An electrostatic MHD theory for helical instabilities of arc discharges

Summary form only given. An analytic linear study for "slow" magnetic helical instabilities of arc discharges in a cylindrical plasma is developed in this paper. Based on a set of electrostatic magnetohydrodynamic (MHD) equations, we investigate "slow" m=1 helical modes with an external axial magnetic field. The stability analysis by the criterion obtained in this paper shows that the "slow" resistive-viscous helical instabilities are linearly stable in both long wave-length and short wave-length limits. These results are in agreement with numerical results. To the most dangerous instabilities with a wave-length of order of the length of a discharge arc, the helical mode are marginally stable. The theory shows that an external axial magnetic field can destabilize those helical modes. This result contradicts to ideal MHD "fast" kink mode theory with a growth rate much faster than the resistive viscous dissipation, such as the ideal MHD kink mode theory for tokamaks where a strong axial field stabilizes the mode, and the previous theory for electric furnace arc discharges. However helical instabilities generated by an axial external field are indeed observed in recent experiments.