The energy equations were simplified by the correct electrostatic ordering under electrostatic approximation. The effects of the external axial magnetic field

the current profiles and arc currents on the helical instabilities of arcs were studied by using numerical method. In the presence of the external magnetic field

numerical results show that when the current profile of an arc column is the uniform distribution

the short wavelength perturbation can be stabilized by positive direction magnetic field

whereas the long wavelength perturbation can be stabilized by reverse magnetic field. When the current profile of an arc column has a parabolic distribution

in the short wavelength perturbation case

the effect of positive direction magnetic field on the arc stability is very small. However

its stabilizing effect is enhanced for the long wavelength perturbation. The intermediate and long wavelength perturbations can also be stabilized by reverse magnetic field.