Free-falling Test Masses Research Articles

Rotational disturbance in laser-interferometric gravity gradiometry

Laser interferometers have been used for precise measurements of gravity and related effects. These include experiments to search for a fifth force and absolute ballistic gravimeters, which use a Michelson-type laser interferometer to measure the acceleration of a free-falling test mass. In these methods of instrumentation, the motion of free-falling test masses is measured using corner-cube laser interferometers, in which at least one retroreflector is embedded in each test mass. However carefully each of such test masses is released into free fall, a small amount of rotation is unavoidable which changes the optical path length and causes acceleration disturbance. This rotational disturbance could ultimately limit the measurement sensitivity of the laser interferometers. Various experimental and theoretical studies have been conducted to minimise the rotational disturbance in absolute ballistic gravimeters. This paper focuses on the rotational disturbance in laser-interferometric gravity gradiometers (LIGGs) that measure differential acceleration between two test masses freely falling at different heights in a vacuum. LIGGs can be configured to measure not only vertical gravity gradients, but also horizontal gradients, or gradients in both horizontal and vertical directions. However, only those to measure vertical gravity gradients have been constructed so far. Hence, in this paper, the term LIGGs specifically indicates the gravity gradiometers that measure vertical gravity gradients. Unlike absolute ballistic gravimeters, the LIGGs are, in principle, insensitive to ground vibrations; they can potentially detect some effects that are buried in seismic noise in absolute gravity data. To fully leverage this advantage of the LIGGs, it is crucial to keep the rotational disturbance to a minimum. Expressions for the rotational disturbance are derived and its magnitude is estimated based on available experimental data. The results show that the magnitude would not be more than 0.1 μGal /m in the measurement of vertical gravity gradients in a compact LIGG. Alternative designs and requirements for increasing the sensitivity of the LIGGs are also discussed.

Study of quantum electron diffraction for the LISA test-mass charging

The future Laser Interferometer Space Antenna (LISA) for gravitational wave detection in space and the precursor LISA Pathfinder missions rely on metal test masses (TMs) playing the role of free-falling geodesic-reference and interferometer end mirrors. Charge deposited on the TMs by high-energy particles of galactic and solar origin couples with stray electric fields thus perturbing the free-falling geodesic motion. In previous works it has been shown that sub-keV electrons play a relevant role for TM charging. In particular, electrons with energies below 100 eV show a wave-like behavior when impacting on the gold coatings of the TMs and electrode-housing (EH), the capacitive position sensor/actuator that surrounds the TMs. We aim at studying the effects of quantum diffraction of electrons on LISA Pathfinder and LISA TMs and EH gold lattice. We calculate the quantum diffraction probability of electrons with energies < 100 eV impinging on gold lattice from different directions by using the methods of quantum mechanics. The effects of electron quantum diffraction on LISA TM charging are reported here for the first time. This work is also of interest for the second-generation LISA-like space interferometers and for all space missions whose performance relies on free-falling metal test masses.

Test mass charge estimation for the space inertial sensor with extended Kalman filter

Charge Management System (CMS), aimed at mitigating charge-induced noise on an isolated free-falling test mass (TM), is a crucial component of space inertial sensors in various spaceborne gravitational missions. The estimation of TM charge is one of the tasks of CMS, directly impacting CMS performance. However, current methods for TM charge estimation suffer from slow response and significant estimation errors. This paper presents a new charge estimation method that combines the force modulation principle with an extended Kalman filter (EKF). We analyzed the relationship between the TM surface potential and TM motion, then established a mathematical model. The estimation of TM charge is accomplished through the EKF algorithm. A charge estimation simulation model was developed in Simulink, and experiments were conducted to evaluate the performance of the charge estimation methods under varying charge conditions. The experimental results demonstrate that the EKF method obtains more accurate estimation results and faster convergence rates, compared with Kalman Filter (KF) and Quadrature demodulation (QD) methods. The KF and QD methods show larger errors when the estimated charge is greater than 106e order, meanwhile the QD method exhibits slower convergence rates. The presented method is expected to be beneficial for the CMS of on-orbit inertial sensors.

