LISA Pathfinder Mission Research Articles

Finite Element Analysis of Electrostatic Coupling in LISA Pathfinder Inertial Sensors

In the LISA Pathfinder (LPF) mission, electrostatic noise can reach the femto-Newtonian level despite the fact that the LPF’s sensors are equipped with potential shielding. Most of the existing simulation studies focus on the electrostatic edge effect and related fields, while the simulation study of the patch effect is neglected. For that reason, this paper analyzes the basic principle of electrostatic noise and constructs a simulation model for studying the coupling effects of a TM’s residual charge and stray bias voltage. The patch effect and other perturbation factors are simulated by the simulation model with finite element operation, focusing on the suppression effect of the protective ring on the edge effect, the realization of the patch effect in the simulation model, and the possible influence. The results show that electrode area and the spacing between the electrode and the TM together limit the suppression effect of the protective ring on the edge effect. The spatial and temporal variations of the patch effect significantly affect the distributed electric field between the electrodes and the TM, as well as the charge distribution density of the TM. In the worst-case scenario of LPF electrostatic input parameters, the electrostatic noise is about 1.03 × 10−15 m/s2/√Hz at 1 mHz, which is about 6% different from the expected performance estimate. Finally, considering the limitations of multiple environmental factors on the inertial sensors, the present model will be useful to explore the interactive effects of multi-field coupling and to further investigate the impact of low-energy electron charging on the performance of the inertial sensors.

Tilt-to-length coupling in LISA Pathfinder: Long-term stability

The tilt-to-length coupling during the LISA Pathfinder mission has been numerically and analytically modeled for particular time spans. In this work, we investigate the long-term stability of the coupling coefficients of this noise. We show that they drifted slowly (by 1 μm/rad and 6×10−6 in 100 days) and were strongly correlated to temperature changes within the satellite (8 μm/rad/K and 30×10−6/K). Based on analytical tilt-to-length coupling models, we attribute the temperature-driven coupling changes to rotations of the test masses and small distortions in the optical setup. Particularly, our findings lead to the conclusion that LISA Pathfinder’s optical baseplate was bent during the cooldown experiment, which started in late 2016 and lasted several months. Published by the American Physical Society 2024

Bridging machine learning and diagnostics of the ESA LISA space mission with equation discovery via explainable artificial intelligence

The Laser Interferometer Space Antenna (LISA) of the European Space Agency will be the first interferometer for low-frequency (10-4–10-1 Hz) gravitational wave detection in space. LISA will detect spurious accelerations of the test masses, the end mirrors of the interferometer, of the order of femto-g. Amongst spurious signals, Coulomb forces due to stray electric fields coupling with charge deposited on the test masses by galactic and solar particles and the noise associated to the charging process must be monitored during the mission lifetime. Precious clues on spurious forces acting on the test masses have been studied with the LISA Pathfinder mission, meant for the testing of the instrumentation that will be placed on board LISA, in 2016–2017. In this work we present the design and implementation of a workflow leading to equation discovery for the relationship between solar wind speed, galactic cosmic-ray variations and interplanetary magnetic field intensity observations for the diagnostics of LISA. The workflow exploits explainable artificial intelligence tools to build a bridge between the opaque predictions obtained with machine learning (ML) models and data analysis performed by humans with space mission observations. The core step of the workflow is the implementation, tuning and optimisation of an opaque ML regressor explicitly designed for the future LISA mission, based on input observations of the galactic cosmic-ray flux and of the interplanetary magnetic field intensity. The regressor is aimed at reconstructing the solar wind speed, a parameter of fundamental importance, but not available, for the mission environment monitoring. The workflow ends with the application of explainable clustering techniques to the opaque model in order to (i) obtain human-interpretable outputs instead of opaque ones without any noticeable loss in the predictive performance and (ii) discover an equation describing the quantitative relationship between the involved variables, currently missing in the literature. The correlation amongst the transit of interplanetary structures, galactic cosmic-ray variations and LISA test-mass charging is illustrated here.

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.

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.

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.

An Improved Next Generation Gravity Mission

There is an opportunity to make a major reduction in the acceleration noise level for the first Next Generation Gravity Mission by replacing the accelerometers used on the GRACE Follow-On Mission by a highly simplified version of the Gravitational Reference Sensors flown very successfully on the LISA Pathfinder mission of ESA. The reduced measurement noise level can make possible much-improved measurements of the short-period and short-wavelength variations in the geopotential. This would be particularly from the along-track analysis of the results, which can permit repeat measurements about half a day apart along ground tracks within 200 km of each other over a substantial part of the globe. Such a mission would permit considerably improved testing of geophysical models for the geopotential variations due to changes in the Earth’s mass distribution.

