Space Gravitational Wave Detection Research Articles

Research on Semi-Physical Simulation Testing of Inter-Satellite Laser Interference in the China Taiji Space Gravitational Wave Detection Program

To guarantee a smooth in-orbit space gravitational wave detection for the Taiji mission, a semi-physical simulation test of inter-satellite laser interference is carried out. The semi-physical simulation test consists of three aspects: the establishment of the inter-satellite laser link, interferometry of the inter-satellite ranging, and simulation of the space environment. With the designed specifications for the semi-physical simulation platform, the test results for the inter-satellite laser interference can be obtained. Based on the semi-physical simulation test, the risks of inter-satellite laser interference technology can be mitigated, laying a solid foundation for the successful detection of in-orbit gravitational waves.

A low frequency horizontal active vibration isolation bench for testing the performance of high-precision space inertial sensors

High-precision space inertial sensors are one of the most important payloads in satellite Earth’s gravity measurement and space-based gravitational wave detection due to their extremely high sensitivity. However, seismic noise affects its terrestrial-based performance validation, so that it is very significant to develop low frequency horizontal vibration isolation system to suppress the impact of seismic noise. In this article, a horizontal active vibration isolation bench for terrestrial-based investigation of space accelerometer is developed, on which the motion in three dimensions is monitored by two tri-axis seismometers and actively controlled by three voice coil motors. The principle and potential performance of this bench are theoretically analyzed and estimated in details. The experimental result shows that the bench can achieve high vibration isolation performance in horizontal translation direction. The residual horizontal vibration noise of this bench due to seismic can be suppressed by about 40 dB at 0.35 Hz. Finally, the potential of this design as a vibration pre-isolation stage to investigate the performance of the inertial sensors dedicated to satellite gravity measurement and space gravitational wave detection is discussed.

Time-frequency-domain method for thrust noise characteristics of electric thrusters

Electric thrusters are considered to be the most promising propulsion system of choice for space gravitational wave detection. However, the requirement of high accuracy and drag-free control results in significant challenges in thrust measurements. To better understand the thrust noise characteristics, this work proposes a time-frequency-domain method for thrust noise analysis, i.e., a scalogram method attained through wavelet analysis. Unlike the conventional Fourier transform method, it can provide 3-D relationships for the time-frequency and thrust noise. A free-state thrust measurement experiment identified that the environmental temperature produces the dominant impact in the thrust noise. During a 70,000 s measurement, even without thruster operation, the thrust noise increased from 0.3 μN/Hz1/2 to 19 μN/Hz1/2 as the environmental temperature increased from −1 °C to 3 °C. The corresponding frequency of peak thrust noise for the entire period tends to be the same of 0.1 Hz. Additionally, a Hall thruster thrust measurement experiment was conducted to verify the method's time-varying analysis capability for thrust noise. The complete time-frequency thrust noise variation throughout the entire operating process of a Hall thruster was observed. The results at different stages of thruster operation indicate that thrust noise has the greatest influence 150–300 s after ignition. This is because the thrust stand will take hundreds of seconds to reach thermal equilibrium after ignition. Another finding during the Hall thruster operation is that the 0.1 Hz frequency corresponding to the peak thrust noise is highly consistent with the frequency of peak thrust noise in the free-state thrust experiment. This reveals the fact that the 0.1 Hz frequency should be the dominant frequency for thrust noise caused by temperature drift in our thrust measurement system.