Impact dynamics of a free-falling reference test mass in space

Outer space may constitute a privileged environment for experiments involving impacts. In fact, disturbing phenomena like drag or weight forces are negligible and a nearly pure free-fall state may be achieved for the impacting bodies. The case analysed in this manuscript comes from the initialization of the science phase of a space mission (LISA Pathfinder, flown in 2015), in which an extended metallic body – starting from a caged configuration – was released to free-fall inside a spacecraft by a dedicated mechanism, the grabbing positioning and release mechanism (GPRM). During the release phase, the test mass (TM) experienced some impacts with the GPRM end effector, before being electrostatically controlled to its nominal position, i.e. still in the centre of the hosting electrode housing. The impact dynamics of the TM therefore resulted critical, since it helped reduce its kinetic energy with respect to the spacecraft. In this paper, the TM position and attitude telemetry signals are analysed, and the impacts coefficient of restitution is calculated, providing reference values for similar space instruments, where a free-falling reference body is used (for instance, for geodesy and/or spacecraft navigation).

Effect of solar proton events on test mass for gravitational wave detection in the 24th solar cycle

Free-falling cubic Test Masses (TMs) are a key component of the interferometer used for low-frequency gravitational wave (GW) detection in space. However, exposure to energetic particles in the environment can lead to electrostatic charging of the TM, resulting in additional electrostatic and Lorentz forces that can impact GW detection sensitivity. To evaluate this effect, the high-energy proton data set of the Geostationary Operational Environmental Satellite (GOES) program was used to analyze TM charging due to Solar Proton Events (SPEs) in the 24th solar cycle. Using the Geant4 Monte Carlo toolkit, the TM charging process is simulated in a space environment for SPEs falling into three ranges of proton flux: (1) greater than 10 pfu and less than 100 pfu, (2) greater than 100 pfu and less than 1000 pfu, and (3) greater than 1000 pfu. It is found that SPEs charging can reach the threshold within 535 s to 18.6 h, considering a reasonable discharge threshold of LISA and Taiji. We demonstrate that while there is a somewhat linear correlation between the net charging rate of the TM and the integrated flux of ge 10 MeV SPEs, there are many cases in which the integrated flux is significantly different from the charging rate. Therefore, we investigate the difference between the integral flux and the charging rate of SPEs using the charging efficiency assessment method. Our results indicate that the energy spectrum structure of SPEs is the most important factor influencing the charging rate. Lastly, we evaluate the charging probability of SPEs in the 24th solar cycle and find that the frequency and charging risk of SPEs are highest in the 3rd, 4th, 5th, 6th, and 7th years, which can serve as a reference for future GW detection spacecraft.

Charging of free-falling test masses in orbit due to cosmic rays: Results from LISA Pathfinder

A comprehensive summary of the measurements made to characterize test mass charging due to the space environment during the LISA Pathfinder mission is presented. Measurements of the residual charge of the test mass after release by the grabbing and positioning mechanism, show that the initial charge of the test masses was negative after all releases, leaving the test mass with a potential in the range $-12$ mV to $-512$ mV. Variations in the neutral test mass charging rate between $21.7$ e s$^{-1}$ and $30.7$ e s$^{-1}$ were observed over the course of the 17-month science operations produced by cosmic ray flux changes including a Forbush decrease associated with a small solar energetic particle event. A dependence of the cosmic ray charging rate on the test mass potential between $-30.2$ e s$^{-1}$ V$^{-1}$ and $-40.3$ e s$^{-1}$ V$^{-1}$ was observed and this is attributed to a contribution to charging from low-energy electrons emitted from the gold surfaces of the gravitational reference sensor. Data from the on-board particle detector show a reliable correlation with the charging rate and with other environmental monitors of the cosmic ray flux. This correlation is exploited to extrapolate test mass charging rates to a 20-year period giving useful insight into the expected range of charging rate that may be observed in the LISA mission.

