Effect of solar proton events on test mass for gravitational wave detection in the 24th solar cycle

Free-falling cubic Test Masses (TMs) are a key component of the interferometer used for low-frequency gravitational wave (GW) detection in space. However, exposure to energetic particles in the environment can lead to electrostatic charging of the TM, resulting in additional electrostatic and Lorentz forces that can impact GW detection sensitivity. To evaluate this effect, the high-energy proton data set of the Geostationary Operational Environmental Satellite (GOES) program was used to analyze TM charging due to Solar Proton Events (SPEs) in the 24th solar cycle. Using the Geant4 Monte Carlo toolkit, the TM charging process is simulated in a space environment for SPEs falling into three ranges of proton flux: (1) greater than 10 pfu and less than 100 pfu, (2) greater than 100 pfu and less than 1000 pfu, and (3) greater than 1000 pfu. It is found that SPEs charging can reach the threshold within 535 s to 18.6 h, considering a reasonable discharge threshold of LISA and Taiji. We demonstrate that while there is a somewhat linear correlation between the net charging rate of the TM and the integrated flux of ≥ 10 MeV SPEs, there are many cases in which the integrated flux is significantly different from the charging rate. Therefore, we investigate the difference between the integral flux and the charging rate of SPEs using the charging efficiency assessment method. Our results indicate that the energy spectrum structure of SPEs is the most important factor influencing the charging rate. Lastly, we evaluate the charging probability of SPEs in the 24th solar cycle and find that the frequency and charging risk of SPEs are highest in the 3rd, 4th, 5th, 6th, and 7th years, which can serve as a reference for future GW detection spacecraft.