Abstract: Regarding the LHC-3L hollow cathode developed by the Lanzhou Institute of Physics, this study investigates the issue of increased anode voltage during the activation and burn-in stages of screening tests. By applying the drift-diffusion theory, a model for electron current collection along the axial direction in the plume region of the anode was established. Theoretical analysis was conducted on the factors contributing to the increase in anode voltage, and corresponding experimental verification results were presented. This research provides support for improving hollow cathode testing methods and ultimately establishing testing standards. The anode voltage of a hollow cathode is a critical indicator for evaluating its discharge stability. An increase in anode voltage can lead to a shortened lifespan of the hollow cathode and oscillation in the thrust output of the electric propulsion system. Therefore, screening is necessary after the mass production of hollow cathodes. With the growing demand for electric propulsion in space applications, there is an urgent need to establish a refined evaluation system and unified screening test standards. This paper begins by introducing the electron emission principle and screening test methods of the LHC-3L hollow cathode developed by the Lanzhou Institute of Physics. A formula for the axially collected electron current density J_e at the anode of hollow cathode, based on drift-diffusion theory, was established. The functional relationship between J_e and ν_en （the electron-Xenon atom collision frequency）, ν_ei（the electron-Xenon ion collision frequency）, V_k（the keeper voltage of hollow cathode）, V_a（the anode voltage of hollow cathode）, d_ak（the distance between the keeper and anode in hollow cathode）, n_k（the plasma density at the keeper orifice）, n_a（the plasma density at the anode）as well as T_e（electron temperature in plasma）was presented. Finally, verification tests were conducted on the TS-5C hollow cathode screening test system using the typical LHC-3L products to examine the effect of the number of screening tests, d_ak, \dot m_\textXe （the mass flow rate of Xenon）, V_k on the increase in anode voltage. The verification results were consistent with the predictions of the theoretical formula. This study provides a reference for refining the screening test methods of hollow cathodes and establishing a unified testing standard.