Thermal Noise Decoupling of Micro-Newton Thrust Measured in a Torsion Balance

The space gravitational wave detection and drag free control requires the micro-thruster to have ultra-low thrust noise within 0.1 mHz–0.1 Hz, which brings a great challenge to calibration on the ground because it is impossible to shield any spurious couplings due to the asymmetry of torsion balance. Most thrusters dissipate heat during the test, making the rotation axis tilt and components undergo thermal drift, which is hysteretic and asymmetric for micro-Newton thrust measurement. With reference to LISA’s research and coming up with ideas inspired from proportional-integral-derivative (PID) control and multi-timescale (MTS), this paper proposes to expand the state space of temperature to be applied on the thrust prediction based on fine tree regression (FTR) and to subtract the thermal noise filtered by transfer function fitted with z-domain vector fitting (ZDVF). The results show that thrust variation of diurnal asymmetry in temperature is decoupled from 24 μN/Hz1/2 to 4.9 μN/Hz1/2 at 0.11 mHz. Additionally, 1 μN square wave modulation of electrostatic force is extracted from the ambiguous thermal drift background of positive temperature coefficient (PTC) heater. The PID-FTR validation is performed with experimental data in thermal noise decoupling, which can guide the design of thermal control and be extended to other physical quantities for noise decoupling.

Drop tower tests of Taiji-1 inertial sensor substitute

Taiji-1, which is the first technical verification satellite of China’s Space Gravitational Wave Detection Program, was successfully launched on August 31, 2019. The mission aimed to investigate the key technologies used in space gravitational wave detection. The inertial sensor, which was one of the main payloads, measured the residual acceleration of the satellite, and verified the drag-free control technology. Its performance was crucial to the success of the Taiji-1 mission. To ensure its performance in orbit, the inertial sensor was fully evaluated prior to launch. Owing to the gravitational acceleration on the ground, it is impossible to verify all the properties of the inertial sensor in a routine laboratory. A feasible method to conduct such tests is to use a drop tower. To guarantee the safety of the inertial sensor, a substitute was used with similar structure and circuit design. A total of 20 falls in three groups were completed, a set of research methods was established, and the importance of conducting simulations before the drop tests was verified. For the first time, the switch of different circuit gains in a drop tower test has been achieved and the National Microgravity Laboratory of China (NMLC) drop tower’s residual accelerations in three dimensions were measured. The results demonstrated that the microgravity level of the drop tower can reach about 58 μg0 in the fall direction and 13 μg0 along the horizontal axes.

Role of plasmons in the LISA test-mass charging process

High-energy particles of galactic and solar origin will charge the test-masses on board laser interferometer space antenna (LISA) and other interferometers for gravitational-wave detection in space. The stochastic noise associated with this charging process is estimated to limit the sensitivity of space interferometers at low frequencies. In a previous paper we have reported a detailed study of low-energy electromagnetic processes affecting the LISA test-mass charging. In particular, we have discussed ionization and electron kinetic emission due to electrons and ions, while the role of plasmons in generating low-energy electrons has been deemed as negligible. Recently, the decay of plasmons has been observed to modify the energy distribution of electrons emitted by ions incident on foils of carbon and gold. Our work is consolidated here accordingly. The contribution of plasmon decay will be considered in future Monte Carlo simulations of LISA test-mass charging in the energy range of a few eV in addition to electron quantum diffraction and backscattering.

Temperature stability of the Taiji-1 satellite in operational orbit

The Taiji-1 satellite is a pioneering space technology mission designed by the Chinese Academy of Science (CAS) to test key technologies required for gravitational wave detection in space. Temperature stability is a critical element because it can couple with the gravitational wave measurement. A dedicated thermal control with a three-level control method was used on the Taiji-1 satellite science module. The simulation analysis shows that the temperature stability control level of its scientific instrument temperature stability can reach ± 1.7 mK. Combined with the in-orbit temperature results, the temperature stability obtained by using the linear smoothing filter and the Kalman filter reached ± 1.1 and ± 0.5 mK, respectively, which were in good concerted with the simulation data, indicating that the thermal control level of Taiji-1satellite science module reached a high precision.

