Modeling the effects of an axial magnetic field on the vacuum arc

A quantitative two-dimensional model of a vacuum arc in an applied magnetic field is presented. For the particular case, a uniform axial magnetic field B_Z, it provides a unified condition for the two regimes of arc voltage versus B_Z, i.e. ? the steeply falling voltage branch (low B_Z), and the slowly rising voltage branch (high B_Z, which characterizes the diffuse arc mode). The transition to the high-B_Z regime is complete when the average mixing distance of the individual expanding cathode-spot plasma jets, measured from the cathode plane, is equal to the contact gap length. The model also predicts the observed smooth transition and minimum arc voltage between the two branches, and the independence of the are voltage on the arc current in the high-B_Z regime. Calculated results are found to be in good agreement with reported experimental data from several independent investigations over a wide range of gap, B_Z and arc current I_ARC