A precise characterization of the magnetic properties of LISA Pathfinder free falling test-masses is of special interest for future gravitational wave observatory in space. Magnetic forces have an important impact on the instrument sensitivity in the low frequency regime below the millihertz. In this paper we report on the magnetic injection experiments performed throughout LISA Pathfinder operations. We show how these experiments allowed a high precision estimate of the instrument magnetic parameters. The remanent magnetic moment was found to have a modulus of (0.245 + 0.081) nAm2, the x-component of the background magnetic field within the test masses position was measured to be (414 + 74) nT and its gradient had a value of (-7.4 + 2.1) mu T/m. Finally, we also measured the test mass magnetic susceptibility at 5 mHz to be (-3.3723 + 0.0069) x 10-5. All results are in agreement with on-ground estimates.

LISA Pathfinder was a mission designed to test key technologies required for gravitational wave detection in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime, which corresponds to the measurement band of interest for future space-borne gravitational wave observatories. Magnetically induced forces couple to the test mass motion, introducing a contribution to the relative acceleration noise between the free-falling test masses. In this Letter we present the first complete estimate of this term of the instrument performance model. Our results set the magnetic-induced acceleration noise during the February 2017 noise run of 0.25_{-0.08}^{+0.15}  fm s^{-2}/sqrt[Hz] at 1 mHz and 1.01_{-0.24}^{+0.73}  fm s^{-2}/sqrt[Hz] at 0.1 mHz. We also discuss how the nonstationarities of the interplanetary magnetic field can affect these values during extreme space weather conditions.

The LISA Pathfinder (LPF) mission successfully demonstrated the feasibility of the technology needed for the future space borne gravitational wave observatory LISA. A key subsystem under study was the laser interferometer, which measured the changes in relative distance in between two test masses (TMs). It achieved a sensitivity of 32.0 thorn 2.4 -1.7 fm=ffiffiffiffiffiA/Hz, which was significantly better than the prelaunch tests. This improved performance allowed direct observation of the influence of laser frequency noise in the readout. The differences in optical path lengths between the measurement and reference beams in the individual interferometers of our setup determined the level of this undesired readout noise. Here, we discuss the dedicated experiments performed on LPF to measure these differences with high precision. We reached differences in path length difference between (368 +/- 5) mu m and (329.6 +/- 0.9) mu m which are significantly below the required level of 1 mm or 1000 mu m. These results are an important contribution to our understanding of the overall sensor performance. Moreover, we observed varying levels of laser frequency noise over the course of the mission. We provide evidence that these do not originate from the laser frequency stabilization scheme which worked as expected. Therefore, this frequency stabilization would be applicable to other missions with similar laser frequency stability requirements.

Electrostatic force actuation is a key component of the system of geodesic reference test masses (TM) for the LISA orbiting gravitational wave observatory and in particular for performance at low frequencies, below 1 mHz, where the observatory sensitivity is limited by stray force noise. The system needs to apply forces of order 10$^{-9}$ N while limiting fluctuations in the measurement band to levels approaching 10$^{-15}$ N/Hz$^{1/2}$. We present here the LISA actuation system design, based on audio-frequency voltage carrier signals, and results of its in-flight performance test with the LISA Pathfinder test mission. In LISA, TM force actuation is used to align the otherwise free-falling TM to the spacecraft-mounted optical metrology system, without any forcing along the critical gravitational wave-sensitive interferometry axes. In LISA Pathfinder, on the other hand, the actuation was used also to stabilize the TM along the critical $x$ axis joining the two TM, with the commanded actuation force entering directly into the mission's main differential acceleration science observable. The mission allowed demonstration of the full compatibility of the electrostatic actuation system with the LISA observatory requirements, including dedicated measurement campaigns to amplify, isolate, and quantify the two main force noise contributions from the actuation system, from actuator gain noise and from low frequency ``in band'' voltage fluctuations. These campaigns have shown actuation force noise to be a relevant, but not dominant, noise source in LISA Pathfinder and have allowed performance projections for the conditions expected in the LISA mission.

