International Journal of Modern Physics A

The Taiji-1 satellite is a pilot satellite mission of Taiji program, which is used to verify Taiji’s key technology and also to testify the feasibility of Taiji roadmap. Taiji-1 was launched on 31st August 2019 and its designed mission was completed. The results of Taiji-1 first scientific run are briefly introduced. A detailed analysis on how Taiji-1 can bridge the gap between ground experiment and Taiji pathfinder is presented. To report current progresses and achievements on Taiji program made by Taiji scientific collaboration, we publish this special issue with including 26 articles.

As an important part of laser interferometry system, optical bench is one of the core technologies for the detection of spaceborne gravitational waves. As the first step of the space Taiji program, Taiji-1 provides the measurement accuracy of laser interferometry system better than 100 pm/Hz${}^{1/2}$(@10 mHz–1 Hz). Taiji-1 is required to be able to track the motion of test mass in inertial sensor. According to the requirements, four interfering optical paths were designed. By adopting an integrated satellite design and selecting the optical and mechanical materials with low linear expansion coefficient, the high stability of optical path was achieved. By using the DOE method, the alignment errors (position/attitude) of four optical paths were all reduced to below 50 $\mu$ m/100 $\mu$ rad. In the performance test, the accuracy of laser interferometry system was better than 100 pm/Hz${}^{1/2}$(@10 mHz–1 Hz), and the modulation signal of inertial sensor was successfully detected. The results show that all technical indexes of optical bench have met or exceeded the design requirements.

As the first technology verification satellite of the space-based gravitational wave detection in China, Taiji-1 has tested the high-precision space laser interferometer, the inertial sensor, the micro thruster and the hyperstatic satellite platform in orbit. The micro thruster plays an important role in the micro propulsion system. The purposes of the research are to investigate the relationship between the thrust and the interference, and then get a comprehensive understanding about the maximum effect of the thrust in Taiji-1. The transfer function between the thrust and the optical path difference fluctuations is established through the modeling, the simulation and the data postprocessing of Taiji-1. In addition, the maximum effect of the thrust in Taiji-1 is about 32 pm/$\sqrt{\mathrm{\text{Hz}}}$ with an integration time of 100 s. It can be neglected compared to the requirement of 100 pm/$\sqrt{\mathrm{\text{Hz}}}$ for the interferometer stability in Taiji-1.

Space-borne gravitational wave detection imposes a demanding requirement on the sensitivity of the laser interferometer. Among all disturbances that affect the measurement accuracy of the laser interferometer, temperature fluctuations contribute significantly. In this paper, the structure model and the interference path design of Taiji-1 laser interferometer have been used to conduct a preliminary simulation analysis of the temperature fluctuation noise through the finite element method. The temperature, the displacement and the optical path difference fluctuations have been obtained and theoretically analyzed. The preliminary simulation results are consistent with the theoretical analysis, which shows that the thermal–structural–optical simulation scheme adopted in this paper is reasonable. With the preliminary simulation results and the actual temperature control of Taiji-1 laser interferometer, we estimate that in Taiji-1 laser interferometer system, the temperature fluctuation is below the order of mK, the node displacement is within $100$pm, and the interference arm length difference fluctuation amplitude of the laser interferometer is also within $100$pm.

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 100pm/$\sqrt{\mathrm{\text{Hz}}}$. The experimental results from in-orbit tests of Taiji-1 demonstrate that the interferometer can reach a sensitivity of 30pm/$\sqrt{\mathrm{\text{Hz}}}$ in the frequency range of 0.01–10Hz, which satisfies the requirements of Taiji-1 mission.

Taiji-1 is the first demonstrated experimental satellite of Taiji program in China. Phasemeter is one of the key components of the laser interferometer which is responsible for phase extraction of the heterodyne signals. In this paper, we present the architecture and implementation of Taiji-1 phasemeter. The DPLL architecture is used in Taiji-1 which is generally regarded as the best choice for space missions. We test the phasemeter on the ground and the results show that the phasemeter reaches the sensitivity of 600 $\mu$rad/$\sqrt{Hz}$ in the frequency range of 0.01–1Hz. It is further shown that it can reach the accuracy of 30 $\mu$rad/$\sqrt{Hz}$ in the frequency range of 0.1–1Hz, both of which are within the technical requirements of Taiji-1 mission.

A high stability Laser source at 1064 nm for Taiji-1 satellite is reported. The key component of the Laser source is a nonplanar ring oscillator (NPRO) solid laser with linewidth of 260 Hz. Frequency noise and power noise of Laser source are greatly improved by applying precision driving current control and temperature control. The frequency noise of 0.1 MHz/sqrt(Hz)@ 0.1 Hz and the power noise of 0.02%@0.1 Hz are obtained. Its working performances in-orbit are analyzed and compared with the ground test, showing negligible variation.

