# Simulation of Patch Field Effect in Space-Borne Gravitational Wave Detection Missions

## TL;DR

This paper introduces a new simulation method to study patch field effects in space-based gravitational wave detectors, improving sensor accuracy.

## Contribution

A novel boundary element partitioning and octree-based simulation algorithm is proposed to model electrostatic and geometric impacts of patch fields.

## Key findings

- ΔFx and ΔKxx show linear dependence on patch potential variation (Δu).
- Patch effects can be modeled using a quartic polynomial dependent on patch radius (rₘ).
- The new method efficiently models both electrostatic and geometric impacts with low computational complexity.

## Abstract

Space-borne gravitational wave detection missions demand ultra-precise inertial sensors with acceleration noise below 3×10−15 m/s2/Hz. Patch field effects, arising from surface contaminants and nonuniform distribution of potential on the test mass (TM) and housing surfaces, pose critical challenges to sensor performance. Existing studies predominantly focus on nonuniform potential distributions while neglecting bulge effects (surface deformation caused by the adhesion of pollutants or oxides, production and processing defects, and other factors) and rely on commercial software with limited flexibility for customized simulations. This paper presents a novel boundary element partitioning and octree-based simulation algorithm to address these limitations, enabling efficient simulation of both electrostatic and geometric impacts of patch fields with low spatiotemporal complexity (O(n)). Leveraging this framework, we systematically investigate the influence of single patches on the TM electrostatic force (ΔFx) and stiffness (ΔKxx) through parametric studies. Key findings reveal that ΔFx and ΔKxx exhibit linear dependence on patch potential variation (Δu) and can be fitted by a quartic polynomial (which can be simplified in some cases, such as only a cubic term) about patch radius (rₘ). The proposed method’s capability to concurrently model geometric bulges and potential nonuniformity offers significant advantages over conventional approaches, providing critical insights for gravitational wave data analysis. These results establish a foundation for optimizing mitigation strategies against patch-induced noise in future space missions.