Key technologies analysis and design of ultra-clean & ultra-stable spacecraft for gravitational wave detection

The observation of gravitational wave enables human to explore the origin, formation and evolution of universe governed by the gravitational interaction and the nature of gravity beyond general theory of relativity. The groundbreaking discovery of Gravitational Wave by Laser Interferometer Gravitational-Wave Observatory provides a brand-new observation way. While detecting gravitational wave on ground is limited by noises and test scale, space detection is an optimized alternative to learn rich sources in range of 0.1 mHz–1 Hz. Considering the great significance of space gravitational wave detection, ESA proposed LISA project, CAS also proposed Taiji project. Due to the extremely weak gravitational wave signal and high measurement accuracy requirement, the spaceborne GW observation antenna is accomplished by three spacecrafts constitute isosceles triangle formation intersatellite interferometer. The arm length of the interferometer reaches millions of kilometers between them, and the measurement accuracy reaches pico-meter magnitude. There are many key technologies including pm magnitude space laser interferometer metrology, drag-free control using TM of Gravity Reference Sensor, [Formula: see text]N micro thruster, ultra-clean & ultra-stable spacecraft, etc. This paper focuses on key technologies of the ultra-clean & ultra-stable spacecraft, analyzing the design of mechanical, thermal control and magnetic clean. Moreover, it reports the preliminary results of the technological breakthrough.

Ground performance tests and evaluation of RF ion microthrusters for Taiji-1 satellite

The “Taiji-1” satellite is a test satellite for the verification of those key technologies involved in the “Taiji Program in Space”, China’s space gravitational wave detection project; and the spacecraft drag-free control technology is one of its key technologies used to improve the microgravity level of spacecraft. Thus, a demand for a high-precision and continuously adjustable micronewton-level thrust has been proposed on the spacecraft micro-propulsion system. In allusion to such a task, a set of micronewton-level RF ion propulsion system was designed based on the principle of self-sustained discharge of RF plasma so as to conduct studies on the parameter optimization and engineering of RF ion thruster, and an engineering prototype of the micronewton-level continuously adjustable RF ion thruster was successfully developed to meet the design index requirements. The operating parameters have been solidified through further studies on the extreme operating conditions of the engineering prototype, and a series of ground simulation tests of space environment were successfully passed. The ground test and calibration experiment results of the micro-propulsion engineering prototype show that the engineering prototype has fully met the requirements of the Taiji-1 mission, thus having laid a solid foundation for the successful space verification of the key technologies for the “Taiji-1” satellite.

A temperature measurement system with high resolution and low noise

Due to the temperature fluctuation, both the self-gravity disturbance level of the gravitational wave detection vehicle and the laser interference measurement system are affected, which brings great noise to the gravitational wave measurement, and the temperature field fluctuation has become one of the most important noise sources of the inertial sensor. In order to ensure the noise level of the inertial sensor to meet the needs of detection, this paper uses the AC bridge to reduce the self-noise of the temperature measurement system, improve the resolution of the temperature measurement system, and realize a high-resolution and low-noise temperature measurement system. The experimental results show that the effective value of self-noise of the temperature measurement system is about 3.65 × 10[Formula: see text], and the long-period noise is less than 1 × 10[Formula: see text]. It can be used in the space gravitational wave detection test and control system.

Dependence of the detected signal on the kinematic parameters of the satellite in the S-LIGO-E2R space system