Deep UV AlGaN LED reliability for long duration space missions

Space-based gravitational wave detection will be carried out by the laser interferometer space antenna (LISA), a joint European Space Agency and NASA collaboration. The configuration of this antenna will include three identical spacecraft in a triangular formation separated by 2.5×106km, flying in a drag-free formation around free-falling test masses. Charging of the test masses by cosmic ray fluxes and solar energetic particles must be compensated by photons that contain more energy than the effective work function of gold (4.3±0.4eV). The UV photons will be provided by AlGaN light emitting diodes, which must operate reliably for the duration of the mission. We have tested a large number (96 for dc and pulsed testing, more than 200 for all tests) of UV LEDs over a period of up to 600 days to characterize their performance over a wide range of operating conditions, assessing the lifetime performance under dc (1–80mA drive current) and pulsed conditions (500–100 000 pulses per second) and temperatures ranging from 20 to 80°C. Degradation of UV light output is faster at elevated temperatures and dc conditions. Preselection of LEDs based on initial spectral ratio of peak-to-midgap emission and ideality factor provides a positive correlation with subsequent reliability. The UV LEDs used for LISA will need to support 2 years of cruise and commissioning plus a 4-year baseline science mission.

Measurement of stray electric fields in a capacitive inertial sensor using contactless test-mass charge modulation

We present a new technique for measuring the stray electric field in precision space inertial sensors by modulating the electric charge of a free-falling test mass and measuring the resulting coherent Coulomb force. The free charge of the test mass is controlled by ultraviolet photoemission using a pulsed light source synchronized with an oscillating potential capacitively induced on the test mass. We can modulate the test mass charge sinusoidally at an arbitrarily chosen frequency by varying the phase of the UV light pulses relative to the induced test mass potential at the appropriate rate. This technique allows us to optimize the precision of the measurement by choosing a modulation frequency that is within the most sensitive band of the sensor. We present an experimental validation of this approach using an inertial sensor integrated with a torsion pendulum, measuring the equivalent stray potential of the sensor with milliVolt precision in ${10}^{4}\text{ }\text{ }\mathrm{s}$. We discuss the applicability of this technique for the upcoming Laser Interferometer Space Antenna (LISA) gravitational-wave observatory.

Compact Active Vibration Isolation and Tilt Stabilization for a Portable High-Precision Atomic Gravimeter

In high-precision atomic gravimeters, a rest mass is needed to provide a gravity reference, which is typically the retro-reflecting mirror of the Raman laser beams that addresses the two hyperfine ground states of the specific free-falling atomic test mass. We constructed a compact active feedback control system for the retro-reflecting mirror that provides vibration isolation in the vertical axis as well as two rotation stabilization in the horizontal plane. The active feedback control provides vertical vibration reduction of up to a factor of 300 in the frequency range of 0.03 to 10 Hz and tilt stabilization of approximately $\pm$ 1 $\mu$rad in the noisy lab environment. This system has enabled high-precision gravity measurements on a portable gravimeter with sensitivity reaching $6.4\times 10^{-8}$ g/$\sqrt{\text{Hz}}$ and resolution of $2.8\times 10^{-9}$ g after an integration time of 4000 s.

Bridging the gap between Monte Carlo simulations and measurements of the LISA Pathfinder test-mass charging for LISA

Context. Cubic gold-platinum free-falling test masses (TMs) constitute the mirrors of future LISA and LISA-like interferometers for low-frequency gravitational wave detection in space. High-energy particles of Galactic and solar origin charge the TMs and thus induce spurious electrostatic and magnetic forces that limit the sensitivity of these interferometers. Prelaunch Monte Carlo simulations of the TM charging were carried out for the LISA Pathfinder (LPF) mission, that was planned to test the LISA instrumentation. Measurements and simulations were compared during the mission operations. The measured net TM charging agreed with simulation estimates, while the charging noise was three to four times higher. Aims. We aim to bridge the gap between LPF TM charging noise simulations and observations. Methods. New Monte Carlo simulations of the LPF TM charging due to both Galactic and solar particles were carried out with the FLUKA/LEI toolkit. This allowed propagating low-energy electrons down to a few electronvolt. Results. These improved FLUKA/LEI simulations agree with observations gathered during the mission operations within statistical and Monte Carlo errors. The charging noise induced by Galactic cosmic rays is about one thousand charges per second. This value increases to tens of thousands charges per second during solar energetic particle events. Similar results are expected for the LISA TM charging.

