Abstract: Argon discharge at the gap,between power-line and J-clamp in connecting live-wire,was empirically approximated,mathematically modeled,theoretically analyzed and numerically simulated in finite element method.The influence of the period and phase on the Max electron-density was investigated.The simulated results show that the period and phase have a major impact.Specifically,in the 1^st-period,the Max e-density in positive phase is larger than that in negative phase,the high e-density(red) region moves to the other electrode before the voltage passes zero.As period-number increases,the red-region disappearance/appearance times change in a delay-ahead mode when positive voltage passes zero,and the time difference(Δt₁) varies in an increase-decrease manner; in contrast,when negative voltage passes zero,an ahead-delay mode for the disappearance/appearance times and a decrease-increase manner for Δt₂.We suggest the simulation be of technological interest in live operation of powerline.