The changes of distances less than ~10–21 are registered during the gravitational wave experiment. This feature determines the minimum size of experimental installations and the frequency range of gravitational wave detectors. To expand the frequency range and increase the sensitivity of gravitational interference detectors, it is necessary to increase the linear dimensions of the detector significantly as big as Earth and even more. The Republic of Belarus has experience in the development, launch and operation of satellites, the use of which can significantly increase the linear dimensions of the gravitational space detector. The satellite systems as a space detector of gravitational waves S-LIGO-NxR-zy are considered. The S-LIGO-NxR-zy space gravitational wave detector is a system of laser interferometers consisting of x number of satellites with given z-type orbits, in orbit of planet N of the solar system. The interferometers in such systems are identical to interferometers with oscillating mirrors due to the complex satellite motion. The purpose of this work is to study the influence of the kinematic parameters of satellites on the detected signal in the S-LIGO-E2R-z2 system. The configuration of the space detector determines the set of satellite orbits, direction and initial phase of movement. The detector signals depend on the instantaneous distance between the satellites and can be described as periodic functions. There are obtained the equations that describe the periodic changes in the signal between satellites as a result of their relative motion, depending on the initial conditions for launching the satellites. The general case for arbitrary oriented orbits and two special cases for collinear and orthogonal circular orbits in space gravitational wave detectors S-LIGO-E2R-z2-p and S-LIGO-E2R-z2-o are considered in the paper. The graphs of the dependences of the detected signal on the kinematic parameters of the satellites of the detectors S-LIGO-E2R-z2-p and S-LIGO-E2R-z2-o are presented. It is shown that the detected signals contain sections of zero intensity, and the duration and frequency of sections of zero intensity are related to the kinematic parameters of satellites.

Orbital evolution of neutron-star–white-dwarf binaries by Roche lobe overflow and gravitational wave radiation

ABSTRACT We investigate the effects of mass transfer and gravitational wave (GW) radiation on the orbital evolution of contact neutron-star–white-dwarf (NS–WD) binaries, and the detectability of these binaries by space GW detectors (e.g. Laser Interferometer Space Antenna, LISA; Taiji; Tianqin). A NS–WD binary becomes contact when the WD component fills its Roche lobe, at which the GW frequency ranges from ∼0.0023 to 0.72 Hz for WD with masses ∼0.05–1.4 M⊙. We find that some high-mass NS–WD binaries may undergo direct coalescence after unstable mass transfer. However, the majority of NS–WD binaries can avoid direct coalescence because mass transfer after contact can lead to a reversal of the orbital evolution. Our model can well interpret the orbital evolution of the ultra-compact X-ray source 4U 1820–30. For a 4-yr observation of 4U 1820–30, the expected signal-to-noise-ratio (SNR) in GW characteristic strain is ∼11.0/10.4/2.2 (LISA/Taiji/Tianqin). The evolution of GW frequencies of NS–WD binaries depends on the WD masses. NS–WD binaries with masses larger than 4U 1820–30 are expected to be detected with significantly larger SNRs. For a $(1.4+0.5) \, {\rm M}_{\odot }$ NS–WD binary close to contact, the expected SNR for a one week observation is ∼27/40/28 (LISA/Taiji/Tianqin). For NS–WD binaries with masses of $(1.4+\gtrsim 1.1) \, {\rm M}_{\odot }$, the significant change of GW frequencies and amplitudes can be measured, and thus it is possible to determine the binary evolution stage. At distances up to the edge of the Galaxy (∼100 kpc), high-mass NS–WD binaries will be still detectable with SNR ≳ 1.

Adaptive preload controller design and analysis for electrostatic suspension system

The electrostatic suspension control system (ESCS) is the core component of the inertial sensor in space gravitational wave detection. To adapt to the changes in orbit environment and satellite platform vibration, the test mass stable is kept in the center of the electrode cage, the ESCS requires high-precision parameters calibration and high-stability verification of the control system. This paper studied the ESCS method, an adaptive controller with variable preload was proposed, and the stability conditions of the control system are given to provide a theoretical basis for the design of the controller. The structure and working principle of the system were also introduced. The electrostatic control system model was derived, and the performance of adaptive preload controller was analyzed. Finally, a simulation was conducted under different disturbance conditions. The results show that the control method proposed in this paper can achieve stable control in difference disturbance, and the preload voltage will change with the conditions. Compared with the traditional fixed preload method, we can see that our method has significantly improved the stability margin and the control quality during the process of dynamic response. This paper provides a solid foundation for the future exploration of space gravitational waves in China and clears the optimization direction for the next step.

