Space Gravitational Wave Detection Research Articles

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%.

Using DWS Optical Readout to Improve the Sensitivity of Torsion Pendulum.

In space gravitational wave detection missions, a drag-free system is used to keep the test mass (TM) free-falling in an ultralow-noise environment. Ground verification experiments should be carried out to clarify the shielding and compensating capabilities of the system for multiple stray force noises. A hybrid apparatus was designed and analyzed based on the traditional torsion pendulum, and a technique for enhancing the sensitivity of the torsion pendulum system by employing the differential wavefront sensing (DWS) optical readout was proposed. The readout resolution experiment was then carried out on an optical bench that was designed and established. The results indicate that the angular resolution of the DWS signal in optical readout mode can reach the level of 10 nrad/Hz1/2 over the full measurement band. Compared with the autocollimator, the sensitivity of the torsional pendulum is noticeably improved, and the background noise is expected to reach 4.5 × 10-15 Nm/Hz1/2@10 mHz. This method could also be applied to future upgrades of similar systems.

Design and analysis of ultra-low moment noise flexure pivot in space gravitational wave detectors

To control the pointing accuracy of the telescope in the space gravitational wave detector at the nano-radian level, it is essential to design a flexure pivot with extremely low rotational moment nonlinearity during rotation. This study derives the theoretical equation of the nonlinear rotational moment of flexure pivot based on the beam bending strain energy equation and completes the design of ultra-low moment noise flexure pivot by integrating the structural form of conventional cross-spring flexure pivot. The nonlinear moment noise distribution in the frequency domain of three kinds of flexure pivots is then compared regarding TianQin’s circular high orbits. Then the relevant finite element simulation analysis will be performed for the flexure pivot structures, respectively, to ensure the accuracy of its rotational stiffness model and verify the correctness of nonlinear moment theory optimization through physical experiments. The results show that the optimized flexure pivot can effectively reduce the nonlinearity, and basically meet the nonlinear moment requirements in space gravitational wave detection.

Development and experimental investigation of a high-precision capacitive displacement transducer of the inertial sensor for TianQin

Capacitive sensing electronics are critical to space gravitational wave detection missions, providing the test mass motion information for the inertial sensor’s non-sensitive axis control and the drag-free control of the satellite. For the TianQin mission, the capacitive sensor requirement is at 6 mHz, corresponding to a displacement noise of . This paper presents the system design scheme, noise analysis, and performance testing of the capacitive sensor for the TianQin mission. Based on the previous work of our group, a capacitive sensing scheme based on a transformer bridge and modulation–demodulation is adopted. A transformer with a better high LQ product is fabricated, and the preamplifier current noise is reduced to further improve the performance above mHz. The amplitude stability of the AC carrier and the performance of the lock-in amplifier circuit are further improved to reduce the low-frequency noise at and below. Finally, a capacitive sensor prototype is developed and tested, the experimental results show that the capacitance measurement noise is better than above 1 mHz and better than at about , which meets the overall performance requirement of the TianQin mission.

Event-triggered robust model reference adaptive control for drag-free satellite

Aiming at the requirement of bounded disturbance suppression for low-frequency space gravitational wave detection satellite, a robust model reference adaptive drag-free control scheme is proposed in this paper via linear matrix inequalities (LMIs) approach. The multivariable model reference adaptive control (MRAC) scheme is applied to the drag-free control system with parameter uncertainties, which realizes the adaptive tracking to the reference state. The LMI system is established as an adaptive compensation term, which provides robustness against nonlinear disturbances. To reduce the communication burden of the actuation information and further save the total energies, an event-triggered mechanism (ETM) is introduced, with both the actuation inputs and the adaptive laws of the feedback gains updated only at the triggering time instants. The ultimately uniformly boundedness of the closed-loop signals is proved by Lyapunov analysis, with each system state convergence. From the feasibility analysis, Zeno behavior can be further proved to be strictly excluded. The numerical simulation verifies that the proposed scheme has efficient robustness to nonlinear disturbances with low energy cost, and achieves good effect in response to the requirements of space gravitational wave detection mission.

High-Precision Inertial Sensor Charge Management Based on Ultraviolet Discharge: A Comprehensive Review.

