Effect of Ion Beam Balancing on Frequency Split for Fourth Harmonic Mass Defect of Hemispherical Resonator

Based on the energy equation of the hemispherical resonator, this study analyzes the influence of ion beam balancing on the frequency split of the hemispherical resonator. Firstly, the formula for mass defects and the resonant frequency of the resonator is obtained through the energy equation. All mass defects of the resonator are equivalent to fourth harmonic wall thickness defects. The quantitative relationship between harmonic wall thickness defects and the resonant frequency and the geometric relationship between the heavy axis of the resonator and the distribution of mass defects are determined. Secondly, the balancing function is introduced into the resonant frequency equation of the hemispherical resonator, and a mathematical model is established for the resonant frequency, defect wall thickness, and balancing depth of the hemispherical resonator. By introducing relevant errors, the impact of balancing errors on the frequency characteristics of the hemispherical resonator is calculated. Finally, an ion beam balancing experiment is designed to verify the effectiveness of the theory. The results show that the frequency split can be better than 0.001 Hz after balancing, effectively improving the hemispherical resonator's performance.