Conceptual design and science cases of a juggled interferometer for gravitational wave detection

The Juggled interferometer (JIFO) is an earth-based gravitational wave detector using repeatedly free-falling test masses. With no worries of seismic noise and suspension thermal noise, the JIFO can have much better sensitivity at lower frequencies than the current earth-based gravitational wave detectors. The data readout method of a JIFO could be challenging if one adopts the fringe-locking method. We present a phase reconstruction method in this paper by building up a complex function which has a fringe-independent signal-to-noise ratio. Considering the displacement noise budget of the Einstein Telescope (ET), we show that the juggled test masses significantly improve the sensitivity at 0.1-2.5$\,$Hz even with discontinuous data. The science cases brought with the improved sensitivity would include detecting quasi-normal modes of black holes with $10^4-10^5\,M_{\odot}$, testing Brans-Dicke theory with black-hole and neutron-star inspirals, and detecting primordial-black-hole-related gravitational waves.

Drag-free design based on Embedded Model Control for TianQin project

With the ability to detect low-frequency gravitational waves (GWs), space-borne detectors will play an important role in exploring the universe in the future. The TianQin project proposed in China participates in this challenge by aiming to detect millihertz GWs. The TianQin GW detector consists of three spacecraft forming a triangular constellation. Each spacecraft carries a pair of test masses (TM) which, inside shielding cages, are left to free fall along the local geodesic. In this way, a pair of TMs on two separate spacecraft can be each other aligned to become the gravitational references of the GW detector, made by an inter-satellite laser interferometer. Each free-falling TM is limited by parasitic forces to be appropriately bounded. The relevant acceleration bound has been fixed to 10−15 m/s2/Hz within the TianQin measurement bandwidth (MBW) ranging from 0.1mHz to 0.1Hz. In turn, TM to cage fluctuations must be kept below 4nm/Hz to limit the stiffness coupling with the spacecraft displacement caused by non-gravitational disturbances, such as solar radiations and the thruster noise. Suppression of such disturbances calls for a challenging drag-free control technology, since the center of mass (CoM) of a single spacecraft cannot track the separated CoMs of two TMs simultaneously, and consequently tracking must be limited to three degrees of freedom (DoF): two non-orthogonal sensitive axes (one for each TM) and the perpendicular direction to their plane. Control design and simulated tests of this paper will be restricted to the drag-free control along the sensitive axes. The remaining nine DoFs of the two TMs (position and attitude) are controlled by electrostatic suspensions, not to be treated here, but accounted for in the simulated trials. The design of the two-DoF drag-free control relies on a model-based control methodology, the Embedded Model Control (EMC), capable of predicting and suppressing unknown disturbances within the required bandwidth and of decoupling the TM dynamics along the non-orthogonal sensitive axes. The paper starts with the nonlinear model of the TM to cage dynamics, followed by the relevant EMC design, restricted to the sensitive axes. Numerical simulations are employed to validate closed-loop performance and robust stability. Simulated results show that the residual TM to cage fluctuations can be kept below 3nm/Hz, which leaves a margin within the required spectral bound. The EMC methodology discussed in the paper can provide a reference for future developments and implementations.

