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The critical breakdown path (CBP) has a significant impact on the breakdown voltage curve and the ignition time of heaterless hollow cathodes (HHCs).To determine the patt of the variation in the CBP position and its impact on ignition performance,a numerical model named the CBP evaluation (CBPE) was established in this paper to calculate the CBP of a HHC.The CBPE model can be used to screen various potential breakdown paths to identify those that are most likely to satisfy the Townsend breakdown conditions,which are denoted as CBPs.To verify the calculation accuracy of the CBPE model,4.5 A-level HHC ignition tests were conducted on HHCs with three different structures.By comparing the test results and the calculated results of the breakdown voltage,the calculation errors of the CBPE under three HHC conditions ranged from 1.6％ to 5.8％,and the trends of the calculated results were consistent with those of the test results.The ignition test also showed the characteristics of the breakdown voltage curve and the ignition time for the three HHCs.Based on the CBPE model,an in-depth analysis was conducted on the mechanism of the patts revealed by the tests.The main conclusions are presented as follows: (1) the CBP always shifts from the long path to the short path in the HHCs with an increasing gas flow rate;and (2) the ignition time of the HHCs depends on the position of the CBP because different CBP positions can cause different mechanisms of heat transfer from the plasma to the emitter.This study can guide the optimization of the CBP position and the corresponding ignition times of HHCs.