Interplanetarymedium monitoring with LISA: Lessons from LISA Pathfinder

The Laser Interferometer Space Antenna (LISA) of the European Space Agency (ESA) will be the first low-frequency gravitational-wave observatory orbiting the Sun at 1 AU. The LISA Pathfinder (LPF) mission, aiming at testing the instruments to be located on board the LISA spacecraft (S/C), hosted, among the others, fluxgate magnetometers and a particle detector as parts of a diagnostics subsystem. These instruments allowed us to estimate the magnetic and Coulomb spurious forces acting on the test masses that constitute the mirrors of the interferometer. With these instruments, we also had the possibility to study the galactic cosmic-ray short term-term variations as a function of the particle energy and the associated interplanetary disturbances. Platform magnetometers and particle detectors will also be placed on board each LISA S/C. This work reports on an empirical method that allowed us to disentangle the interplanetary and onboard-generated components of the magnetic field by using the LPF magnetometer measurements. Moreover, we estimate the number and fluence of solar energetic particle events expected to be observed with the ESA Next Generation Radiation Monitor during the mission lifetime. An additional cosmic-ray detector, similar to that designed for LPF, in combination with magnetometers, would permit to observe the evolution of recurrent and non-recurrent galactic cosmic-ray variations and associated increases of the Interplanetary Magnetic Field at the transit of high-speed solar wind streams and interplanetary counterparts of coronal mass ejections. The diagnostics subsystem of LISA makes this mission also a natural multi-point observatory for space weather science investigations.

Investigation of the in-flight anomalies of the LISA Pathfinder Test Mass release mechanism

The LISA Pathfinder mission was flown to test some key technologies for the in-flight detection of gravitational waves. The mechanism developed to initialise the science phase, releasing the test mass into a geodesic trajectory, produced unexpected test mass states, requiring dedicated in-flight and on-ground test campaigns. Due to the limited information available from the telemetry, the analysis of the results required a combination of experimental and analytical approaches. A dynamic model of the release mechanism, integrated by an impact model, is developed to explain the in-flight test results. The proposed interpretation of the mechanism anomalies may provide useful guidelines for the design and development of the flight units for the forthcoming LISA 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.

A New Method to Model Magnetic Cloud-driven Forbush Decreases: The 2016 August 2 Event

Abstract Interplanetary coronal mass ejections (ICMEs), generally containing magnetic clouds (MCs), are associated with galactic-cosmic ray (GCR) intensity depressions known as Forbush decreases (FDs). An ICME was observed at L1 between 2016 August 2 at 14:00 UT and August 3 at 03:00 UT. The MC region was identified and its magnetic configuration was retrieved by using the Grad–Shafranov (GS) reconstruction. A weak FD in the GCR count-rate was observed on 2016 August 2 by a particle detector on board the European Space Agency LISA Pathfinder mission. The spacecraft orbited around L1 and the particle detector allowed us to monitor the GCR intensity at energies above 70 MeV n −1. A 9% decrease in the cosmic-ray intensity was observed during the ICME passage. The first structure of the ICME caused a 6.4% sharp decrease, while the MC produced a 2.6% decrease. A suited full-orbit test-particle simulation was performed on the MC configuration obtained through the GS reconstruction. The FD amplitude and time profile obtained through the simulation show an excellent agreement with observations. The test-particle simulation allows us to derive the energy dependence of the MC-driven FD providing an estimate of the amplitude at different rigidities, here compared with several neutron monitor observations. This work points out the importance of the large-scale MC configuration in the interaction between GCRs and ICMEs and suggests that particle drifts have a primary role in modulating the GCR intensity within the MC under study and possibly in at least all slowly expanding ICMEs lacking a shock/sheath region.

Drag-free control methods for space-basedgravitational-wave detection

In order to meet the requirements of “high precision” for space-based gravitational-wave detection, the design of control systems for a drag-free satellite is researched from the point of view of dynamics and control theory. Based on the LISA Pathfinder mission, the drag-free satellite contains two test masses, and its control system includes an attitude control loop, a drag-free control loop, and an electrostatic-suspension control loop. Drag-free control technology is employed for the drag-free control loop, where a test mass is in a state of free fall, and the satellite platform is controlled to follow the test mass “strongly” in order to achieve a high-level microgravity of the satellite platform and the test mass. Active vibration-isolation control technology is applied in the electrostatic-suspension control loop, where the other test mass is controlled to follow the satellite platform “weakly” and is isolated from vibrations of the satellite platform, so as to achieve high-level microgravity of the test mass and avoid collisions between the test mass and the satellite platform. The frequency-domain characteristics of the two control technologies are analyzed, assuming them to be based on the PID control algorithm. A set of formulas for calculating the parameters for the PID controllers are established, so that the parameters can be determined quickly according to the performance requirements for these controllers. On this basis, a control strategy is proposed and the PID controllers are designed. The effectiveness of the control strategy and the accuracy of the controller parameters are verified through numerical simulations.

