Superconducting Gravity Gradiometer Research Articles

Effect of Magnetic Shielding on Levitation Characteristics of Superconducting Gravimeter

The superconducting gravimeter is currently the most accurate instrument in relative gravity measurement, so the high-precision calculation and analysis of superconducting magnetic levitation system is crucial to the development work of superconducting gravimeter. Shielding material can weaken the influence of external magnetic field source fluctuation on the internal levitation magnetic field and provide a stable electromagnetic environment for the magnetic levitation system. But at the same time, shielding material will also have an impact on the internal suspended magnetic field itself, which will lead to large deviations in the study of electromagnetic characteristics of the magnetic levitation system. This article establishes and optimizes the simulation calculation model of a superconducting gravimeter magnetic levitation system based on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> method, and studies the effect of magnetic shielding on the magnetic field, levitation force, and magnetic force gradient of the internal levitation system. After that, the simulation calculation results are compared with the experimental results, and the simulation calculation error of superconducting levitation force and magnetic gradient is less than 1%, which verifies the correctness of the optimized simulation model. This study is an important guide for the accurate calculation of the electromagnetic properties of all superconducting systems containing magnetic shielding materials, such as superconducting gravimeter, superconducting gravity gradiometer, etc.

Superconducting pancake coil FEM analysis for very low frequency levitated gravity accelerometers

State-of-the-art detectors are necessary to measure very tiny variations of gravity produced by spiraling neutron stars, merging black holes and moving tectonic plates. We are developing a superconducting gravity gradiometer and aim to achieve 0.1 mE Hz−1/2 (1 E ≡ 10–9 s–2) in the frequency band of 0.1 mHz to 0.1 Hz. The superconducting test masses are levitated by a superconducting current-carrying monolayer pancake coil, which is one of the key components of the instrument. However, the nonlinear aspect of the pancake coil inductance with respect to the coil to test mass separation imposes one of the main constraints to achieve such sensitivity at low frequencies. In this paper, we investigate the causes of that nonlinearity by finite element method using COMSOL Multiphysics® simulation software. Inductances were measured with an experimental setup where a gap spacing, created by a pancake coil and a niobium plate, could be adjusted. The inductances computed with a 2D axis-symmetric model satisfactorily agreed with the experimental data. We extensively studied several mechanisms for cancelling the nonlinearity of the inductance. A solenoid next to the pancake coil is possibly the most effective and practical way to mitigate it. Our approach may also be useful for obtaining a simple and effective model to study magnetostatic problems in a superconductor.

A horizontal linear vibrator for measuring the cross-coupling coefficient of superconducting gravity gradiometers

This paper presents a specialized horizontal linear vibrator with small accompanying motions for precisely measuring the cross-coupling coefficient of superconducting gravity gradiometers(SGGs). The vibrator is suspended by leaf springs and actuated by superconducting coils(SCs) and permanent magnets(PMs). Innovative distribution of SCs and PMs can generate frictionless, small nonlinear and controllable driving forces, and it also can provide large force moments to cancel the accompanying angular motions. Besides, the vibrator can be incorporated into the liquid helium Dewar and work at a low temperature. The experimental results show that the accompanying motions related to the amplitude ratio of the accompanying vertical acceleration(az) and angular accelerations(αx and αy) to the actuated horizontal linear acceleration(ax) at 1 Hz are as small as 1.4 × 10−4, 4.7 × 10−4 rad/m and 2.8 × 10−4 rad/m, respectively. With this vibrator, the measurement resolution for cross-coupling coefficients can be estimated to be 1.8 × 10−8 rad.

Analysis of limitations on recovery of gravity field based on satellite gravity gradient data

Although satellite gravity gradient data plays a great role in determining short-wavelength part of static gravity field model, accuracy of the long-wavelength part of gravity field model recovered by them are poor, which leads to only a few applications in time-variable gravity investigation. The reason is that some factors limit the accuracy of the gravity field recovered using gradient data, including accuracy of the gravity gradient observations, measurement bandwidth (MBW) of gradiometer, satellite inclination, etc. This paper aims at analyzing the influence of these limitations on gravity field recovery and discusses the possibility of time-variable gravity field detection by using gravity gradient observations. Firstly, for arbitrary satellite orbit inclination, we give the frequency distributions of all the components of gravity gradients (i.e. Txx,Tyy,Tzz,Txy,TxzandTyz, ). The results show that the maximum frequency of each component of the gravity gradients is the same, i.e. l/Ts (l is degree of the gravity field model, Ts is the orbital periods), and it is not influenced by the inclination of the satellite orbits. Secondly, the paper gives a theory proof to explain why only the low orders of the coefficients are influenced by polar gaps. Big polar gaps are experimented by a numerical test with inclination of 45°. Finally, considering that the measurement bandwidth can be expanded and accuracy of gradient observations can be improved by superconducting gravity gradiometer (SGG) compared to gradiometer used in Gravity field and steady-state Ocean Circulation Explorer (GOCE), the possibility of detecting time-variable gravity using gravity gradient observations is discussed. The results show that the SGG creates errors in MBW with magnitude of 0.014 mE, which is smaller than the magnitude of the time-variable gravity gradient signals (i.e., 0.02 mE) derived from Gravity Recovery and Climate Experiment (GRACE) gravity field models. This indicates the potential of SGG in time-variable gravity detection.

