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• On-orbit non-intrusive perturbation measurement of Hall effect thrusters. • 10 kHz to 100 kHz analysis better than full frequency domain. • Perturbation signal amplified by scatter numbers in the far-zero region. • The physical core represented by the scatter numbers is the dwell time. • Dwell time is mainly related to breathing oscillations. The failure of Hall effect thruster (HET) is usually the result of the accumulation of several tiny abnormal disturbances during operation. Timely and accurate early warning of perturbations is an important guarantee for the normal operation of thrusters. In this study, when the perturbation rate of HET signal (anode voltage or anode flow rate) is −4% to 4%, the time scale signal of breathing oscillation (BO) in the frequency range of 10 kHz to 100 kHz is statistically analyzed. Experiments show that when the signal is perturbed, the balance between ionization and acceleration of plasma in the discharge channel is destroyed, resulting in the dwell time of the wave peaks and valleys of BO in the far-zero region with the perturbation law, which visually shows that the number of scattered points at the corresponding current value changes regularly. According to the above statistical characteristics, this paper proposes a new condition monitoring index, namely the number of scattered points in the wave peaks side of the far-zero point area, and designs a perturbation indicator for the operating condition of the HET. Compared with direct monitoring of discharge current in engineering, this indicator can amplify the influence of the perturbation signal on BO, and has better identification and accuracy. Meanwhile, the indicator does not use invasive measurement and complex equipment, and is promising to be applied to the monitoring and diagnosis of the perturbation operation state of the on-orbit thruster. [ABSTRACT FROM AUTHOR]