Space Gravitational Wave Detection Research Articles

Gravitational waves produced by domain walls during inflation

We study the properties of the stochastic gravitational-wave background (SGWB) produced by domain walls (DWs) during inflation without forming a network. We numerically simulate the DW production caused by a second-order phase transition and calculate the SGWB spectrum using a 1000×1000×1000 lattice. We show that the SGWB can be observed directly by future terrestrial and space gravitational-wave detectors and through the B-mode spectrum in the cosmic microwave background. With numerical simulations, we derive an empirical formula for the strength and qualitative features of the SGWB spectrum. The details of the SGWB spectrum also contain information about the later evolution of the Universe. Published by the American Physical Society 2024

Experimental demonstration of constant amplitude modulation heterodyne interferometry.

In the space gravitational wave detection, numerous laser interferometer strategies have been proposed to reduce the complexity of traditional heterodyne interferometers. Previously, we proposed a novel interferometric strategy and simulated its effectiveness, called CAM (constant amplitude modulation) heterodyne interferometry. Compared with other methods, the CAM can introduce the OPT (optical pilot tone) for the common-mode noise rejection. In this paper, we present the first, to our knowledge, experimental verification of this technique. The experimental results indicate that OPT can successfully eliminate sampling jitter, enabling the corrected noise to meet the requirements of space gravitational wave detection. This provides a new approach for further optical optimization and noise elimination in the future.

Research on High-Stability Composite Control Methods for Telescope Pointing Systems under Multiple Disturbances.

During the operation of space gravitational wave detectors, the constellation configuration formed by three satellites gradually deviates from the ideal 60° angle due to the periodic variations in orbits. To ensure the stability of inter-satellite laser links, active compensation of the breathing angle variation within the constellation plane is achieved by rotating the optical subassembly through the telescope pointing mechanism. This paper proposes a high-performance robust composite control method designed to enhance the robust stability, disturbance rejection, and tracking performance of the telescope pointing system. Specifically, based on the dynamic model of the telescope pointing mechanism and the disturbance noise model, an H∞ controller has been designed to ensure system stability and disturbance rejection capabilities. Meanwhile, employing the method of an H∞ norm optimized disturbance observer (HODOB) enhances the nonlinear friction rejection ability of the telescope pointing system. The simulation results indicate that, compared to the traditional disturbance observer (DOB) design, utilizing the HODOB method can enhance the tracking accuracy and pointing stability of the telescope pointing system by an order of magnitude. Furthermore, the proposed composite control method improves the overall system performance, ensuring that the stability of the telescope pointing system meets the 10 nrad/Hz1/2 @0.1 mHz~1 Hz requirement specified for the TianQin mission.

Multi-frequency signal acquisition and phase measurement in space gravitational wave detection.

To enhance the accuracy of phase measurement and to prevent tracking errors, it is crucial to effectively read the multi-frequency signal in space gravitational wave detection. In this paper, a novel signal acquisition method called the multi-frequency acquisition algorithm is proposed and implemented. Different from the traditional single-frequency acquisition, the signal characteristics of amplitude and frequency are both considered to better distinguish different frequency components. A phasemeter integrated with the acquisition method and narrow-bandwidth digital phase-locked loop is constructed for the method test and verification. The results show that the multi-frequency acquisition unit can capture all the frequencies of an input signal in several milliseconds. The precision is better than ±200Hz under a low SNR (signal-to-noise ratio) of 0 dB. The phase noise can reach 2 µrad/Hz1/2 in the frequency range of 0.1-1Hz and satisfy the requirement of the space gravitational wave detection in all frequency ranges.

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.

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.

