = 10–5)
Newtonian
(10%)
A
cc
e
le
ra
tio
n
, 1
0
m
/s
–
1
8
2
Fig. 3. Newtonian and Yukawa signals versus source
position.
impurities will reduce Hc locally. The magnetic field
will also be stronger near sharp edges. These effects
cause the magnetic fields to be trapped, contributing
to damping of the motions through flux creep.
The situation improves dramatically in orbit. The
gravity level is reduced by five to six orders of magni-
tude, so the test masses can be supported with weaker
magnetic springs, permitting the realization of both
the lowest resonance frequency and lowest dissipa-
tion. Our calculations show that, even on such a rela-
tively noisy platform as the ISS, the space experiment
will have at least 100 times better resolution over the
ground experiment.
4. Experimental hardware
Overview of the apparatus
Figure 4 shows a cross-sectional view of the appara-
tus. The entire housing is fabricated from niobium.
The source mass is made out of tantalum, which
closely matches Nb in thermal contraction. This source
disk is suspended by cantilever springs at the edge and
driven magnetically. A thin Nb shield provides elec-
trostatic and magnetic shielding between the source
and each test mass. The test masses are suspended and
aligned by magnetic fields from various coils. Two
auxiliary three-axis superconducting accelerometers
are mounted on opposite sides of the housing to pro-
vide linear and angular acceleration signals.
The entire assembly weighs 6.0 kg and fits within
the 20-cm diameter envelope of the LTMPF instru-
ment well (see Fig. 5). The masses need not be caged
during launch and ISS maneuvers since their sway
space will be limited to � 50 �m by mechanical stops.
The ISLES cryogenic and electrical requirements
will be met with the standard LTMPF provision with
minor modifications. The entire apparatus is fastened
to the second-stage thermal platform of the cryo-insert
of LTMPF (Fig. 5). That platform and the instrument
will be temperature stabilized to 5 �K. The orienta-
tion of the detector is chosen so that its sensitive axis
is aligned with the pitch (y) axis of the ISS when
LTMPF is mounted on JEM-EF. This orientation
reduces the centrifugal acceleration noise almost a
hundred-fold.
Source and test masses
The source mass is a disk 2.0 mm thick by 140 mm
in diameter, with mass M = 510 g. The source mass,
cantilever springs, and rim are machined out of a sin-
gle plate of Ta. Ta is chosen for its high density
(16.6 g/cm3), which increases the signal, and its re-
latively high Hc. Each test mass is a Nb disk 0.25 mm
thick by 63 mm in diameter, with a rim 0.25 mm thick
by 2.0 mm wide, which has 5� slant from the axis. The
mass of each test mass is m = 7.5 g. For the 100-�m
gap, the test masses are separated by a baseline � =
= 2.45 mm. The position of each test mass is measured
by a capacitor plate located near its center (see Fig. 2)
The equilibrium spacing between the source and each
test mass is 100 �m. They are shielded from each other
by means of a 12.5-�m thick Nb shield, located at
25 �m from the surface of the test mass. The source
mass is driven magnetically by coupling a small ac
640 Fizika Nizkikh Temperatur, 2003, v. 29, No. 6
Donald M. Strayer, Ho Jung Paik, and M. Vol Moody
Fig. 4. Cross-section of the ISLES apparatus. Fig. 5. The ISP mounted on the cryo-insert.
current to a superconducting circuit carrying a large
persistent current.
Superconducting circuitry and setup procedure
Schematics of the superconducting circuits for the
detector are shown in Fig. 6. These circuits are similar
to the standard differencing circuit used in the SGG
[4]. The test masses are suspended radially by storing
persistent currents IR1 and IR2 in ring coils LR1 and
LR2 and the pancake coils, as shown in Fig. 6,a. Due
to the slanted rim of the test masses, currents IR1 and
IR2 will exert an axially outward force on the test
masses. This force is balanced by the axially inward
forces provided by the currents in the sensing, align-
ment, and feedback circuits, shown in Fig. 6,b–d. The
suspension is stable for all degrees of freedom, except
for roll about the sensitive axes.
