Helical instability of arcs with electrical conductivity of parabolic distribution under electrostatic approximation

摘要

A simplified linear analysis of the helical instability of arc discharges in a cylindrical plasma is given. The starting equations in describing the movement of an arc plasma are the electrostatic magnetohydrodynamic (MHD) equations. The terms ρ{sub}m dh/dt and {partial deriv}P/{partial deriv}t in the energy equation are neglected under the electrostatic approximation. Thus, brief analytic expressions are obtained for the terms of the thermal stabilizing Ω{sub}p, the self-magnetic field destabilization Ω{sub}s, the external magnetic field destabilization Ω{sub}e and the boundary effect Ω{sub}b, from which the growth rate and the stability criterion can be shown. In the case of the applied uniform magnetic field, theoretical results are in good agreement with the experimental measurements. At the same time, we have calculated the growth rate of the instability generated by the self-magnetic field. The results are in perfect agreement with those of complicated calculations in previous works.