Antenna for the detection of electromagnetic audio-band disturbances on-board LISA

The LISA mission will be the first observatory to detect gravitational waves from space within the millihertz frequency band. Magnetic forces have an important impact on the instrument’s sensitivity below the millihertz. Hence, monitoring the magnetic environment within each of the LISA spacecrafts is of utmost importance. In this Letter we present the characterization of the coils that were used in LISA Pathfinder (LPF) when operating as magnetic sensors in the audio frequency band. The necessity of implementing this type of magnetometer is presented in order to monitor high frequency magnetic signals from the electronics on-board. We show that the LPF coils have a performance one order of magnitude better than the current requirements set by the LISA mission at the low end of the audio-band frequency. The LPF coils are able to measure a magnetic noise level of 1.45 $\rm pT/\sqrt{\rm{Hz}}$ at 50 Hz and 0.17 $\rm pT/\sqrt{\rm{Hz}}$ at 500 Hz. Additionally, the LPF coils can reach a magnetic noise floor of 0.1 $\rm pT/\sqrt{\rm{Hz}}$ at frequencies above 1 kHz.

💡 Research Summary

The paper proposes and validates a novel use of the magnetic injection coils that were originally employed on the LISA Pathfinder (LPF) mission as high‑frequency magnetic sensors for the upcoming LISA (Laser Interferometer Space Antenna) observatory. While LISA’s primary science band lies in the millihertz range, electronic subsystems on board the spacecraft generate magnetic fields in the audio band (20 Hz–20 kHz) that can, through nonlinear coupling, produce forces on the test masses (TMs) and potentially contaminate the low‑frequency gravitational‑wave signal. The authors first develop a theoretical model of how a high‑frequency magnetic dipole field, generated by spacecraft electronics, can be amplitude‑modulated at low frequencies. This modulation leads to a force term proportional to the product of the TM’s permanent magnetic moment, its magnetic susceptibility, and the spectral density of the modulation. Using realistic TM parameters (magnetic moment ≈ 0.14 nA·m², susceptibility |χ| ≈ 1, distance ≈ 0.3 m) and assuming a 20 % modulation depth, the resulting acceleration noise is estimated at ~3 × 10⁻¹⁶ m s⁻² Hz⁻¹/², roughly 3 % of the total LPF noise budget. If the modulation were more abrupt (e.g., square‑wave), the contribution could increase by an order of magnitude, underscoring the need for a dedicated high‑frequency magnetic monitor.

Search‑coil magnetometers (SCS) are identified as the most suitable technology for this task. An SCS operates on Faraday’s law: a time‑varying magnetic flux through a multi‑turn coil induces a voltage V = N ω π a² B, where N is the turn count, a the coil radius, and ω the angular frequency. The authors deliberately choose an air‑core design to avoid low‑frequency thermal noise associated with ferromagnetic cores, which is critical for the ultra‑low‑noise environment required by LISA. The equivalent circuit of the coil includes resistance (R), inductance (L), and inter‑turn capacitance (C), forming an RLC network. A parallel load resistor (R₀) is added to flatten the frequency response and suppress resonance. Because the induced signal is weak, a low‑noise non‑inverting operational amplifier is employed, with gain G = 1 + R₂/R₁ · (1 + i ω R₂ C). The additional capacitor C provides a low‑pass filter that limits high‑frequency amplifier noise.

Experimental validation was performed in a laboratory magnetic shield. The LPF coils were driven with calibrated currents to generate known magnetic fields, and the output voltage spectra were recorded. The measured magnetic noise spectral density reached 1.45 pT · Hz⁻¹/² at 50 Hz, 0.17 pT · Hz⁻¹/² at 500 Hz, and fell below 0.1 pT · Hz⁻¹/² for frequencies above 1 kHz. These figures comfortably satisfy LISA’s requirement S₁/₂ < 10⁶ f² pT · Hz⁻¹/² (with f in Hz) and are an order of magnitude better at the low end of the audio band. The sensitivity follows the theoretical N π a² ω dependence, and the bandwidth is limited by the L/R ratio and the coil’s self‑capacitance, with a roll‑off observed beyond ~10 kHz.

A simple spacecraft model was used to estimate the detectable magnetic disturbance amplitudes in situ. The analysis shows that typical on‑board electronics, which can produce magnetic fluctuations of order 10 pT, would be readily detectable by the repurposed coils. Consequently, these sensors can be integrated into LISA’s Science Diagnostics Subsystem (SDS) to provide real‑time flags for anomalous high‑frequency magnetic activity, enabling operators to assess data quality and, if necessary, apply post‑processing corrections.

In conclusion, the study demonstrates that LPF injection coils, when operated as air‑core search‑coil magnetometers, meet and exceed the magnetic sensor specifications required for LISA’s audio‑band monitoring. The work quantifies the potential impact of high‑frequency magnetic fields on test‑mass acceleration noise, provides a detailed circuit design that minimizes additional noise contributions, and validates the approach experimentally. Future work will involve long‑duration space‑environment testing, deployment of multiple coils for spatial mapping, and correlation studies between measured magnetic disturbances and test‑mass acceleration data to further refine LISA’s noise budget.