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

The LISA Pathfinder (LPF) mission successfully demonstrated the feasibility of the technology needed for the future space borne gravitational wave observatory LISA. A key subsystem under study was the laser interferometer, which measured the changes in relative distance in between two test masses (TMs). It achieved a sensitivity of 32.0−1.7+2.4 fm/Hz, which was significantly better than the prelaunch tests. This improved performance allowed direct observation of the influence of laser frequency noise in the readout. The differences in optical path lengths between the measurement and reference beams in the individual interferometers of our setup determined the level of this undesired readout noise. Here, we discuss the dedicated experiments performed on LPF to measure these differences with high precision. We reached differences in path length difference between (368±5) μm and (329.6±0.9) μm which are significantly below the required level of 1 mm or 1000 μm. These results are an important contribution to our understanding of the overall sensor performance. Moreover, we observed varying levels of laser frequency noise over the course of the mission. We provide evidence that these do not originate from the laser frequency stabilization scheme which worked as expected. Therefore, this frequency stabilization would be applicable to other missions with similar laser frequency stability requirements.2 MoreReceived 2 October 2023Accepted 9 January 2024DOI:https://doi.org/10.1103/PhysRevD.109.042003Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasGravitational wave detectionMetrologyNoiseOptics & lasersPhysical SystemsLaser applicationsTechniquesData analysisGravitational wave detectorsOptical interferometrySatellite data analysisGravitation, Cosmology & AstrophysicsAtomic, Molecular & Optical

We present an in-depth analysis of the LISA Pathfinder differential acceleration performance over the entire course of its science operations, spanning approximately 500 days. We find: (1) The evolution of the Brownian noise that dominates the acceleration amplitude spectral density (ASD), for frequencies f greater than or similar to 1 mHz, is consistent with the decaying pressure due to the outgassing of a single gaseous species. (2) Between f = 36 mu Hz and 1 mHz, the acceleration ASD shows a 1/f tail in excess of the Brownian noise of almost constant amplitude, with similar or equal to 20% fluctuations over a period of a few days, with no particular time pattern over the course of the mission. (3) At the lowest considered frequency of f = 18 mu Hz, the ASD significantly deviates from the 1/f behavior, because of temperature fluctuations that appear to modulate a quasistatic pressure gradient, sustained by the asymmetries of the outgassing pattern. We also present the results of a projection of the observed acceleration noise on the potential sources for which we had either a direct correlation measurement or a quantitative estimate from dedicated experiments. These sources account for approximately 40% of the noise power in the 1/f tail. Finally, we analyze the possible sources of the remaining unexplained fraction and identify the possible measures that may be taken to keep those under control in LISA.

We present a study of the tilt-to-length coupling noise during the LISA Pathfinder mission and how it depended on the system's alignment. Tilt-to-length coupling noise is the unwanted coupling of angular and lateral spacecraft or test mass motion into the primary interferometric displacement readout. It was one of the major noise sources in the LISA Pathfinder mission and is likewise expected to be a primary noise source in LISA. We demonstrate here that a recently derived and published analytical model describes the dependency of the LISA Pathfinder tilt-to-length coupling noise on the alignment of the two freely falling test masses. This was verified with the data taken before and after the realignments performed in March (engineering days) and June 2016, and during a two-day experiment in February 2017 (long cross-talk experiment). The latter was performed with the explicit goal of testing the tilt-to-length coupling noise dependency on the test mass alignment. Using the analytical model, we show that all realignments performed during the mission were only partially successful and explain the reasons why. In addition to the analytical model, we computed another physical tilt-to-length coupling model via a minimizing routine making use of the long cross-talk experiment data. A similar approach could prove useful for the LISA mission.

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.

In a previous article [1], we have reported on the first subpicometer interferometer flown in space as part of ESA's LISA Pathfinder mission, and have shown the residual sensor noise to be on the level of 32.0 thorn 2.4 -1.7 fm/ . This review provides a deeper and more complete overview of the full system and its ffiffiffiffiffiHz interferometric mission performance under varying operational conditions, allowing a much more detailed view on the noise model. We also include the optical measurements of rotations through differential wave ffiffiffiffiffifront sensing (DWS), which reached a sensitivity of as good as 100 prad/ Hz. We present more evidence for the long-term stability of the interferometric performance and components. This proves a solid foundation for future interferometry in space such as the LISA mission.

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. We aim to bridge the gap between LPF TM charging noise simulations and observations. 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. 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.

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.

We present an in depth analysis of the transient events, or glitches, detected at a rate of about one per day in the differential acceleration data of LISA Pathfinder. We show that these glitches fall in two rather distinct categories: fast transients in the interferometric motion readout on one side, and true force transient events on the other. The former are fast and rare in ordinary conditions. The second may last from seconds to hours and constitute the majority of the glitches. We present an analysis of the physical and statistical properties of both categories, including a cross-analysis with other time series like magnetic fields, temperature, and other dynamical variables. Based on these analyses we discuss the possible sources of the force glitches and identify the most likely, among which the outgassing environment surrounding the test-masses stands out. We discuss the impact of these findings on the LISA design and operation, and some risk mitigation measures, including experimental studies that may be conducted on the ground, aimed at clarifying some of the questions left open by our analysis.