LISA and LISA-like mission test-mass charging for gamma-ray burst detection

Cubic gold-platinum test-masses (TMs) play the role of free-falling geodesic reference and interferometer end mirrors of the future Laser Interferometer Space Antenna (LISA) observatory for low-frequency gravitational wave detection in space. A similar arrangement has been proposed for the Chinese missions Taiji and TianQin and for the LISA follow-on missions such as ALIA and BBO. The TMs are charged by high-energy particles and photons. The deposited charge couples with stray electric fields surrounding the TMs thus inducing spurious forces that limit the sensitivity of the mission mainly at low frequencies. The TM charging was measured in space in 2016-2017 with LISA Pathfinder (LPF), meant for the testing of the LISA instrumentation. Unfortunately, during the time LPF remained in orbit, no solar energetic particle events or major astrophysical phenomena were observed. We aim at estimating the LISA TM charging attributable to long, short gamma-ray bursts (GRBs) and magnetar flares in comparison to that of charged particles of galactic and solar origin. The contribution of these major astrophysical phenomena to the LISA TM charging is discussed here for the first time. The results found here can be extended to LISA-like missions. The response of the radiation monitors hosted on the three LISA S/C is also evaluated. We show that long, intense extragalactic GRBs and galactic magnetar flares at kpc distances can be detected and monitored through a sudden change from positive to negative charging of the TMs and an increase of the TM charging noise. This is a unique signature since both galactic and solar particles charge positively the LISA TMs. This peculiar behavior of the TM charging would allow monitoring the whole dynamics of GRBs. The suggestion reported in the literature, about the detection of long GRBs and gravitational waves from the same sources, in principle, may apply to LISA and other LISA-like missions since the increase of the TM charging noise during these extreme transient phenomena is estimated to remain below the mission sensitivity while particle detectors are expected to saturate.

Improving the environmental temperature adaptability of an electric temperature measurement subsystem by matching temperature coefficients of substitutable resistors

The electrical temperature measurement subsystem in space gravitational wave detectors requires micro-Kelvin precision in the submillihertz band. However, the low-frequency stability of the measurement circuit, excluding the sensor, is susceptible to environmental temperature fluctuations, closely related to the residual temperature coefficient of the circuit. This paper proposes a method to minimize the residual temperature coefficient for a thermistor-based temperature measurement , enabling the circuit to be mounted on surfaces with less stringent thermal stability requirements. Through extensive testing of resistors with the same nominal resistance, a best-matched pair is selected to compensate for the residual temperature coefficient by replacing two gain resistors in the low-pass filter. Our assessment demonstrates that this matching and replacement process reduces the residual temperature coefficient of the circuit from −0.135 mV K−1 to −0.027 mV K−1, resulting in a significant five-fold improvement in the subsystem’s adaptability to environmental temperatures within the specified frequency band. This method contributes to the development of measurement subsystems that meet stringent stability requirements.

Noise and thermal performance of a sub-attofarad capacitance sensor for precision measurements, with applications in gravitational wave detectors.

We describe the design principles, fabrication, and characterization of a precision AC resonant capacitance bridge (RCB) sensor, based on a resonant differential planar printed circuit board transformer with a solid (ungapped) MnZn ferrite core, demonstrating a short-term sensitivity at 293K of 0.225 ± 0.005 aF/√Hz at around 120kHz resonance frequency and 1Hz Fourier measurement frequency. At 120K, the RCB short term noise sensitivity is 0.118 ± 0.005 aF/√Hz. We compare the ungapped configuration to five different RCBs: three with a core gap of 65 μm and two with a core gap of 130 μm. Their average room temperature short term noise sensitivities are 0.30 ± 0.01 and 0.45 ± 0.01 aF/√Hz, while the cryogenic operation of these transformers at 120K resulted in averaged sensitivities of 0.23 ± 0.01 and 0.36 ± 0.01 aF/√Hz, respectively. Multi-hour room temperature runs, with one core of each of the three gap types, proved the stability of their long-term sensitivities of 0.234 ± 0.005, 0.338 ± 0.009, and 0.435 ± 0.010 aF/√Hz for the ungapped (40-h duration) and the 65 and 130 μm (28-h duration) cores, respectively. At 0.1mHz, a critical frequency for space gravitational wave detectors, the respective sensitivities are 0.25 ± 0.02, 0.35 ± 0.02, and 0.53 ± 0.07 aF/√Hz. Measurements with the ungapped transformer configuration for temperatures from 325 to 349K further validate the dependence of the noise model on temperature and permeability. The performance of our RCB with an ungapped core matches the calculated performance value and shows an improvement in signal-to-noise ratio of two or more compared with capacitance bridges developed for similar applications. A further factor of about two noise reductions is achieved by cooling to 120K.