Due to their excellent noise performance and technical maturity, ultra-stable continuous-wave neodymium-doped yttrium aluminum garnet lasers are one of the major light sources in a series of precision measurements such as ground and space-based gravitational wave detection, inter-satellite laser ranging and coherent optical communication. As the first step of developing an ultra-stable spaceborne laser, we carried out the design, development and environmental test of an all-solid-state Nd:YAG NPRO spaceborne laser. The laser deliveries 11.48 mW of optical power at 1064.405 nm, exhibits intensity and frequency noises less than 1 × 10${}^{-2}$/$\surd$Hz and 1 MHz/$\surd$Hz (Fourier frequencies $>$ 10 mHz), respectively, passed environmental tests and has been onboard the first satellite of the Taiji program for one year. The work laid a solid foundation for realizing ultra-stable lasers for the Taiji program as well as being used in many space applications.

Taiji-1 is the first step of China’s efforts on the detection of gravitational waves in space. It is a one-year quick mission, which aims to verify the key technologies on orbit. The detection of gravitational waves at mHz frequency band needs to exceptionally focus on small spatial deviations between two inertial references several million kilometers apart. The inertial reference on Taiji-1 spacecraft (S/C) has been developed based on a capacitive readout and actuation scheme to meet the requirements of accelerometer. In this paper, the development condition, ground tests and on-orbit performance of this inertial reference are described.

Based on the working principle of the signal detection and servo feedback control of the electrostatic accelerometer, in this paper, the main electronic noise components affecting the measurements of the accelerometer are analyzed and the corresponding expressions are determined. The resolution of the designed electrostatic accelerometer is lower than 10${}^{-9}$m/s²/Hz${}^{1/2}$, which cannot be verified directly due to limitations imposed by the vibration of the ground environment. However, it can be evaluated indirectly by the testing of electronic noise under open-loop conditions. Through this process, the resolution of 3× 10${}^{-9}$m/s²/Hz${}^{1/2}$ of the Taiji-1 inertial sensor was verified and found to be in agreement with results obtained in orbit.

As the key measurement load of Taiji-1 satellite, inertial sensor detects the acceleration disturbance of test mass (TM) under nonconservative force in line with the basic principle of capacitive sensing, while keeping the TM in equilibrium position through electrostatic drive. In order to ensure the smooth progress of the mission, it is necessary to test and evaluate the performance of inertial sensor on the ground. In this paper, a torsion pendulum system is designed to eliminate the influence of the Earth’s gravity so as to meet the requirements of ground test. The experimental results show that the inertial sensor in closed-loop control mode can stably keep the TM at equilibrium position. At the same time, the ground detection of acceleration resolution of inertial sensor is greatly affected by ground vibration noise. If the inertial sensor operates normally in space, its acceleration resolution can reach$3.96\times {10}^{-9}\mathrm{\text{m}}/{\mathrm{\text{s}}}^2/\sqrt{\mathrm{\text{Hz}}}$, thus meeting the requirement of Taiji-1.

Taiji-1 satellite was successfully launched on 31 August 2019, and it has been operating normally in orbit until now. A series of in-orbit experiments were carried out with the inertial sensor, which included the micro-thrust test, drag-free control test and laser interferometer test. Comprehensive performance simulations and tests of the inertial sensor were also carried out prior to the launch of Taiji-1, including the calibration and drop-tower tests. These tests were one of the preconditions for the success of these experiments. The calibration experiments were conducted in a cave-lab using the gravity-inclination method and the scale factors of the inertial sensor along Y- and Z-axis were measured. In addition, 20 drop-tower tests were carried out in the National Microgravity Laboratory of China (NMLC) drop tower and the control stability of all the axes was tested and optimized. A simulation model was used before each test, and the results showed that an accurate simulation prior to each experiment had an important role in ensuring the efficiency and accuracy of the experiment. The circuit-gain switch was realized for the first time during the drop-tower tests. The test results indicated that the microgravity level of the NMLC drop tower could reach about 13 $\mu$g₀ along the horizontal axes, offering an important reference for researchers planning to conduct microgravity experiments in the NMLC drop tower.

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.

The Hall Micro Thrusters (HMTs) use cold gas or accelerated plasma dual mode to provide ultra-precise spacecraft altitude control. They were operated in space for the first time as part of the demonstration payloads on Chinese Academy of Science’s (CASs) Taiji-1 spacecraft since September 2019. Hall Micro Thruster Assemblies (HMTAs) were the actuators in drag-free control, and will compensate the nonconservative force for gravity wave observatories. The HMTAs meet the requirements of operating at 5–100 $\mu$ N of thrust with 0.7 $\mu$ N resolution and $\le$0.6 $\mu$ N/Hz${}^{1/2}$ (0.01–1 Hz) noise to deliver the nanometer-level precision control as fast as 30 ms measured by Gravitational Reference Sensor (GRS). A transfer function model in z-domain was fit and used to filter HMTs cathode voltage to predict GRSs thrust noise response. Simulations of a single or dual-frequency disturbance and the corresponding compensation demonstrated that HMTAs could deliver the required thrust profile expected. The capability to meet the requirements of thruster noise in drag-free control is critical for future missions because the acceleration noise on test mass directly relates to the gravity wave signa l. Preliminary in-orbit verification of Taiji-1 has showed HMTAs’ great potential in future, and the data in the experiments are presented in this paper.