A Full-Tensor Superconducting Gravity Gradiometer System Composed of Levitation-Type Accelerometers

In this paper, a superconducting gravity gradiometer system that is designed to measure full-tensor gravity gradients based on levitation-type component accelerometers without using mechanical springs is presented. All components of the gradiometer system are made of a superconducting material, niobium. Working principles are the flux quantization and the perfect diamagnetism of the superconductor. Each component of the gravity gradient tensor is obtained from the differential gravity measured by using two accelerometers, each of which is composed of a cubic test mass, a flat sensing coil, and a flat counter coil to balance the repulsive force of the sensing coil and ambient gravity. The measured signals are amplified by using superconducting quantum interference devices. The full-tensor gradiometer system consists of three perpendicularly aligned sets of gradiometers, each of which measures one diagonal and two off-diagonal components. The details of the structure of the system, the dynamics of the gradiometer, the transfer function, the common mode rejection, and the optimum conditions are discussed.

Measuring gravitational constant using a planetary system constructed with levitated superconducting test masses

Newton’s gravitational constant G is the least known fundamental constant of nature, partly because the gravity signal produced in the laboratory is extremely weak and difficult to measure accurately. There also seem to be unknown systematics in many G measurements. Since Cavendish made the first measurement of G with a torsion balance over two hundred years ago, torsion balances have been used in many G experiments, but uncorrected anelasticity of torsion fibers make the results questionable. We present a new method of G measurement by using a superconducting gravity gradiometer constructed with levitated test masses, which is free from the irregularities of mechanical suspension. The detector is rotated to null the gravity field from the source mass by centrifugal acceleration, forming an artificial planetary system. We show that this experiment can potentially measure G with accuracy better than 10 ppm.

Concept study of measuring gravitational constant using superconducting gravity gradiometer

Newton’s gravitational constant G is the least known fundamental constant of nature. Since Cavendish made the first measurement of G with a torsion balance over two hundred years ago, the best results of G have been obtained by using torsion balances. However, the uncorrected anelasticity of torsion fibers makes the results questionable. We present a new method of G measurement by using a superconducting gravity gradiometer constructed with levitated test masses, which is free from the irregularities of mechanical suspension. The superconducting gravity gradiometer is rotated to generate a centrifugal acceleration that nulls the gravity field of the source mass, forming an artificial planetary system. This experiment has a potential accuracy of G better than 10 ppm.

Tuning the Stiffness Balance Using Characteristic Frequencies as a Criterion for a Superconducting Gravity Gradiometer.

Tuning the stiffness balance is crucial to full-band common-mode rejection for a superconducting gravity gradiometer (SGG). A reliable method to do so has been proposed and experimentally tested. In the tuning scheme, the frequency response functions of the displacement of individual test mass upon common-mode accelerations were measured and thus determined a characteristic frequency for each test mass. A reduced difference in characteristic frequencies between the two test masses was utilized as the criterion for an effective tuning. Since the measurement of the characteristic frequencies does not depend on the scale factors of displacement detection, stiffness tuning can be done independently. We have tested this new method on a single-component SGG and obtained a reduction of two orders of magnitude in stiffness mismatch.

Sensitive Superconducting Gravity Gradiometer Constructed with Levitated Test Masses

Over the years, a compact, superconducting gravity gradiometer has been discussed, with the potential for important applications in planetary science, the measurement of gravity waves, and even early warning against earthquakes. Its test-mass dynamics, levitation, and successful operation still need to be verified, though. This study describes the design and construction of the instrument, and reports detailed results and the issues encountered along the way. The data suggest that this promising technology could deliver otherwise unobtainable gravity maps, which can be translated to planetary structural data.