The charge accumulation caused by cosmic rays and solar energetic particles poses a significant challenge as a source of noise for inertial sensors used in space gravitational wave detection. To address this issue, the implementation of charge management systems based on ultraviolet discharge becomes crucial. This paper focuses on elucidating the principles and methods of using ultraviolet discharge for charge management in high-precision inertial sensors. Furthermore, it presents the design and implementation of relevant payloads. Through an analysis of the charge accumulation effect and its impact on noise, key considerations regarding coatings, light sources, and optical paths are explored, and some current and valuable insights into the future development of charge management systems are also summarized. The conclusions drawn from this research also provide guidance for the advancement of higher precision ultraviolet discharge technology and the design of charge management systems.

Analysis and elimination of translation disturbance for patch effect measurement with a torsion pendulum

Patch effect on conductive surfaces is one of the critical noise sources in many scientific experiments like space gravity programs and gravitational wave detection missions. A high-precision probe-torsion instrument has been developed on ground for measuring patch effect. However, the translation mode of the probe resulting from the environmental disturbance will inevitably affect the measurement in the concerned torsion degree of freedom. In this paper, combining the theoretical analysis as well as the confirmatory experiment, the method based on data analysis is adopted to eliminate the translation effect, finally realizing the best surface potential resolution level of 20 µV Hz.

A closed-loop torsional micro-thrust measurement system

In view of the future space gravitational wave detection mission, a closed-loop monofilament torsional pendulum micro-thrust measurement system has been developed according to the requirements of the drag-free control of the satellite platform for the thrust of the micro-thruster. In this paper, we present the design of the micro-thrust measurement system, the electromagnetic force generation device, and the angular displacement differential measurement. By calibrating the electromagnetic force generation device, the functional relationship between micro-thrust and torsional angular displacement of the torsion scale is obtained, and then the micro-thrust measurement is carried out. The analysis considers the impact of the experimental device’s structure and environment on the micro-thrust measurement system. The range for measuring thrust is 1–246 μN, with a resolution of 0.1 μN and a relative uncertainty of 1.174%. Ensure that the thrust resolution and accuracy of the micro-thruster are met according to the measurement requirements.

The Influence of On-Orbit Micro-Vibration on Space Gravitational Wave Detection

Large-aperture space telescopes have played an important role in space gravitational wave detection missions. Overcoming the influence of the space environment on interstellar laser distance measurement and realistic high-concentration laser distance measurement is one of the topics that LISA and Taiji are working hard on. It includes solar temperature, spatial stress relief, pointing shake and tilt, etc. However, when considering the impact of vibration on the telescope, both LISA and Taiji only consider the resonance impact of vibration on structural parts, which greatly ignores the impact of high-frequency micro-vibration on space ranging. This paper first considers space gravitational wave detection. Then, we establish the heterodyne interference model and demodulation algorithm of the optical phase-locked loop, and then introduce the vibration component for theoretical analysis. The results show that, although the resonance effect of low-frequency vibration on the system structure is avoided in space gravitational wave detection, the influence of high-frequency micro-vibration on heterodyne interference cannot be ignored. At the same time, we quantitatively analyze the influence efficiency of amplitude and frequency; in the premise of small amplitudes, the influence of vibration frequency is related to the frequency of the heterodyne signal, which has important guiding significance in engineering.

Hardware design of electrostatic levitation accelerometer control system

The electrostatic levitation accelerometer is a high-precision inertial instrument for measuring small displacement and acceleration, and it plays a very important role in global gravity field measurement, space gravitational wave detection, and other space missions as a key payload for satellites. It can realize the measurement of three-axis linear acceleration and three-axis angular acceleration. The open loop is unstable, and the control system needs to control six degrees of freedom at the same time so that the test mass can be stably suspended in the center position of the capacitive pole plate. For the demand of multi-channel simultaneous control of electrostatic levitation accelerometer, this paper designs an eight-channel digital control system hardware circuit with DSP as the core and FPGA as the co-processor, which can realize the data acquisition and feedback control of six degrees of freedom, writes the driver using hardware description language (Verilog), and simulates and analyzes the driver timing by the timing simulation software Modelsim. Finally, the hardware circuit was tested for the onboard drive. The results show that the system can work normally, the average sampling error of ADC is 0.00198 V, and the output error of DAC is 0.004 V, which is small enough to meet the system requirements.

Potential tertiary effects on the LISA verification binary HM Cancri

ABSTRACT Two groups recently analysed the long-term orbital evolution of HM Cancri, which is one of the most important verification binaries for the space gravitational wave detector LISA. By using the reported first and second derivatives of its orbital frequency f, we discuss potential tertiary effects on this binary. We found that, in contrast to the first derivative $\dot{f}$, the second derivative $\ddot{f}$ might be strongly affected by a dark tertiary component such as an old white dwarf with an outer orbital period of ∼250 yr.