The scale factors of the component accelerometers
are matched by adjusting currents IS1 and IS2 in pan-
cake coils IS1 and IS2, as shown in Fig. 6,b. The
SQUID measures the differential acceleration aD, or
gravity gradient, along the y axis. To align an individ-
ual test mass parallel to its shield and to also align its
axis parallel to the axis of the other mass, two align-
ment circuits are provided for each test mass, one per
degree of freedom. Figure 6,c shows the alignment cir-
cuit of test mass 1 about the x axis. This alignment is
accomplished by tuning currents I�11 and I�12 in re-
motely coupled pancake coils L�11 and L�12 (see also
Fig. 2). Note that the unique property of long-term
stability of persistent currents in superconductors pre-
serves the CMRR tuning over long periods.
The balance procedure matches the linear compo-
nents of the scale factors but does not completely
match the nonlinearity. This mismatched nonlinearity
is troublesome since it down-converts the wide-band
acceleration noise to the signal frequency. A standard
approach to suppressing the nonlinearity is applying a
negative feedback to the test masses, which actively
stiffens the mode. The feedback circuit is given in
Fig. 6,d. The common-mode (CM) and differen-
tial-mode (DM) outputs iFC and iFD are fed back to
Short-range inverse-square law experiment in space
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6 641
Fig. 6. Superconducting circuits for the detector.
the test masses. The CM output is derived from the
auxiliary accelerometers. Currents IF1 and IF2 are ad-
justed to null the effect of the CM feedback on the
DM output.
Coarse and fine heat-switches
Due to the high vibration levels of the ISS
( ))� �10 6 2 1 2m (s Hz , a special provision must be
made to be able to control the magnetic fluxes trapped
in various superconducting loops with adequate preci-
sion. Coarse heat-switches, denoted by Hij’s, warm up
a short length of the Nb wire to a resistance R � 1 m�,
resulting in an L/R time of about 10 ms. These coarse
switches are used to store currents initially to obtain,
for example, the desired spring constants for the sus-
pended masses. Fine heat-switches, denoted by hij’s,
couple a low-resistance path with R� � 0.1 �� to the
circuit, resulting in a time constant of about 100 s.
With 1-ms time resolution of the heat-switch, fluxes
can then be adjusted to one part in 105. This added
precision of the trapped currents gives the ability to
match the scale factors to 10�5 and to align the sensi-
tive axes to 10�5 radian, resulting in an initial CMRR
of 105 in all three linear degrees of freedom.
Heat-switch HSD in Fig. 6,b is turned on to protect
the SQUID from a current surge whenever a current is
adjusted in the sensing circuit. The output
heat-switches HiC’s and HiD’s are turned on to pas-
sively damp the corresponding modes in the event
large motions of the test masses are excited. While we
expect this tuning to maintain its high degree of noise
rejection throughout the 5-month period of the experi-
ment on ISS, we use the vibrationally noisy periods of
Shuttle dockings and orbit reboosts, when gravity
data are unusable or degraded, to test the CMRR and
to readjust current values, as found necessary.
Auxiliary superconducting accelerometers
Figure 4 shows two three-axis auxiliary supercon-
ducting accelerometers mounted symmetrically on the
two sides of the housing. Each test mass is a hollow
20-gram Nb cube, suspended and sensed by Nb pan-
cake coils adjacent to its six faces. The suspension of
the cube is stable in all degrees of freedom. The acce-
lerometers are coupled to SQUIDs, two SQUIDs per
degree of freedom, to measure three linear (ai) and
two angular (�i) acceleration components, as well as a
gravity gradient component (�ij).
Figure 7 shows the superconducting circuit for the y
axis of the auxiliary accelerometers. The four pancake
coils separated along the y axis are combined to sum
and difference the signals. The CM and DM signals
correspond to ay and �yy, respectively. The gravity gra-
dient signal is used to monitor and remove gravita-
tional disturbances from the detector. The pancake
coils separated along the x and z axes are combined in
similar circuits to measure ax and �z, and az and �x, re-
spectively. The only component that is not measured is
�y, which is not needed for error compensation.
The intrinsic noise of the accelerometers at f � 0 02. Hz,
assuming the noise spectrum of commercial Quantum
Design SQUIDs, are S fa
1 2( ) � 1 10–11m/(s2 Hz1/2),
S f�
1 2( ) � 3 10–11rad/(s2 Hz1/2), and S f�
1 2( ) �
� 3 10–11s–2 Hz–1/2).