Application of LISA Gravitational Reference Sensor Hardware to Future Intersatellite Geodesy Missions

Like gravitational wave detection, inter-spacecraft geodesy is a measurement of gravitational tidal accelerations deforming a constellation of two or more orbiting reference test masses (TM). The LISA TM system requires TM in free fall with residual stray accelerations approaching the fm/s2/Hz1/2 level in the mHz band, as demonstrated in the LISA Pathfinder “Einstein’s geodesic explorer” mission. Current geodesy missions are limited by accelerometers with 100 pm/s2/Hz1/2 level, due to intrinsic design limitations, as well as the challenging low Earth orbit environment and operating conditions. A reduction in the TM acceleration noise could lead to an important improvement in the scientific return of future geodesy missions focusing on mass change, especially in a scenario with multiple pairs of geodesy satellites. We present here a preliminary assessment of how the LISA TM system, known as the “gravitational reference sensor” (GRS), could be adapted for use in future geodesy missions aiming at residual TM accelerations noise at the pm/s2/Hz1/2 level, addressing the major design issues and performance limitations. We find that such a performance is possible in a geodesy GRS that is simpler and smaller than that used for LISA, with a lighter, sub-kg TM and gaps reduced from 4 mm to less than 1 mm. Acceleration noise performance limitations will likely be closely tied to the required levels of applied actuation forces on the TM.

Detection and characterization of instrumental transients in LISA Pathfinder and their projection to LISA

The LISA Pathfinder (LPF) mission succeeded outstandingly in demonstrating key technological aspects of future space-borne gravitational-wave detectors, such as the Laser Interferometer Space Antenna (LISA). Specifically, LPF demonstrated with unprecedented sensitivity the measurement of the relative acceleration of two free-falling cubic test masses. Although most disruptive non-gravitational forces have been identified and their effects mitigated through a series of calibration processes, some faint transient signals of yet unexplained origin remain in the measurements. If they appear in the LISA data, these perturbations (also called glitches) could skew the characterization of gravitational-wave sources or even be confused with gravitational-wave bursts. For the first time, we provide a comprehensive census of LPF transient events. Our analysis is based on a phenomenological shapelet model allowing us to derive simple statistics about the physical features of the glitch population. We then implement a generator of synthetic glitches designed to be used for subsequent LISA studies, and perform a preliminary evaluation of the effect of the glitches on future LISA data analyses.

The LISA DFACS: Model Predictive Control design for the test mass release phase

This paper presents a Model Predictive Control (MPC) design for the test mass release phase of the LISA space mission. LISA is a gravitational wave observatory consisting of a triangular constellation of three spacecraft. The gravitational waves are detected by measuring the relative distance between free falling test masses by means of a laser interferometer. Each test mass is a cubic body located inside an electrostatic suspension that is initially locked by a clamp mechanism. Once the plungers are retracted, the test masses are released with high initial offsets and velocities. To detect the gravitational waves, each test mass must be accurately positioned at the cage centre and its attitude must be aligned with the local cage frame. However, the low actuation authority of the electrostatic suspension along with the critical initial conditions, make the attitude and translation control a difficult task. MPC is a suitable technique for this application because it can systematically account for command saturations, state constraints and can provide optimal (or sub-optimal) control inputs by solving an optimization problem online. In this paper, an MPC controller is designed and validated by means of Monte Carlo simulations, achieving satisfactory results.

First-order velocity memory effect from compact binary coalescing sources

It has long been known that gravitational waves from compact binary coalescing sources are responsible for a first-order displacement memory effect experienced by a pair of freely falling test masses. This constant displacement is sourced from the non-vanishing final gravitational-wave strain present in the wave's after-zone, often referred to as the non-linear memory effect, and is of the same order of magnitude as the strain from the outgoing quadrupole radiation. Hence, this prediction of general relativity is verifiable experimentally by measurement of the final relative separation between test masses that comprise gravitational-wave detectors. In a separate context, independent calculations have demonstrated that exact, sandwich, plane wave spacetimes exhibit a velocity memory effect: a non-zero relative velocity, gained by a pair of test masses in free fall, after the passage of a gravitational wave. In this paper, we find that in addition to the known constant displacement memory effect test masses experience, a velocity memory effect at leading order arises due to the non-linear nature of gravitational waves from compact binary sources. We discuss the magnitude of the first-order velocity memory effect in the context of observing gravitational-wave radiation from super massive binary black hole mergers in LISA.

