Abstract: A new linear analysis for magnetic helical instabilities of arc discharges in a cylindrical plasma is deve-loped based on a set of electrostatic magnetohydrodynamic(MHD) equations.By the correct electrostatic ordering the perturbed energy equations are simplified.The effects of the external axial magnetic field,the arc currents and the relative rates of arc column radius on the arc helical instabilities are studied by numerical method.