The traditional arc-sheath growth continuous transition model（CTM） can be adopted to study the motion migration process of post-arc particles

however

it only focuses on the post-arc process and does not consider the influence of the arcing process on the post-arc process. In this paper

the effect of the arcing process before the zero-crossing current on the migration and diffusion of the particles after the arc is reflected in the traditional CTM model

and an improved CTM model is established. This improved model is a function of the arc current frequency. According to this model

the research shows that

under the frequency range of 50～50 000 Hz

the frequency does not have a linear relationship with the growth of the sheath after the arc

and the sheath growth first becomes slower and then becomes faster as the frequency increases. As the frequency increases

the leading role of fast ions and slow ions in the growth of the sheath will change. When fast ions dominate

the sheath will grow faster. In contrast

slow ions dominate and the sheath grows more slowly. The results of this paper can guide the selection of the medium frequency reverse current frequency of the mechanical vacuum DC circuit breaker.