Dynamic test of the continuously variable weak force by a torsion pendulum with pre-applied stress

High-precision, continuously variable weak force testing is required for high-precision drag-free control with micro-thrust of spacecrafts, which is a key technology for space gravitational wave detection programs, such as TianQin, LISA, and Taiji. The continuously variable micro-thrust range is 0.1∼100μN, and the noise is below 0.1 μNHz−1/2 from 10−4Hz to 1 Hz. The torsion pendulum is considered as the most classical weak force measurement tool. However, the large response of non-sensitive modes makes it unsuitable for dynamic weak force measurements. In this study, a dynamic test system is developed for continuously varying weak forces using a torsion pendulum. We pre-applied a stress to the torsion pendulum using a double wire structure, which can effectively reduce the interference of other modes, and used feedback control to improve the stability. The evaluation results obtained using the external continuously variable electrostatic force indicate that the measurement range of the system covers 100 μN, the response time is approximately 1.6 s, and the noise is below 0.1 μNHz−1/2 from 0.9×10−4Hz to 1.4 Hz, which can meet the requirements of the micro-thrust test in space gravitational wave detection missions.

High-Precision Inertial Sensor Charge Ground Measurement Method Based on Phase-Sensitive Demodulation

Inertial sensors are the key payloads in space gravitational wave detection missions, and they need to ensure that the test mass (TM), which serves as the inertial reference, freely floats in the spacecraft without contact, so that the TM is not disturbed by the satellite platform and the cosmic environment. Space gravitational wave detection missions require that the residual acceleration of the TM should be less than 3×10−15ms−2Hz−1/2. However, the TM with charges will interact with surrounding conductors and magnetic fields, introducing acceleration noise such as electrostatic force and Lorentz force. Therefore, it is necessary to carry out charge management on the TM, in which the high-precision measurement of charge is crucial. Space gravitational wave detection missions require a residual charge measurement accuracy of 3×10−13C for the TM. In this paper, we design a high-precision inertial sensor charge measurement method based on phase-sensitive demodulation (PSD). By establishing a torsion pendulum rotation model based on the force modulation method, the characteristics of the TM torsion angle signal are analyzed. The PSD is used to extract the amplitude of the specific frequency signal component containing the charge information, and then to calculate the value of the accumulated charges. The method is compared with the Butterworth band-pass filtering method, and the simulation results show that the method has a higher measurement accuracy, shorter settling time, and stronger anti-interference ability, meeting the TM residual charge measurement accuracy index requirement.

Research and analysis of a laser pointing jitter noise suppression system more compatible with space gravitational wave detection

Research and analysis of a laser pointing jitter noise suppression system more compatible with space gravitational wave detection

Study of the thrust response characteristics of Hall Micro Thruster

An advanced Watt class Hall Micro Thruster (HMT) is offered for Space Gravitational Wave Detection (SGWD), and an investigation has been conducted on its start-up, shutdown, rise, and fall response times. The research involved creating a circuit for thruster discharge and signal acquisition, using a Faraday probe to measure the plasma plume signal generated by the thruster, and characterizing the thrust directly. Ultimately the response time of the thruster is extracted from the discharge current and Faraday current signals. The experimental results demonstrate that the HMT has a response time ranging from 1.08 ms to 16.76 ms at mass flow rates of 0.02 mg/s and 0.04 mg/s, meeting the SGWD requirements for micro thruster response time. This research provides a physical foundation and explanation for the variation of HMT response time with discharge voltage versus mass flow rate with several key parameters that affect HMT plasma discharge, such as neutral gas number density (nn) and ionization mean free path (λi). Furthermore, we have examined several anomalies in the signal. Overall, this research provides a brand-new method for measuring the thrust response time of electric thrusters.

