# Charge-induced force-noise on free-falling test masses: results from LISA Pathfinder

## TL;DR

This paper presents detailed measurements of charge-induced electrostatic forces on free-falling test masses in space, demonstrating control of acceleration noise to levels suitable for gravitational wave detection.

## Contribution

First in-space measurements of charge-induced forces on test masses relevant for space-based gravitational wave detectors, validating electrostatic models and noise control techniques.

## Key findings

- Charge-induced acceleration noise maintained near 1.0 fm/s^2/√Hz
- Charge build-up due to cosmic rays characterized
- Electrostatic model predictions agree with measurements

## Abstract

We report on electrostatic measurements made on board the European Space Agency mission LISA Pathfinder. Detailed measurements of the charge-induced electrostatic forces exerted on free-falling test masses (TMs) inside the capacitive gravitational reference sensor are the first made in a relevant environment for a space-based gravitational wave detector. Employing a combination of charge control and electric-field compensation, we show that the level of charge-induced acceleration noise on a single TM can be maintained at a level close to 1.0 fm/s^2/sqrt(Hz) across the 0.1-100 mHz frequency band that is crucial to an observatory such as LISA. Using dedicated measurements that detect these effects in the differential acceleration between the two test masses, we resolve the stochastic nature of the TM charge build up due to interplanetary cosmic rays and the TM charge-to-force coupling through stray electric fields in the sensor. All our measurements are in good agreement with predictions based on a relatively simple electrostatic model of the LISA Pathfinder instrument.