Sensor Noise in LISA Pathfinder: In-Flight Performance of the Optical Test Mass Readout.

We report on the first subpicometer interferometer flown in space. It was part of ESA's Laser Interferometer Space Antenna (LISA) Pathfinder mission and performed the fundamental measurement of the positional and angular motion of two free-falling test masses. The interferometer worked immediately, stably, and reliably from switch on until the end of the mission with exceptionally low residual noise of 32.0_{-1.7}^{+2.4} fm/sqrt[Hz], significantly better than required. We present an upper limit for the sensor performance at millihertz frequencies and a model for the measured sensitivity above 200mHz.

Effect of Earth-Moon’s gravity on TianQin’s range acceleration noise

TianQin is a proposed space gravitational-wave detection mission using circular high Earth orbits. The geocentric concept has raised questions about the disturbing effect of the nearby gravity field of the Earth-Moon system on the highly-sensitive intersatellite ranging measurements. Here we examine the issue through high precision numerical orbit simulation with detailed gravity-field models. By evaluating range accelerations between distant free-falling test masses, the study shows that the majority of the Earth-Moon's gravity disturbances are not in TianQin's detection frequency band above $10^{-4}$ Hz, and hence present no showstoppers to the mission.

Low-energy electromagnetic processes affecting free-falling test-mass charging for LISA and future space interferometers

Galactic cosmic rays and solar energetic particles charge gold-platinum, free-falling test masses (TMs) on board interferometers for the detection of gravitational waves in space. The charging process induces spurious forces on the test masses that affect the sensitivity of these instruments mainly below 10−3 Hz. Geant4 and FLUKA Monte Carlo simulations were carried out to study the TM charging process on board the LISA Pathfinder mission that remained into orbit around the Sun–Earth Lagrange point L1 between 2016 and 2017. While a good agreement was observed between simulations and measurements of the TMs net charging, the shot noise associated with charging fluctuations of both positive and negative particles resulted 3–4 times higher that predicted. The origin of this mismatch was attributed to the propagation of electrons and photons only above 100 eV in the simulations. In this paper, low-energy electromagnetic processes to be included in the future Monte Carlo simulations for LISA and LISA-like space interferometers TM charging are considered. It is found that electrons and photons below 100 eV give a contribution to the effective charging comparable to that of the whole sample of particles above this energy. In particular, for incident protons ionization contributes twice with respect to low energy kinetic emission and electron backscattering. The other processes are found to play a negligible role. For heavy nuclei only sputtering must be considered.

Characterisation of Au surface properties relevant for UV photoemission-based charge control for space inertial sensors

Precision space inertial sensors used for satellite geodesy missions, tests of fundamental physics, and gravitational wave observation utilise UV photoemission to control the electric potential of free-falling test masses with respect to their surrounding electrode housings. Successful generation of photoelectrons requires UV light energies greater than the work function of the illuminated surface. To ensure bi-polar test mass charge control (positive and negative charge rates), the quantum yields of the test mass and electrode housing surfaces must be well-balanced. LISA Pathfinder used mercury vapour lamps at 254 nm to discharge the gold coated test mass by likely relying on contaminants to lower the work function of gold from its nominal value of 5.2 eV. The LISA gravitational wave mission plans to use UV light emitting diodes (LEDs) instead of mercury vapour lamps. These UV LEDs have a lower mass, higher power efficiency, and produce light at wavelengths below 240 nm. In this paper, we measure the quantum yields of several Au-coated surfaces over a range of UV wavelengths and environmental conditions, varying temperature, vacuum pressure, and measuring over long periods of time. We use these data to draw conclusions and make recommendations for the development and handling of precision space inertial sensors for LISA and for other missions in the future.