The SIMPLE algorithm is used to solve the MHD equations and the solutions of MHD equations are presented for the whole free-burning arc, excluding the electrodes. The SIMPLE algorithm has been revised in order to solve MHD equations and the flow chart is showed. A self-consistent numerical solution of the MHD equations yields the temperature and velocity distributions. And different types of radiation term are examined on the numerical results and it is found that the radiation term redults in a small decrease on the temperature of the arc.

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.

A simplified linear analysis of the helical instability of arc plasmas is given. Explicit analytic results are obtained. In case of the applied uniform magnetic field, theoretical results are in good agreement with the experimental measurements. At the same time it also calculates the growth rate of the instability generated by the self magnetic field. The results are in agreement with those of complicated calculations once perfectly.