Precise measurement and control of radon progeny on detector surfaces

In low-background particle physics experiments, surface deposition of radon progeny presents a significant background challenge. To characterize this contamination, a high-sensitivity surface $\alpha$-activity measurement system was developed, which employs a 3$\times$3 Si-PIN array operating in vacuum to perform $\alpha$-spectroscopy on samples. The system was calibrated using Poly(Methyl MethAcrylate) (PMMA) plates exposed to a controlled high-radon atmosphere, achieving an energy resolution of 2.09 \% for 5.30~MeV $\alpha$ particles and a one-day measurement sensitivity of 1.27~$\mu$Bq/cm$^2$ for $^{210}$Po surface activity. Using this system and a self-built high radon concentration chamber, the deposition behavior of radon progeny on PMMA surfaces was investigated. Results indicate a non-monotonic dependence on exposure time, a significant enhancement of deposition with increasing negative surface electrostatic potential, and a strong modulation by ambient humidity. This paper details the apparatus design, calibration, and experimental study of radon progeny deposition dynamics on PMMA surfaces.