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.

Drag-free technology functions as the keystone for space-based gravitational wave detection satellites moving along a geodesic path, like the Laser Interferometer Space Antenna (LISA) Pathfinder, to achieve ultra-high microgravity level. Several prerequisites for micro-thrusters operated under the drag-free technique include constantly adjustable thrust, high resolution, low noise and fast response time. Accordingly, a torsional thrust measurement system was methodically devised to measure the thrust response time of such micro-thrusters on the ground. The characteristics of the dynamic thrust change with time are inverted by the angular displacement of the torsional pendulum, established by the dynamic equation of the same, thus, measuring the rise/fall time of the thrust applied to the torsional pendulum. Calibration of the torsional pendulum thrust measurement system is carried out by the standard electrostatic force generated by the electrostatic comb-drive or microelectromechanical actuator, facilitating the suitable identification of the pendulum parameters. Afterwards, the electrostatic and electromagnetic forces generated by the actuator are applied to validate the measurable thrust response time of the torsional thrust stand. The experimental results show that the above-mentioned thrust stand can effectively measure the thrust response time up to 10 ms for a thrust step in 10 s of micronewtons, which qualifies as the thrust response time required by micro-thrusters for space-based gravitational wave detection.

Drag-free control is one of the key technologies for the verification of Taiji-1 satellite. In the direction of sensitive axis, the drag-free controller receives the measurement signal from the high-precision gravitational reference sensor on the satellite, and instructs the micro-thruster system to counteract the disturbance force acting on the sensitive axis, so that the microgravity level in the sensing axis direction of the satellite can reach the order of 10${}^{-9}$ m/s² in the measurement band. In order to fully verify the drag-free control system, a ground one-dimensional drag-free semi-physical simulation system is built to simulate the performance of various payloads in the drag-free control loop, and to verify the performance and technical targets that the drag-free control system can achieve in the ground control loop. Through the small angle approximation, the equivalent relationship between the rotation of the experimental model and the translational motion of the experimental satellite in the direction of drag-free is demonstrated. In the condition of neglecting the stiffness and damping of the suspended pendulum, the parameters of the suspended pendulum are designed according to the principle of equal acceleration, and their effectiveness is verified by numerical simulation. According to the operation mode of on orbit drag-free control, the ground drag-free experimental scheme and drag-free controller are designed, and the experimental research and verification are carried out. The results show that the controller can effectively control the displacement and acceleration of the experimental model, and also can effectively suppress the disturbance of certain amplitude and frequency.

In the initial stage of a radio frequency ion thruster (RIT) ignition, an influx of electrons is required from an external source into the discharge chamber and ionization of the neutral gas propellant. A neutralizer-free method for Townsend breakdown discharge ignition based on Paschen’s law was developed in this study. The feasibility of the ignition method was confirmed by performing thousands of ignition experiments. Metallic Molybdenum (Mo), pyrolytic graphite (PG) and Zr${}_{41.2}$Ti${}_{13.8}$Cu${}_{12.5}$Ni${}_{10}$Be${}_{22.2}$alloy acceleration grids were prepared, and ignition-induced damage on the grids was investigated. A field-emission scanning electron microscope was used to inspect surface damage on the grids after multiple ignitions and to analyze the influence of the ignition method on the lifetime of the ion optical system. Grid materials for space missions that require multiple RIT ignitions (10${}^3)$ should be high-strength blocks that are resistant to sputtering corrosion and high temperature.

Cold Gas Micro Propulsion (CGMP) is a reliable technology for spacecraft attitude and orbit control used in drag-free control system to compensate the environmental disturbance from the aerospace. The CGMP requiring a very fine control resolution and low noise is desired to be used on TAIJI mission for gravitational wave detection which is supported by Chinese Academy of Science (CAS). One of CGMP’s key technologies is high-resolution Gas Mass Flow Sensor (GMFS). In this paper, calorimetric thermal flow sensor characterized with miniaturization, high sensitivity and low noise is studied by simulation method and manufacturing process. By simulating the influence of heating power, electrode distance, temperature, etc. on sensor response, the methods on optimizing sensitivity and accuracy have been proposed. The sensitivity is about 2.53 mV/(m/s)/mW. An amplifier circuit with ultra-low noise of 7.29 nV/$\surd$Hz for reading out has been designed, which is essential for high resolution. The sensor was fabricated and preliminary tests have been conducted. The sensitivity of the sensor is about 100 mV/(m/s).