A new window function for the spectral analysis of effect of celestial body on Taiji mission below 0.1 mHz

The Taiji project is a space gravitational wave detection mission consisting of three satellites that form a large equilateral triangle with a side length of approximately 3×109 m in heliocentric orbit. It may have the potential to detect gravitational waves below 0.1 mHz. Gravitational wave signals in the μHz range have a strain sensitivity as large as 2.9×10-14, or approximately 8.7×10-5 m variation in inter-satellite distance. However, inter-satellite distances are affected by the celestial bodies in the solar system, introducing changes that may reach magnitudes of 3×107 m; thus, the effect of celestial bodies on these distances may exceed the gravitational signals below 0.1 mHz. Therefore, it is necessary to accurately estimate the effect of the gravity of celestial bodies below 0.1 mHz. In this study, based on the inter-satellite distances in the Taiji mission, a window function design method is proposed and a six-term cosine window function is designed. It has a high decay rate of h-12 and a good peak sidelobe level of −88 dB. It improves the attenuation of spectral leakage while maintaining an acceptable minimum number of signal periods, which is beneficial for signals where it is difficult to obtain more periods, such as for the Taiji mission. Based on the analytical results of the states of satellites in cases when the satellites move only in the gravitational field of the Sun, the ability of the new window function is validated.

Active disturbance rejection control of drag-free satellites considering the effect of micro-propulsion noise

The space gravitational wave detection mission requires a super "static and precise" scientific experiment environment. In order to solve the non-conservative force disturbance variation and the actuator noise and measurement noise, this paper designs a drag-free control scheme based on active disturbance rejection control (ADRC) framework to achieve the high-precision index. According to the ultra-high accuracy, low bandwidth limitation, and robustness requirements of drag-free satellite, the H∞ controller satisfying the robustness constraint is designed as an active disturbance rejection feedback controller to achieve the high-precision index. Meanwhile, the non-conservative force disturbance with a wide range of variations is estimated and feedforward compensated by an extended state observer to improve the system robustness. Simulation results show that the control system can achieve the relative displacement of 2nm/Hznm/Hz1/2 for the drag-free satellite platform and the residual acceleration of 1×10-15 m/sm/s2/Hz1/2 for the test mass.

Primordial black holes and induced gravitational waves from double-pole inflation

The primordial black hole (PBH) productions from the inflationary potential with an inflection point usually rely heavily on the fine-tuning of the model parameters. We propose in this work a new kind of the α-attractor inflation with asymmetric double poles that naturally and easily lead to a period of non-attractor inflation, during which the PBH productions are guaranteed with less fine-tuning the model parameters. This double-pole inflation can be tested against the observational data in the future with rich phenomenological signatures: (1) the enhanced curvature perturbations at small scales admit a distinctive feature of ultraviolet oscillations in the power spectrum; (2) the quasi-monochromatic mass function of the produced PBHs can be made compatible to the asteroid-mass PBHs as the dominant dark matter component, the planet-mass PBHs as the OGLE ultrashort-timescale microlensing events, and the solar-mass PBHs as the LIGO-Virgo events; (3) the induced gravitational waves can be detected by the gravitational-wave detectors in space and Pulsar Timing Array/Square Kilometer Array.

Study on the Voltage Reference Noise at Sub-Millihertz Frequencies for Developing an Ultra-Stable Temperature Measurement Subsystem.

A temperature measurement subsystem (TMS) is a critical piece of infrastructure of the space gravitational wave detection platform, necessary for monitoring minuscule temperature changes at the level of 1μK/Hz1/2 within the electrode house, in the frequency range of 0.1mHz to 1Hz. The voltage reference (VR), a key component of the TMS, must possess low noise characteristics in the detection band to minimize the impact on temperature measurements. However, the noise characteristics of the voltage reference in the sub-millihertz range have not been documented yet and require further study. This paper reports a dual-channel measurement method for measuring the low-frequency noise of VR chips down to 0.1mHz. The measurement method makes use of a dual-channel chopper amplifier and an assembly thermal insulation box to achieve a normalized resolution of 3×10-7/Hz1/2@0.1mHz in the VR noise measurement. The seven best-performance VR chips documented at a common frequency range are tested. The results show that their noise at sub-millihertz frequencies can significantly differ from that around 1Hz.