LISA Pathfinder is a technology demonstrator space mission, aimed at testing key technologies for detecting gravitational waves in space. The mission is the precursor of LISA, the first space gravitational waves observatory, whose launch is scheduled for 2034. The LISA Pathfinder scientific payload includes two gravitational reference sensors (GRSs), each one containing a test mass (TM), which is the sensing body of the experiment. A mission critical task is to set each TM into a pure geodesic motion, i.e. guaranteeing an extremely low acceleration noise in the sub-Hertz frequency bandwidth. The grabbing positioning and release mechanism (GPRM), responsible for the injection of the TM into a geodesic trajectory, was widely tested on ground, with the limitations imposed by the 1-g environment. The experiments showed that the mechanism, working in its nominal conditions, is capable of releasing the TM into free-fall fulfilling the very strict constraint imposed on the TM residual velocity, in order to allow its capture on behalf of the electrostatic actuation. However, the first in-flight releases produced unexpected residual velocity components, for both the TMs. Moreover, all the residual velocity components were greater than maximum value set by the requirements. The main suspect is that unexpected contacts took place between the TM and the surroundings bodies. As a consequence, ad hoc manual release procedures had to be adopted for the few following injections performed during the nominal mission. These procedures still resulted in non compliant TM states which were captured only after impacts. However, such procedures seem not practicable for LISA, both for the limited repeatability of the system and for the unmanageable time lag of the telemetry/telecommand signals (about 4400 s). For this reason, at the end of the mission, the GPRM was deeply tested in-flight, performing a large number of releases, according to different strategies. The tests were carried out in order to understand the unexpected dynamics and limit its effects on the final injection. Some risk mitigation maneuvers have been tested aimed at minimizing the vibration of the system at the release and improving the alignment between the mechanism and the TM. However, no overall optimal release strategy to be implemented in LISA could be found, because the two GPRMs behaved differently. (C) 2020 COSPAR. Published by Elsevier Ltd. All rights reserved.

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 200 mHz.

Electrostatic actuation of a free-floating test-mass was tested in the Laser Interferometer Space Antenna (LISA) Pathfinder mission, and it will be integrated into the LISA. We have investigated the LISA Pathfinder actuation accuracy with respect to the precision of fractional digits in the field programmable gate array (FPGA) code of actuation electronics. The LISA Pathfinder data showed that the rounding errors in the FPGA code result in an erroneous force that contaminated the main mission observable, and this error was compensated in the post-processing of the LISA Pathfinder data. To avoid a similar issue for the LISA, the LISA actuation accuracy can be improved by increasing the number of fractional digits in the FPGA code. However, this is restricted by some hardware limitations. In this paper, we investigate the necessary enlargement of the FPGA to fulfill the LISA acceleration requirements and propose a design optimization for LISA actuation electronics.

ABSTRACT LISA Pathfinder (LPF) has been a space-based mission designed to test new technologies that will be required for a gravitational wave observatory in space. Magnetically driven forces play a key role in the instrument sensitivity in the low-frequency regime (mHz and below), the measurement band of interest for a space-based observatory. The magnetic field can couple to the magnetic susceptibility and remanent magnetic moment from the test masses and disturb them from their geodesic movement. LPF carried on-board a dedicated magnetic measurement subsystem with noise levels of 10 $\rm nT \ Hz^{-1/2}$ from 1 Hz down to 1 mHz. In this paper we report on the magnetic measurements throughout LPF operations. We characterize the magnetic environment within the spacecraft, study the time evolution of the magnetic field and its stability down to 20 μHz, where we measure values around 200 $\rm nT \ Hz^{-1/2}$, and identify two different frequency regimes, one related to the interplanetary magnetic field and the other to the magnetic field originating inside the spacecraft. Finally, we characterize the non-stationary component of the fluctuations of the magnetic field below the mHz and relate them to the dynamics of the solar wind.

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 similar to 0.17 mu N/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 similar to 20 mu Hz, more than an order of magnitude below any ground measurement. Spectral lines were observed around similar to 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 similar to 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.

We present two novel methods, tested by LISA Pathfinder, to measure the gravitational constant G for the first time in space. Experiment 1 uses electrostatic suspension forces to measure a change in acceleration of a test mass due to a displaced source mass. Experiment 2 measures a change in relative acceleration between two test masses due to a slowly varying fuel tank mass. Experiment 1 gave a value of G. 6.71 +/- 0.42(x10(-11)) m(3) s(-2) kg(-1) and experiment 2 gave 6.15 +/- 0.35(x10(-11)) m(3) s(-2) kg(-1), both consistent with each other to l sigma and with the CODATA 2014 recommended value of 6.67408 +/- 0.00031(x10(-11)) m(3) s(-2) kg(-1) to 2 sigma. We outline several ideas to improve the results for a future experiment, and we suggest that a measurement in space would isolate many terrestrial issues that could be responsible for the inconsistencies between recent measurements.

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.