Abstract: Based on a two-dimensional axisymmetric magnetohydrodynamic (MHD) model, the vacuum arc characteristics under four kinds of axial magnetic fields (AMFs) are analyzed, which include a bell-shaped AMF generated by a pair of commercial cup-shaped electrodes, and three kinds of saddle-shaped ones generated by three pairs of newly designed electrodes. The simulation result indicates that the effect of AMF on the vacuum arc characteristics is significant. A comparison between the simulation result and experimental one shows that the distribution of the simulated ion density integrated along the viewing path is in agreement with the image of the arc column. Both the simulation result and the experimental one show that, among the four kinds of AMFs, the saddle-shaped one with the highest strength is the best, which could resist the constriction of the vacuum arc more efficiently, while the saddle-shaped one with the lowest strength and the bell-shaped one are the least desirable.