Investigation of charge management using UV LED device with a torsion pendulum for TianQin

TianQin is a Chinese space-based observatory concept with three drag-free spacecraft orbiting the earth to observe gravitational-waves in the millihertz range. Electrical charge is inevitably accumulating on its isolated test masses which are used as the mirrors for interferometers to measure gravity variation. Charge management system based on ultraviolet (UV) light is developed to reduce the charge-induced noises acting on the test mass in space gravitational experiments such as GP-B, LISA, LISA Pathfinder and TianQin mission. The UV LED is a new UV light source with some advantages relative to mercury lamps, such as smaller size, lighter weight, lower power consumption and higher efficiency. For these reasons, ground-based tests for the combination of UV LED and inertial sensor are essential. This paper presents the development of a charge management system based on a UV LED, its application to a torsion pendulum system with a TianQin-like test mass, and assesses the charge-management performance of the system. The experimental results indicate that the isolated test mass can be charged positively or negatively through UV illumination. It demonstrates that the charging and discharging rates can both reach higher than 105 e s−1, as well as spectral measurement of the pendulum charge resulting in a white noise level equivalent to ∼5 × 105 e Hz−1/2, satisfying the TianQin requirement.

Gravitational Waves Detectors

The search for direct detection of Gravitational Wave made a huge step forward in the years between 2015-2017. After the first detection signals from the coalescence of binary black hole systems, we had both the great success of the LISA pathfinder mission and the detection of the first event due to a neutron star - neutron star merger tagged as the birth of the multi messenger astronomy. A new era is now opened where the GW events are detected routinely by the triangular network of LIGO and Virgo that in the nearest future will be enlarged by including KAGRA, the fourth detector in Japan. Here we review the evolution of the existing detectors focusing our attention essentially on the middle and long-term evolution of those on the Earth.

LISA Pathfinder micronewton cold gas thrusters: In-flight characterization

The LISA Pathfinder (LPF) mission has demonstrated the ability to limit and measure the fluctuations in acceleration between two free falling test masses down to sub-femto-g levels. One of the key elements to achieve such a level of residual acceleration is the drag free control. In this scheme the spacecraft is used as a shield against any external disturbances by adjusting its relative position to a reference test mass. The actuators used to move the spacecraft are cold gas micropropulsion thrusters. In this paper, we report in-flight characterization of these thrusters in term of noise and artefacts during science operations using all the metrology capabilities of LISA Pathfinder. Using the LISA Pathfinder test masses as an inertial reference frame, an average thruster noise of ∼0.17 μN/Hz is observed and decomposed into a common (coherent) and an uncorrelated component. The very low noise and stability of the onboard metrology system associated with the quietness of the space environment allowed the measurement of the thruster noise down to ∼20 μHz, more than an order of magnitude below any ground measurement. Spectral lines were observed around ∼1.5 mHz and its harmonics and around 55 and 70 mHz. They are associated with the cold gas system itself and possibly to a clock synchronization issue. The thruster noise-floor exhibits an excess of ∼70% compared to characterization that have been made on ground on a single unit and without the feeding system. However this small excess has no impact on the LPF mission performance and is compatible with the noise budget for the upcoming LISA gravitational wave observatory. Over the whole mission, nominal, and extension, the thrusters showed remarkable stability for both the science operations and the different maneuvers necessary to maintain LPF on its orbit around L1. It is therefore concluded that a similar cold gas system would be a viable propulsion system for the future LISA mission.