In-orbit performance of the laser interferometer of Taiji-1 experimental satellite

Taiji-1, which is the first experimental satellite for space gravitational wave detection in China, relies on key technologies which include the laser interferometer, the gravitational reference sensor (GRS), the micro-thruster and the satellite platform. Similarly to the Laser Interferometer Space Antenna (LISA) pathfinder, except for the science interferometer, the optical bench (OB) of Taiji-1 contains reference and test mass (TM) interferometers. Limited by the lower mechanical strength of the carrier rocket and by the orbit environment, the OB of Taiji-1 is made of invar steel and fused silica, and it is aimed to achieve a sensitivity of the order of 100[Formula: see text]pm/[Formula: see text]. The experimental results from in-orbit tests of Taiji-1 demonstrate that the interferometer can reach a sensitivity of 30[Formula: see text]pm/[Formula: see text] in the frequency range of 0.01–10[Formula: see text]Hz, which satisfies the requirements of Taiji-1 mission.

Laser acquisition experimental demonstration for space gravitational wave detection missions

The laser acquisition-pointing technique is one of the most important techniques for space gravitational wave detection missions, like the Taiji program and the LISA (Laser Interferometer Space Antenna) program. The laser acquisition system suppresses the laser deviation angle to 1 µrad at the receiving aperture. Corresponding to 80 times of telescope magnification, the acquisition accuracy should reach 80 µrad at the acquisition camera. In order to verify the feasibility of the laser acquisition scheme, a laser acquisition ground simulation experimental system is designed and constructed. The experimental system simulates the actual acquisition process of the Taiji from three aspects: optical path, acquisition accuracy and acquisition scanning process. In the experiment, the coupling between the laser acquisition system and the laser pointing system is considered by introducing the DWS (Differential Wave-front Sensing) technique to calibrate the reference position of the acquisition camera and read out the acquisition precision. Due to limited beam propagation distance in the ground experiment, the in-flat top properties of the transmitting beam will greatly affect the acquisition precision. Based on the analysis of the influence, an improved acquisition ground simulation scheme is introduced. The experimental results indicate that the experimental system can achieve the acquisition accuracy of sub-10 µrad magnitude at the acquisition camera. The experimental system realizes methodological demonstration of the acquisition scheme. The results offer the experimental foundation and theoretical basis for the acquisition system of the Taiji/LISA program.

Improvement of the Target Sensitivity in DECIGO by Optimizing Its Parameters for Quantum Noise Including the Effect of Diffraction Loss

The DECi-hertz Interferometer Gravitational-wave Observatory (DECIGO) is the future Japanese, outer space gravitational wave detector. We previously set the default design parameters to provide a good target sensitivity to detect the primordial gravitational waves (GWs). However, the updated upper limit of the primordial GWs by the Planck observations motivated us toward further optimization of the target sensitivity. Previously, we had not considered optical diffraction loss due to the very long cavity length. In this paper, we optimize various DECIGO parameters by maximizing the signal-to-noise ratio (SNR) of the primordial GWs to quantum noise, including the effects of diffraction loss. We evaluated the power spectrum density for one cluster in DECIGO utilizing the quantum noise of one differential Fabry–Perot interferometer. Then we calculated the SNR by correlating two clusters in the same position. We performed the optimization for two cases: the constant mirror-thickness case and the constant mirror-mass case. As a result, we obtained the SNR dependence on the mirror radius, which also determines various DECIGO parameters. This result is the first step toward optimizing the DECIGO design by considering the practical constraints on the mirror dimensions and implementing other noise sources.

Automatic, high-speed, high-precision acquisition scheme with QPD for the Taiji program.

