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