Measurement of the Optical Path Difference Caused by Steering Mirror Using an Equal-Arm Heterodyne Interferometer

In space gravitational wave detection, the inter-satellite link-building process requires a type of steering mirror to achieve point-ahead angle pointing. To verify that the background noise does not drown out the gravitational wave signal, this paper designed a laser heterodyne interferometer specifically designed to measure the optical path difference of the steering mirror. Theoretically, the impact of angle and position jitter is analyzed, which is called tilt-to-length (TTL) coupling. This interferometer is based on the design concept of equal-arm length. In a vacuum (10−3 Pa), vibration isolation (up to 1 Hz), and temperature-controlled (approximately 10 mK) experimental environment, the accuracy is increased by about four orders of magnitude through a common-mode suppression approach and can reach 390 pm/Hz when the frequency is between 1 mHz and 1 HZ. By analogy, the optical path difference caused by the steering mirror reaches 5 pm/Hz in the 1 mHz to 1 Hz frequency band. The proposed TTL noise model is subsequently verified.

The impact of telescope aberrations on the magnitude of tilt to length coupling noise in space based gravitational wave detectors

Tilt-to-length (TTL) coupling noise is one of the main noise sources that affect space gravitational wave detection, and the Tianqin project requires that the internal TTL coupling noise of the telescope used be less than 0.4 pm/Hz1/2 within the frequency band from 0.1 mHz to 1 Hz. In order to design a telescope that meets the requirements of TTL coupling noise and carry out preliminary error allocation research, it is necessary to analyze and calculate the TTL coupling noise, and then guide the design and optimization of the telescope system. This paper establishes a computational analysis model for the non-geometric TTL coupling noise inside the telescope using the first 36-order edge Zernike polynomials. A method was proposed to reduce the internal TTL coupling noise of the telescope by reducing the proportion of sensitive aberrations caused by non-geometric TTL coupling noise. Simulation results show that, with the RMS value of wavefront aberration at the telescope exit pupil unchanged, reducing the proportion of sensitive aberrations at the telescope exit pupil can effectively reduce the internal TTL coupling noise of the telescope. By optimizing the telescope optical system to reduce the proportion of noise-sensitive aberrations, the non-geometric TTL coupling noise inside the telescope has been reduced from 0.34 pm/Hz1/2 @ 0.1 mHz ∼ 1 Hz to 0.25 pm/Hz1/2. This result can provide some guidance for the design of telescope optics based on the suppression of internal TTL coupling noise in the telescope.

Design and Construction of the Optical Bench Interferometer for the Taiji Program.

A kind of full-function two-sided optical bench interferometer (OBI) is designed to meet the practical requirements of the Taiji Program for space gravitational wave detection. The main optical paths are arranged on the A-side for transmission and interference, and other optical paths and electronic devices are placed on the B-side. According to the design scheme, we successfully constructed two OBIs by using hydrogen-oxygen catalytic stress-free bonding technology. When the OBI is installed and adjusted, the position and Angle error of the interference beam are controlled within 30 μm and 50 μrad through the self-designed precision mechanical clamping mechanism and beam position measuring device. The built OBI was placed on the vibration isolation platform in the vacuum tank for the stability test. The test results show that the noise of the OBI is less than 10 pm/√Hz in the frequency band of 0.1 Hz to 1 Hz, which meets the noise budget requirements of the Taiji Pathfinder in the middle- and high-frequency band.

Research and Implementation of a Demodulation Switch Signal Phase Alignment System in Dynamic Environments.