Most of the space gravitational wave detection missions, such as the Taiji program, use space-based laser interferometer to sense the gravitational waves. However, to obtain the interference signal, the inter-satellite laser acquisition scheme is firstly required to establish the laser link. Traditional acquisition sensors are CCD cameras, which cause a serious heating problem and call for high alignment precision. To avoid these questions, a high-speed, high-precision, fully automatic acquisition scheme with quadrant photodetectors (QPD) is proposed in this paper. Incoherent measurement method of the QPD is introduced to fulfill high-speed acquisition, while a dedicated imaging system is involved for automatic acquisition. Also, an improved differential power sensing (DPS) signal is developed. Combined with the down-sampling algorithm and the match filter algorithm, the acquisition scheme can achieve 1 µrad resolution with total scanning time less than 220 s.

Calculation on 2 cm ECRIT Thrust Regulation Based on 3D PIC Numerical Simulation Method

Drag-free control is the key technology for space gravitational wave detection, which will be completed by miniature thruster. 2 cm Electron Cyclotron Resonance Ion Thruster (ECRIT) may be used for the drag-free control. Therefore, the 3D PIC method is used to estimate the thrust regulation of 2 cm ECRIT through simulating the property of ion extracting from the double-grid system. Through analyzing the thrust performance and grid focusing property under different grid apertures, the better grid structure is selected for the subsequent calculation. On this basis, the influence of grid voltage and the ion density on the performance of the thruster is analyzed. The result shows that reducing grid aperture can reduce the thrust, but it also affects the focusing property of the grid. Changing the ion density can adjust the thrust in a wide range. At given grid structure and ion density, there is a suitable grid accelerating voltage range to ensure the best ion focus characteristics. Considering the thrust performance and focusing characteristics, the grid structure with screen and accelerating grid aperture in 0.6 mm and 0.34 mm is selected. When the ion density is 1×1 017, 0.7×1 017, 0.4×1 017 and 0.2×1 017 m-3, the thrust can range from 5.05 to 141.44 μN through adjusting the grid accelerating voltage. This study can provide information for analyzing the possibility of the thruster application.

Coupling of dual mass-transferring white dwarf binaries as a variable gravitational-wave emitter

ABSTRACT We study evolution of a hierarchical four-body (2 + 2) system composed by a pair of mass-transferring white dwarf binaries. Applying a simplified model around the synchronous state of two inner orbital periods, we newly find that the four-body system could settle down to a limit cycle with a small period gap. The period gap generates an amplitude variation of emitted gravitational waves as a beat effect. Depending on model parameters, the beat period could be 1–10 yr and a large amplitude variation might be observed by space gravitational-wave detectors.

Investigation on Stray-Capacitance Influences of Coaxial Cables in Capacitive Transducers for a Space Inertial Sensor.

Ultra-sensitive inertial sensors are one of the key components in satellite Earth’s gravity field recovery missions and space gravitational wave detection missions. Low-noise capacitive position transducers are crucial to these missions to achieve the scientific goal. However, in actual engineering applications, the sensor head and electronics unit usually place separately in the satellite platform where a connecting cable is needed. In this paper, we focus on the stray-capacitance influences of coaxial cables which are used to connect the mechanical core and the electronics. Specially, for the capacitive transducer with a differential transformer bridge structure usually used in high-precision space inertial sensors, a connecting method of a coaxial cable between the transformer’s secondary winding and front-end circuit’s preamplifier is proposed to transmit the AC modulated analog voltage signal. The measurement and noise models including the stray-capacitance of the coaxial cable under this configuration is analyzed. A prototype system is set up to investigate the influences of the cables experimentally. Three different types and lengths of coaxial cables are chosen in our experiments to compare their performances. The analysis shows that the stray-capacitance will alter the circuit’s resonant frequency which could be adjusted by additional tuning capacitance, then under the optimal resonant condition, the output voltage noises of the preamplifier are measured and the sensitivity coefficients are also calibrated. Meanwhile, the stray-capacitance of the cables is estimated. Finally, the experimental results show that the noise level of this circuit with the selected cables could all achieve 1–2 × 10−7 pF/Hz1/2 at 0.1 Hz.