Abstract: The helical instability of an arc column with electrical conductivity of the parabolic distribution and macro velocity is discussed in an axial magnetic field. The magnetohydrodynamic equations serve as the starting point of the theory, in an electrostatic approximation and a linear time dependent perturbation theory, the perturbation equations for the arc column movement are deduced. Solutions of these equations are obtained analytically, from which the stability limit of the cylindrical arc and the growth rate of the helical instability are given.

Key words: electrical arc, helical instability, macro velocity