In the space gravitational wave detection mission, inertial sensors play the role of providing an inertial reference for the laser interferometric measurement system. Among them, the capacitance sensor serves as the core key technology of the inertial sensor, used to measure the relative position of the test mass (TM) in the electrode cage. The capacitance sensor utilizes synchronous demodulation technology to extract signals from the AC induction signal. When the phase of the demodulation switch signal is aligned, the synchronous demodulator can most effectively filter out noise, thus directly influencing the performance of the capacitance sensor. However, since the TM is in a suspended state, the information read by the capacitance sensor is dynamic, which increases the difficulty of demodulation phase alignment. In light of this, a method is proposed for achieving the phase alignment of the demodulation switch signal in a dynamic environment. This is accomplished by adjusting the phase of the demodulation switch signal, and subsequently computing the phase difference between the AC induction signal and the demodulation switch signal. At the same time, a measurement and evaluation method for phase deviation is also proposed. Ultimately, an automatic phase alignment system for the demodulation switch signal in dynamic environments is successfully implemented on an FPGA platform, and tests are conducted on a hexapod PI console platform to simulate dynamic environments. The experimental results demonstrate that the system accurately achieves phase alignment in the static environment, with a phase deviation of 0.1394 rad. In the simulated dynamic environment, the phase deviation is 0.1395 rad.

Method Comparison for Simulating Non-Gaussian Beams and Diffraction for Precision Interferometry.

In the context of simulating precision laser interferometers, we use several examples to compare two wavefront decomposition methods-the Mode Expansion Method (MEM) and the Gaussian Beam Decomposition (GBD) method-for their precision and applicability. To assess the performance of these methods, we define different types of errors and study their properties. We specify how the two methods can be fairly compared and based on that, compare the quality of the MEM and GBD through several examples. Here, we test cases for which analytic results are available, i.e., non-clipped circular and general astigmatic Gaussian beams, as well as clipped circular Gaussian beams, in the near, far, and extremely far fields of millions of kilometers occurring in space-gravitational wave detectors. Additionally, we compare the methods for aberrated wavefronts and their interaction with optical components by testing reflections from differently curved mirrors. We find that both methods can generally be used for decomposing non-Gaussian beams. However, which method is more accurate depends on the optical system and simulation settings. In the given examples, the MEM more accurately describes non-clipped Gaussian beams, whereas for clipped Gaussian beams and the interaction with surfaces, the GBD is more precise.

Experimental study on beam characteristics of μHT-1 thruster under operating conditions adjustment

The micro Hall thruster μHT-1 is designed for space gravitational wave detection missions, and the beam characteristics of the thruster are studied by experiments. A Faraday probe mounted on a three-dimensional moving platform is designed for diagnosing to obtain the beam current density distribution, and the operating conditions of the discharge voltage and the mass flow rate are adjusted in the range of 700∼1200 V and 0.1–0.5 sccm, respectively. In addition, the study further analyze the variation trends of total beam current, discharge current, utilization rate, divergence angle and others. The test results indicate that the μHT-1 thruster can work stably in a wide range of operating conditions, and the beam current expresses a good axisymmetric distribution. Meanwhile, the beam current density gradually decreases along the axial direction and spreads along the radial direction. The current utilization efficiency fluctuates from 53.4 % to 67.7 % when the power is adjusted in the range of 1.45–5.76 W, and the divergence angle increases from 41.3° to 56.7°. The total beam current of the thruster shows a linear increase characteristics with the enhancing of the anode flow and the discharge voltage.

Non-Magnetic Negative Coefficient of Thermal Expansion Support Structure between Payloads in the Taiji Space Gravitational Wave Detection Satellite

The support structure between payloads is an important part of a space gravitational wave detection satellite, and its thermal stability will directly affect the interferometer’s measurement accuracy. However, due to temperature changes, the connecting structure between the loads will generate deformation, and a support structure with the coefficient of thermal expansion (CTE) of −1 × 10−6/K will thus need to be designed to counteract this thermal deformation. In order to solve this problem, this paper adopts the method of mutual offsetting of the thermal deformation of different materials to design a thermally stable support structure satisfying this negative CTE. The structure was optimized by the arithmetic of non-linear programming by the quadratic Lagrangian hybrid algorithm (NLPQL), and the structural parameter satisfying the CTE of −1.008 × 10−6/K was obtained. Meanwhile, the effect of the change in the thermal expansion coefficient of each material on the overall structure under this parameter was sampled and calculated. Moreover, the experimental results show that the CTE of the support structure under the optimized parameters was −1.114 × 10−6/K, which differs from the simulation results by 9.5%.