Taiji is China’s spaceborne gravitational wave (GW) detecting project, which is designed to detect GW sources ranging from 0.1mHz to 1Hz. Taiji-1, launched on 31 August 2019, is a pilot study mission to prepare necessary technology for Taiji pathfinder. Two major technology units were tested on Taiji-1: Optical Metrology System and Drag-free Control System (DFCS). In this paper, we try to illustrate the design of DFCS; the implementation strategy of experiment and the first results of in-orbit experiment. The disturbance reduction capability of Taiji-1’s DFCS is demonstrated by the in-orbit experimental performance analysis.

Taiji-1 is China’s first in-orbit technology validating satellite related to spaceborne gravitational wave (GW) detection. The satellite was launched at 600km sun synchronized orbit on 31 August 2019. It has accomplished its mission goals while all subsystems have validated their key technologies in orbit. The subsystems include optical metrology system (OMS), drag-free attitude control system (DFACS), thermal control subsystem, high-quality microgravity satellite platform and so on. This paper presents system architecture of Taiji-1 analyzing in-orbit experimental results of thermal stability, reaction wheel vibration contributing to the noise of gravitational reference sensor (GRS) measurement noise, and the center-of-mass (CoM) of GRS calibration.

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, $\mu$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.

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.

Taiji-1’s in-orbit magnetic property is significant for the improvement of the satellite’s attitude-control performance and the acceleration noise model of gravitational reference sensor. Test data of satellite drifts have been used to construct the model including interaction among the magnetic field; remnant magnetic moment and induced magnetic moment so as to estimate the satellite’s magnetic property. Using the global optimization method, the remnant magnetic moment of Taiji-1 is estimated to be (-1.42 -0.19 -0.06) Am².

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${{}^{-5}}^{\circ }\text{C}$, and the long-period noise is less than 1 × 10${{}^{-5}}^{\circ }\text{C}$. It can be used in the space gravitational wave detection test and control system.

TAIJI-1 is a micro-gravity experiment spacecraft. The mission target is to verify some key techniques of the spacecraft payloads for the gravitational wave detection, which involve laser interferometer, gravity reference sensor, drag-free control technology, micro-propulsion system, super-quiescent spacecraft platform, etc. The verification of the data processing pipeline required by the next stage of TAIJI Program is also performed. In order to benefit from the joint observatory between TAIJI and LISA in the future, as a space mission, the science operations refer to the existing ESA and NASA standard models, which include the Mission Operations Center (MOC), the Science Operations Center (SOC), the Data Processing Center (DPC), etc. The data processing pipeline connects between SOC and DPC. The SOC obtains the level-0 data from MOC and DPC performs the data processing and distributes the level-2 and level-3 data to SOC. For TAIJI-1 mission, SOC and DPC are two subsystems, which are included into the named science application system (SAS). That is the one of the six-function systems, which operate Chinese space mission. MOC is relevant to the ground support system (GSS) and spacecraft control system, that are also the ones of six-function systems of Chinese space mission. The on-orbit experiment plannings are transported from SAS to GSS, that is similar to from SOC to MOC in NASA standard models. The computer construction and computer software are the basic elements of the SAS, that are constructed completely, before the TAIJI-1 was launched. After TAIJI-1 enters the orbit, the data processing pipeline begins to work and the experimental items of TAIJI-1 are performed in the pipeline. The basic functions, performances and optimization functions of the detection devices in the payloads are verified completely 3 months after launch. In the same time, the methods of data analysis and processing are also verified. As a result, the required indicators of key techniques of the spacecraft for the gravitational wave detection are justified. The data processing pipeline is also reasonable. The relevant codes for data analysis and processing will benefit the next stage of TAIJI Program.

Taiji-1 is the first technology demonstration satellite of the Taiji Program in Space, which, served as the pre-PathFinder mission, had finished its nominal science operational phase and successfully accomplished the mission goal. The gravitational reference sensor (GRS) on-board Taiji-1 is one of the key science payloads that coupled strongly to other instruments, sub-systems and also the satellite platform itself. Fluctuations of the physical environment inside the satellite and mechanical disturbances of the platform generate important noises in the GRS measurements, therefore their science data can also be used to evaluate the performance of the $\mu N$-thrusters and the stability of the platform. In this work, we report on the methods employed in Taiji-1 GRS data processing in the systematical modelings of the spacecraft orbit and attitude perturbations, mechanical disturbances, and internal environment changes. The modeled noises are then removed carefully from the GRS science data to improve the data quality and the GRS in-orbit performance estimations.