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Metal vapour vacuum arcs are capable to generate multiply charged metallicions, which are widely used in fields such as ion deposition, ion thrusters,and ion sources, etc. According to the stationary model of cathode spot, thoseions are generated by electron-impact single ionization in a step-wise manner,which is M -> M+ -> M2+ -> ... mainly. This paper is designed to studyquantitatively the role of double ionization M -> M2+ in the breakdowninitiation of copper vacuum arcs. A direct simulation Monte Carlo (DSMC) schemeof double ionization is proposed and incorporated into a 2D particle-in-cell(PIC) method. The super-particles of Cu2+ ions generated from differentchannels are labelled independently in the PIC-DSMC modelling of vacuum arcbreakdown. The cathode erosion rate based on PIC modelling is about 40{\mu}g/Cin arc burning regime, which agrees well with previous experiments. Thetemporal discharge behaviours such as arc current, arc voltage, and ionizationdegree of arc plasma, are influenced with or without double ionizationnegligibly. However, additional Cu2+ ions are generated near the cathode inbreakdown initiation from the double ionization channel, with a lower kineticenergy on average. Therefore, the results on spatial distribution and energyspectra of Cu2+ ions are different with or without double ionization. Thispaper provides a quantitative research method to evaluate the role of multiplyionization in vacuum arcs.

The role of double ionization on the generation of doubly charged ions  in copper vacuum arcs: insight from particle-in-cell/direct simulation Monte  Carlo methods