5. Dynamic noise rejection
Error compensation
Linear and angular accelerations are rejected to
10�5 and to 10�4 m, respectively, by adjusting persis-
tent currents in the sensing and alignment circuits as
described above. To improve the acceleration rejection
further, we apply an error compensation technique
that has been demonstrated with the SGG [4]. The
linear and angular accelerations of the platform, mea-
sured by the auxiliary accelerometers, are multiplied
by the predetermined error coefficients and subtracted
from the detector output to achieve a further reduc-
tion of noise by the factor 103. By applying the com-
pensation factor 103 demonstrated in the laboratory,
we should be able to achieve a net CMRR of 108 for
linear acceleration and a net error coefficient of 10�7 m
for angular acceleration.
To determine the dynamic error coefficients, acce-
lerations in all degrees of freedom must be provided. If
active vibration isolation is implemented as described
in the next section, a six-axis shaker will be built into
the isolation system that can also be used to apply a si-
nusoidal acceleration signal in each degree of freedom.
If we opt not to employ the vibration isolation system,
we will use the ISS vibration noise itself to shake the
detector. The accelerations will be random and
cross-correlated between degrees of freedom. How-
ever, we can apply a well-established procedure in
electrical engineering for determining the transfer
642 Fizika Nizkikh Temperatur, 2003, v. 29, No. 6
Donald M. Strayer, Ho Jung Paik, and M. Vol Moody
Fig. 7. Superconducting circuit for the y axis of the
coupled three-axis auxiliary accelerometers.
functions for a multiple-input system using noise
alone [13].
Due to the short but finite baseline (� = 2.45 mm),
the 1/r2 law detector is a gravity gradiometer that is
sensitive to attitude modulation of Earth’s gravity
gradient, gravity noise from ISS, and centrifugal ac-
celerations. Fortunately, the auxiliary gradiometer
measures exactly the same gradient noise, except for
gravity disturbances from nearby objects (< 1 m).
This gravity gradient noise can thus be removed from
the detector output by applying the above correlation
method.
Vibration isolation (option)
With the residual acceleration errors compensated,
the most important dynamic error source is the
nonlinearity of the scale factors. Vibration isolation of
the detector is an alternative way of suppressing the
nonlinearity noise.
An active vibration isolation system, combined
with a single-stage passive isolation, was studied for
LTMPF by Ball Aerospace & Technologies Corp. As
LTMPF is designed presently, the sway space is lim-
ited to � 3 mm. This sway amplitude limit constrains
our ability to extend the isolation to below 0.1 Hz.
Eight D-strut isolators were used to attach the facility
frame to the payload interface unit. These isolators
provide a 40-dB/decade attenuation from 1 to 200 Hz.
Each isolator is also equipped with a voice-coil actuator
to provide active isolation. The outputs of the supercon-
ducting accelerometers are fed back to these actuators.
The result is shown in Fig. 8. The first curve is
the passive isolation provided by the eight D-strut
isolators. The first active system (curve 2) em-
ploys only control over the translation degrees of
freedom. The second active system (curve 3) em-
ploys closed-loop control over all six degrees of
freedom. The isolation system provides only a
10-dB isolation at 0.05 Hz. Its main advantage co-
mes from the reduction of high-frequency accelera-
tion noise, reducing the nonlinearity noise.
6. Error budget
Metrology errors
Table 1 lists the metrology errors estimated using a
numerical model. The effects from the finite diameter
of the source and the dynamic mass of the suspension
springs are corrected to 10 and 20%, respectively. Lin-
ear taper and linear density variation of the source
produce second-order errors, which become negligible.
Table 1
Metrology errors
Source Allowance
Error,
10–18 m/s2
Baseline 25 �m 1.0
Source mass
Finite diameter 10% 12
Suspension spring 20% 2.4
Radial taper 2.5 �m 7.8
Radial density variation 10–4 0.2
Test masses
Rim dimension 2.5 �m 1.7
Total error 15
The test masses tend to rotate slowly about the sen-
sitive axis, further averaging out the asymmetry about
the axis. Hence only the radial taper and the radial
density variation are important. Due to the null na-
ture of the source, test mass metrology is not impor-
tant, except for the extended rim. The rim dimension
is corrected to 2.5 �m. The requirements on radial po-
sitioning of the test masses are greatly relaxed by the
cylindrical symmetry. The total metrology error is
1.5 10–17 m/s2.
The dimensional tolerances are achievable using
hand lapping of the parts. Fabrication of the test
masses with a slanted rim will require a special proce-
dure. One possibility is machining the entire structure
in a single piece by combining regular machining with
electric discharge machining. Another possibility is
machining the disk and the rim as separate pieces and
then diffusion-bonding them in a vacuum oven.