LISA Pathfinder platform stability and drag-free performance

The science operations of the LISA Pathfinder mission has demonstrated the feasibility of sub-femto-g free-fall of macroscopic test masses necessary to build a LISA-like gravitational wave observatory in space. While the main focus of interest, i.e. the optical axis or the $x$-axis, has been extensively studied, it is also of interest to evaluate the stability of the spacecraft with respect to all the other degrees of freedom. The current paper is dedicated to such a study, with a focus set on an exhaustive and quantitative evaluation of the imperfections and dynamical effects that impact the stability with respect to its local geodesic. A model of the complete closed-loop system provides a comprehensive understanding of each part of the in-loop coordinates spectra. As will be presented, this model gives very good agreements with LISA Pathfinder flight data. It allows one to identify the physical noise source at the origin and the physical phenomena underlying the couplings. From this, the performances of the stability of the spacecraft, with respect to its geodesic, are extracted as a function of frequency. Close to $1 mHz$, the stability of the spacecraft on the $X_{SC}$, $Y_{SC}$ and $Z_{SC}$ degrees of freedom is shown to be of the order of $5.0\ 10^{-15} m\ s^{-2}/\sqrt{Hz}$ for X and $4.0 \ 10^{-14} m\ s^{-2}/\sqrt{Hz}$ for Y and Z. For the angular degrees of freedom, the values are of the order $3\ 10^{-12} rad\ s^{-2}/\sqrt{Hz}$ for $\Theta_{SC}$ and $3\ 10^{-13} rad\ s^{-2}/\sqrt{Hz}$ for $H_{SC}$ and $\Phi_{SC}$.

Forbush Decreases and <2 Day GCR Flux Non-recurrent Variations Studied with LISA Pathfinder

Abstract Non-recurrent short-term variations of the galactic cosmic-ray (GCR) flux above 70 MeV n−1 were observed between 2016 February 18 and 2017 July 3 on board the European Space Agency LISA Pathfinder (LPF) mission orbiting around the Lagrange point L1 at 1.5 × 106 km from Earth. The energy dependence of three Forbush decreases is studied and reported here. A comparison of these observations with others carried out in space down to the energy of a few tens of MeV n−1 shows that the same GCR flux parameterization applies to events of different intensity during the main phase. FD observations in L1 with LPF and geomagnetic storm occurrence are also presented. Finally, the characteristics of GCR flux non-recurrent variations (peaks and depressions) of duration <2 days and their association with interplanetary structures are investigated. It is found that, most likely, plasma compression regions between subsequent corotating high-speed streams cause peaks, while heliospheric current sheet crossing causes the majority of the depressions.

Space-based gravitational wave detection and how LISA Pathfinder successfully paved the way

In 2016 and 2017, the LISA Pathfinder mission successfully proved that the technologies for the space-based gravitational wave detector LISA are ready. LISA is now scheduled to launch in the early 2030s, to open a so far unexploited scientific field.

Detecting gravitational wave bursts with LISA in the presence of instrumental glitches

The Laser Interferometer Space Antenna (LISA) will open a rich discovery space in the milli-Hertz gravitational wave band. In addition to the anticipated signals from many millions of binary systems, this band may contain new and previously un-imagined sources for which we currently have no models. To detect unmodeled and unexpected signals we need to be able to separate them from instrumental noise artifacts, or glitches. Glitches are a regular feature in the data from ground based laser interferometers, and they were also seen in data from the LISA Pathfinder mission. In contrast to the situation on ground, we will not have the luxury of having multiple independent detectors to help separate unmodeled signals from glitches, and new techniques have to be developed. Here we show that unmodeled gravitational wave bursts can be detected with LISA by leveraging the different way in which instrument glitches and gravitational wave bursts imprint themselves in the time-delay interferometery data channels. We show that for signals with periods longer than the light travel time between the spacecraft, the "breathing mode" or Sagnac data combination is key to detection. Conversely, for short period signals it is the time of arrival at each spacecraft that aids separation. We investigate the conditions under which we can distinguish the origin of signals and glitches consisting of a single sine-Gaussian wavelet and determine how well we can characterize the signal. We find that gravitational waves bursts can be unambiguously detected and characterized with just a single data channel (four functioning laser links), though the signal separation and parameter estimation improve significantly when all six laser links are operational.

Secular gravity gradients in non-dynamical Chern\u2013Simons modified gravity for satellite gradiometry measurements

With continuous advances in related technologies, precision tests of modern gravitational theories with orbiting gradiometers becomes feasible, which may naturally be incorporated into future satellite gravity missions. In this work, we derive, at the post-Newtonian level, the new secular gravity gradient signals from the non-dynamical Chern–Simons modified gravity for satellite gradiometry measurements, which may be exploited to improve the constraints on the mass scale M_{CS} or the corresponding length scale {dot{theta }} of the theory with future missions. For orbiting superconducting gradiometers, a bound M_{CS}ge 10^{-7} mathrm{eV} and {dot{theta }} le 1 mathrm{m} could in principle be obtained, and for gradiometers with optical readout based on the similar technologies established in the LISA PathFinder mission, an even stronger bound M_{CS}ge 10^{-6}–10^{-5} mathrm{eV} and {dot{theta }} le 10^{-1}–10^{-2} mathrm{m} might be expected.