A simplified linear analysis for resistive-viscous magnetic helical instabilities of arc discharges in a cylindrical plasma is developed. Based on a set of electrostatic magnetohydrodynamic (MHD) equations, resistive-viscous m=1 modes with an external axial magnetic field are studied. Explicit analytic results are obtained, from which the growth rate and the stability criterion can be shown, and the electrostatic assumption can be justified. In comparison with the previous channel model calculations, this analytic treatment can provide a simplified model for instability estimates, while avoiding artificial assumptions and misorderings in the energy equation.

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The helical instability of an arc column with electrical conductivity of the distribution of the linear heat flux potential (a new "temperature") is discussed in axial magnetic field. The magnetohy-drodynamic 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. In comparison the results with those of uniform current distribution, it is found that the stable area is enlarged.

The helical instability of an arc column with electrical conductivity of the parabolic distribution and transparent radiation of the parabolic distribution is discussed in axial magnetic field.The magnetohydrodynamic equations serve as the strarting 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.In comparision the results with those of current distribution without radiation,it is found that the radiation in the small middle arc increases the instability.