Intrinsic instrument noise
The intrinsic power spectral density of a super-
conducting differential accelerometer can be written
[4,14] as
Short-range inverse-square law experiment in space
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6 643
Fig. 8. Frequency response of the vibration isolation system
for the y axis: (1) Passive isolation; (2) Active w/transla-
tion loop closing; (3) Active w/6 DOF loop closing.
S f
m
k T
Q
E fa
B D
D
D
A( ) ( )� �
�
�
�
�
�
�
�
�
8
2
2� �
��
, (3)
where m is the mass of each test mass, � �D Df� 2
and QD are the differential mode resonance frequency
and quality factor, � is the electromechanical energy
coupling coefficient, � is the electrical energy cou-
pling coefficient of the SQUID, and EA(f) is the in-
put energy resolution of the SQUID.
Equation (3) shows that the differential-mode fre-
quency fD is a critical parameter for the intrinsic
noise. The microgravity environment on ISS, in prin-
ciple, allows a suspension 106 times softer than on the
ground, which corresponds to fD < 0.01 Hz. On the
other hand, the differential accelerometer’s response
to platform vibrations must be minimized to reduce er-
rors caused by electric charge on the test mass, by
patch-effect fields, by self-gravity of the ISS, and
most importantly by the nonlinearity of the scale fac-
tors. Ideally, one would like to increase the com-
mon-mode frequency fC as much as possible, while
keeping fD low. Unfortunately, the nonlinearity of
the coils couples a fraction of the CM stiffness to DM,
providing a practical limit: fC/fD
4. This limitation
forces us to make a compromise. The test masses must
remain free before a feedback loop is closed either to
the test masses or to the isolator, since otherwise there
will be no signal to feed back. Moreover, we need to
keep the test mass excursion to
10 �m. These consid-
erations require fC � 0.2 Hz and fD � 0.05 Hz. The
result represents a stiffness reduction by 104 from the
ground experiment.
Analysis of ISLES circuits for the masses chosen
shows that I11 = I21 � 4.7 mA and I13 = I23 � 47 mA
gives fD = 0.05 Hz and fC = 0.2 Hz. For feedback oper-
ation of the detector, this choice of mode frequencies,
with signal frequency f = 0.02 Hz, minimizes the total
dynamic noise. The radial translational mode fre-
quency is found to be � 0.06 Hz. The test masses are
free to roll about their axes. Rolling will tend to aver-
age out azimuthal asymmetries of the source and the
test masses. If active vibration isolation is provided,
the optimum frequencies shift slightly to f = 0.05 Hz,
fD = 0.1 Hz and fC = 0.4 Hz. We compute the intrinsic
noise for these two sets of frequencies.
The design values for the other parameters of Eq.
(3) are: T = 2 K, m = 7.5 g, QD = 106, � = � = 0.5, and
EA(f) = 10–30 (1 + 0.1 Hz/f) J/Hz. The SQUID
energy resolution corresponds to the flux noise,
5 0
1 2�� Hz � , originally specified in LTMPF science
requirement document, and coincides with the perfor-
mance typically obtained from commercially available
dc SQUIDs. We assume that this SQUID noise level
can be achieved for ISLES. With the above parameter
values, we find Sa
1/2(f) = 7.0 10–14 m/(s2 Hz1/2)
for f = 0.02 Hz and fD = 0.05 Hz (for feedback), and
Sa
1/2 (f) = 10.8 10–14 m/(s2 �z1/2) for f =
= 0.05 Hz and fD = 0.1 Hz (for vibration isolation).
Acceleration noise
The upper curve of Fig. 9 shows the y-axis linear
acceleration spectrum measured by a SAMS II acceler-
ometer in the US Lab of ISS on a typical day. The
lower curve is the acceleration spectrum with active
isolation, the curve being generated by filtering the
acceleration spectrum with the response function
given in Fig. 8. The noise is quietest at � 0.01 Hz with
a value of ! 10–6 m/(s2 Hz1/2). This noise will be
reduced to 3 10–14 m/(s2 Hz1/2) by the net CMRR of
108. The angular acceleration noise is reduced to
2 10–14 m/(s2 Hz1/2) by the error coefficient of
10 7� m. The centrifugal acceleration noise is negligible.