Future dedicated Venus-SGG flight mission: Accuracy assessment and performance analysis

This study concentrates principally on the systematic requirements analysis for the future dedicated Venus-SGG (spacecraft gravity gradiometry) flight mission in China in respect of the matching measurement accuracies of the spacecraft-based scientific instruments and the orbital parameters of the spacecraft. Firstly, we created and proved the single and combined analytical error models of the cumulative Venusian geoid height influenced by the gravity gradient error of the spacecraft-borne atom-interferometer gravity gradiometer (AIGG) and the orbital position error and orbital velocity error tracked by the deep space network (DSN) on the Earth station. Secondly, the ultra-high-precision spacecraft-borne AIGG is propitious to making a significant contribution to globally mapping the Venusian gravitational field and modeling the geoid with unprecedented accuracy and spatial resolution through weighing the advantages and disadvantages among the electrostatically suspended gravity gradiometer, the superconducting gravity gradiometer and the AIGG. Finally, the future dedicated Venus-SGG spacecraft had better adopt the optimal matching accuracy indices consisting of 3×10−13/s2 in gravity gradient, 10m in orbital position and 8×10−4m/s in orbital velocity and the preferred orbital parameters comprising an orbital altitude of 300±50km, an observation time of 60months and a sampling interval of 1s.

A superconducting gravity gradiometer for measurements from a moving vehicle

A gravity gradiometer designed for operation on an aircraft or ship has been tested in the laboratory. A noise level of 0.53 E (E ≡ 10(-9) s(-2)) rms over a 0.001 to 1 Hz bandwidth has been measured, and the primary error mechanisms have been analyzed and quantified. The design is a continuation in the development of superconducting accelerometer technology at the University of Maryland over more than three decades. A cryogenic instrument presents not only the benefit of reduced thermal noise, but also, the extraordinary stability of superconducting circuits and material properties at very low temperatures. This stability allows precise matching of scale factors and accurate rejection of dynamic errors. The design of the instrument incorporates a number of additional features that further enhance performance in a dynamically noisy environment.

A gravity gradient method for characterizing the post-seismic deformation field for a finite fault

SUMMARY Gravity gradients are an effective method for delineating the extent of subsurface density anomalies. The change in subsurface density contrasts due to the seismic deformation gives rise to detectable gravity changes via the dilatational gravity signal or Bouguer anomaly. Solutions for the corresponding gravity gradients of these signals are developed for a vertical strikeslip fault. Gravity gradient solutions exhibit similar spatial distributions as those calculated for Coulomb stress changes, reflecting their physical relationship to the stress changes. The signals’ magnitudes, of the order of 10 −4 E, are beyond the resolution of typical exploration instruments. Improvements to Superconducting Gravity Gradiometers are necessary for gravity gradients to be used as a viable method for the observation of the stress field changes over large spatial scales.

Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer: principle and experimental considerations

The angular momentum of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of 10−10 of the Newtonian terms arising from the mass of the Earth. Due to the dragging of the local inertial frame by the spinning Earth, there are also secular terms, which grow in time. These fields can be detected in principle by a set of orbiting superconducting gravity gradiometers. The Riemann tensor components for various spacecraft orientations have been computed and the principle of detecting the gravitomagnetic tidal force has been published. In this paper, we review the conclusions of the earlier analyses and discuss the feasibility of the gravity gradiometer experiment.

Liquid helium motion and confinement for a cryogenic gravimetric mission

Within the Gravity Field and Ocean Circulation Explorer (GOCE) mission of the European Space Agency, we are performing a detailed comparison between the expected performances of a superconducting gravity gradiometer to be operated at T ∼ 2K and an electrostatic one to be operated at room temperature. As part of this analysis we have evaluated the gravitational perturbation due to liquid helium motion for the cryogenic instrument and proposed a possible method of helium confinement based on the use of aerogel.

Three-axis superconducting gravity gradiometer for sensitive gravity experiments

Superconducting differential accelerometers have been used to test Newton’s inverse square law and have been proposed for other sensitive experiments. These include searches for spin-mass coupling, detecting Earth’s gravitomagnetic field, and testing the Equivalence Principle. This article discusses the principle and performance of a sensitive three-axis gravity gradiometer. This device utilizes quantized flux and the Meissner effect to provide stable test mass levitation and signal coupling, and superconducting quantum interference devices to provide very low-noise amplification of the signals. The instrument comprises a total of nine superconducting accelerometers, six linear and three angular. This configuration permits simultaneous measurement of the diagonal components of the gravity gradient tensor as well as platform acceleration in all six degrees of freedom. An analysis of this instrument is presented along with experimental results. Methods to correct for various motion-induced errors are demonstrated. Other error sources are also discussed. The resulting performance of the superconducting gravity gradiometer is 2×10−11 s−2 Hz−1/2.

