I. Introduction
Vacuum arc (VA) is the metal vapor arc in the vacuum environment, which appears in many fields, such as, vacuum interrupters, ion sources, coatings, thrusters, and accelerators. VA can be simply divided into three regions, which are cathode spots and mixing region, arc column regions, and anode regions. When the arc current is not very high, the cathode spots are the main plasma source of arc column, and when the arc current is very high, anode will become very active, and anode melting and evaporation will become significant, anode will become another plasma source. For gas arc, such as air arc and SF6 arc, the gas blowing technology always is adopted as the arc extinguishment tool. Different from gas arc, magnetic field always is adopted to control the VA. At present, axial magnetic field (AMF) and transverse magnetic field (TMF) are the popular controlling technologies of VA. Experiments still are the main research tool of VA, while modeling and simulation technology has gotten the rapid progress in recent years. In this paper, modeling and simulation of VA and anode activity under AMF will be mainly reviewed. The challenge of VA modeling in the future will also be discussed.