Using the nonlinearity coefficient measured in the
SGG [4], we estimate the nonlinearity-induced noise
as plotted in Fig. 10. The upper curve is the noise
without active isolation or feedback, which is 103
times higher than the intrinsic noise of the instrument
at 0.01 Hz. The middle curve shows the result of ap-
plying the active isolation. At 0.01 Hz, the
nonlinearity noise is at 1 10–13 m/(s2 Hz1/2). The
lower curve shows the nonlinearity noise expected in
the detector under a feedback control that stiffens the
common mode frequency to 10 Hz.
Assuming that the above acceleration noise repre-
sents the actual noise that will be experienced by the
ISLES detector, we find a total acceleration noise to
be 6.3 10–14 m/(s2 Hz1/2) at f = 0.02 Hz for the
feedback option, and 5.9 10–14 m/(s2 Hz1/2) at
f � 0 05. Hz for the vibration isolation option.
644 Fizika Nizkikh Temperatur, 2003, v. 29, No. 6
Donald M. Strayer, Ho Jung Paik, and M. Vol Moody
10–2 10–1 100 101
Frequency , Hz
10–7
10–6
10–5
10 4–
10–3
Y
-a
cc
e
le
ra
tio
n
,m
·s
–
·H
z–
/
2
2
1
Fig. 9. Linear acceleration along y axis: actual (upper)
and with active isolation (lower).
Gravity noise
Helium tide is absent due to the Earth-fixed orien-
tation of the ISS. Helium sloshing is of minor concern
since it is expected to occur at a sufficiently low fre-
quency, � 2.5 mHz. The gravity gradiometer along the
x axis will be used to monitor gravitational distur-
bances of the experiment. The gravity noise from mo-
dulation of the Earth’s gravity gradient and ISS
self-gravity, including the activities of astronauts,
will be taken out, along with the centrifugal accelera-
tion, by the error measurement and compensation
scheme.
Magnetic crosstalk
Trapped flux is not of concern if the flux is strongly
pinned. Cooling and performing the experiment in a
low magnetic field will minimize flux creep. For this
purpose, LTMPF is equipped with a cryoperm shield.
Material processing and the insertion of flux dams can
reduce flux motion that might be induced by the inci-
dence of charged particles in orbit.
With the high magnetic field required to drive the
source mass, magnetic crosstalk between the source
and the detector is a very important potential source
of error. To solve this problem, the entire housing is
machined out of Nb and a Nb shield is provided be-
tween the source and each test mass. High-purity Nb
will be used. The Nb will be heat-treated to bring the
material very close to a type-I superconductor, thus
minimizing flux penetration. The superconducting
shield is expected to provide over 200 dB isolation
[15]. This isolation, combined with 60 dB rejection
expected from the second harmonic detection, should
provide the required isolation between the source
drive signal and the test masses in excess of 260 dB.
Electric charge effects
Levitated test masses in orbit will accumulate elec-
tric charge from cosmic rays and from high-energy
protons, as the spacecraft traverses through the South
Atlantic Anomaly. Scaling from the charge computed
for STEP test masses [16], we find that the total
charge accumulated in each ISLES test mass over the en-
tire duration of the experiment will be Q � 1.5 10–13 C.
In deriving this number, we used a charge trapping effi-
ciency 10% that of STEP to account for the difference in
shape: the ISLES test masses are extremely thin (250
�m) and do not trap charge as efficiently as the much
thicker STEP test masses.
The charge trapped in the test mass will induce im-
age charges on the neighboring coils and supercon-
ducting ground planes. Most of the trapped charge
will appear on the surfaces of the test masses facing
the shields since the gap is smallest there (� 20 �m).
This will generate a differential force Q2/�0 A, where
�0 is the permittivity of vacuum and A is the area of
the test mass. The force results in the maximum differ-
ential displacement at the end of the mission:
x
Q
A m
D
D
,max � � �
2
0
2
91
7 10
" �
m. (4)
A differential displacement affects the CMRR through
mismatches in the coil areas, gaps and currents. With
the initial coil gap of 10–4 m and a mismatch of 10%,
we find that the CMRR is affected by 7 ppm at most.
This should allow the passive CMRR to remain at the
required level of 105 throughout the mission. So
ISLES does not require a discharging system. To make
sure that the trapped charge remains below the thresh-
old, the charge will be measured after each 30-day
data run and the test masses will be discharged, if ne-
cessary, by simply pushing it against the shields. This
may necessitate a recalibration of the detector.