Sensitivity limitation of a superconducting quantum interferometer sensor-based gravity gradiometer

Differential displacement due to a gravitational force gradient, acting on two superconducting test masses which are elastically suspended from the instrument frame, is sensed by a superconducting quantum interference device (SQUID), coupled to the masses by a current flowing in the sensing circuits. The SQUID transducer absorbs energy from the masses, and, hence, it reacts with a random force (fluctuation-dissipation principle). This force increases if the coupling current grows. Additionally, the transducer outputs an amplification noise that is independent of the coupling. This output noise is equivalent to a force, applied to the masses, which decreases with stronger coupling, Hence, the strength of the total equivalent gravity gradient noise has a minimum with respect to the coupling. The minimum is found to be about 1.5/spl epsiv//sub A//spl omega//sub 0//sup 2//(ml/sup 2/), where /spl epsiv//sub A/ means the equivalent energy sensitivity, in the white noise limit, of the SQUID junctions; /spl omega//sub 0/ is the natural frequency of the mass suspension; m is the test mass, and l is the base length,.

Characterization of a dc SQUID based accelerometer circuit for a superconducting gravity gradiometer

A demonstrator set-up to test superconducting components has been designed and fabricated in order to characterize their functionality for use in a superconducting gravity gradiometer. The displacement of a freely oscillating levitated niobium proof mass in this acceleration transducer is measured inductively and read out by a direct current superconducting quantum interference device. It has been confirmed experimentally that the oscillation frequency depends on the current of the levitation magnet that is operated in persistent-current mode. The results allow us to establish testing and operational procedures that can be used in a more complex multichannel system to confirm functionality and to adjust the levitated proof mass.

Superconducting gravity gradiometers on STEP and GEM

The superconducting gravity gradiometers for the European STEP and GEM missions have common design features. Both gradiometers have their test masses magnetically levitated, stiff against all unwanted degrees of freedom. The sensitive axes of the component accelerometers are aligned to with respect to each other, by adjusting persistent currents in the alignment coils, to improve the common-mode rejection ratio to . The axial displacements of the two test masses in each gradiometer are coupled through two superconducting circuits to two DC SQUIDs. Persistent currents are stored in the circuits such that the acceleration signals are summed and differenced at the respective SQUID inputs. This signal differencing before detection reduces the linearity and dynamic range requirements of the electronics by several orders of magnitude. The STEP gradiometer will be a single-axis device with a baseline of about 60 cm and with its sensitive axis oriented along the orbit normal. Its intrinsic noise is expected to be above . Below this frequency 1/f power noise should appear. A compact three-axis superconducting gravity gradiometer with a baseline of 12 cm is proposed for GEM. This gradiometer will have an intrinsic noise of above . Below this frequency 1/f noise will dominate.

A performance comparison between an electrostatic and a superconducting gravity gradiometer

In connection with the Gravity Explorer Mission study of the European Space Agency we have made an independent comparison of the noise performance and the disturbance rejection ability of a superconducting and of a capacitive gravity gradiometer. 0490, 0630G, 0707M, 9385, 9555

Mission concepts for the Superconducting Gravity Gradiometer

The Superconducting Gravity Gradiometer (SGG), which can measure gravitational field fluctuations to unprecedented precisions, is currently being evaluated for use in an Earth-orbiting platform. Two missions are planned: a Shuttle-based demonstration flight and a dedicated gravity surveying mission. The Shuttle mission will feature a fully functional, self-contained instrument with an intrinsic noise level of 10 −3 E Hz −1 2 , where E is defined at 10 −9m s −2 m −1. Calibration hardware, residual error correction techniques, and surface tension devices which control liquid helium motion in the dewar will be tested. For a dedicated free-flier gravity mission, two concepts have been studied. Both have been formulated to achieve low cost while maintaining an instrument sensitivity of 10 −3 E Hz −1 2 . One concept uses the spacecraft developed for the Sub-millimeter Wave Astronomical Satellite (SWAS), and would be in a polar orbit, decaying from an initial altitude of 380 km. A mission lifetime of 6–9 months is planned. The other concept is based on a re-usable SPARTAN 400 carrier which would be deployed from, and retrieved by, the Shuttle. The carrier can be periodically reboosted and would maintain an altitude between 275 and 350 km. The mission lifetime is restricted to about 3 months, and the orbit inclination is limited to 57 °, the maximum the Shuttle can reach. Since the carrier is retrieved, the instrument could be periodially reflown. The free-flier missions, including experiment and spacecraft design, are described.