The energetic charged particles will also impart mo-
mentum and cause heating of the test masses. These
effects were found to be less important than the electro-
static force for STEP. In addition, patch-effect poten-
tial will be modulated as charge builds up in the test
masses, causing a time-varying acceleration. These ac
disturbances occur mostly outside the signal band and
therefore are averaged out. The Casimir force is not of
concern for the present experiment where the gap be-
tween the masses is much more 1 �m [17].
Temperature noise
The modulation of the penetration depth of a super-
conductor with temperature and residual thermal expan-
sion coefficients for different materials give rise to tem-
perature sensitivity in a superconducting accelerometer.
Short-range inverse-square law experiment in space
Fizika Nizkikh Temperatur, 2003, v. 29, No. 6 645
10 10– 10 10
Frequency , Hz
10
10
10
10
10
10
N
o
n
lin
e
a
ri
ty
,m
·s
–
·H
z–
/
–2 1 0 1
–15
–14
–13
–12
–11
–10
2
2
1
Fig. 10. Nonlinearity error for y axis: actual (upper),
with active isolation (middle), and with feedback (lower).
These occur through temperature gradients as well as mis-
matches in the accelerometers [14]. From our experience
with the SGG, however, this noise is expected to be negli-
gible with the platform temperature stabilized to 5 �K.
Total errors
Table 2 combines all the errors for the two scenarios:
one with feedback and the other with vibration isola-
tion. To reduce the random noise to the levels listed, a
90-day integration was assumed. The vibration isolation
approach does not reduce the total noise, but is worth
considering because it greatly simplifies the detector de-
sign and operation. It allows the use of a slightly stiffer
suspension, which will reduce the disturbances from the
trapped charge. Therefore, we plan to have a trade
study at the beginning of the flight definition phase,
comparing the risks and benefits, and the costs of im-
plementing these approaches.
Table 2
Error budget
Error source
Error, 10–18 m/s2
w/feedback w/isolation
Metrology 15 15
Random (90 days) (90 days)
Intrinsic 25 39
ISS vibration 23 21
Gravity noise <1 <1
Vibration coupling <1 <1
Magnetic coupling <10 <10
Electric charge <10 <10
Other (30% margin) 33 41
Total 52 64
7. Expected resolution
By equating the noise with the expected Yukawa sig-
nal, we compute the minimum detectable �. Figure 1
shows the 1–� error plotted as a function of � for the
feedback approach. The case with active isolation is very
similar. The best resolution of ISLES is �� � = 1 10–5 at
� = 100 �m–1 mm. ISLES will test the 1/r2 law with a
resolution of 10–2 at � = 10 �m. Figure 1 shows that the
string theory predicted violation with R2 � 5 �m will be
detected and axions with strength 10–100 times below
the maximum will be detected.
ISLES will use the SGG technology fully devel-
oped at the University of Maryland. The SGG has
been used to perform a null test of Newton’s law at a
sensitivity ten times beyond that of the other methods
at 1-meter distance [18]. The instrument proposed for
ISLES is very similar to the existing SGG and will ap-
ply noise-compensating techniques already demon-
strated on the SGG. The experimental procedure and
error analysis are also similar to those in the me-
ter-scale 1/r2 law test, also previously carried out
with the SGG.
For the modest cost of the ISS experiment, the sci-
entific gain from ISLES is tremendous. ISLES consti-
tutes a new test of general relativity in the hitherto
largely untested range and will perform the first ever
test of a prediction of string theory. The experiment
will push the frontiers of searching for new weak
forces by several orders of magnitude, with a poten-
tial to discover new particles.
It should be noted that the instrument will launch
while completely inactive, with no currents stored
and no electronics turned on. Once on orbit, the
SQUIDs and the temperature control circuits will be
activated, and the «levitation» currents will be set.
Then the tuning of the CMRR will proceed, and the
error coefficients will be measured. With these data
stored, the data for testing the 1/r2 law can be gath-
ered. This passive launch implies that no exchange gas
need be placed in the vacuum space during launch, so
the lowest possible residual gas levels will be ob-
tained in the space around the instrument. Thus, high
Q-values can be expected for the test mass motions.
Also, being able to adjust all experimental parameters
while the instrument is on orbit means that the expe-
rimenter is able to monitor and correct any error-in-
ducing disturbances that might occur during the ex-
periment’s tenure.
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