Stability of a Plasma with Loss from the Ends of an Axially Symmetric Magnetic Bottle

Abstract

Interchange stability and drift motion of a plasma losing unsteadily are analysed in a low β limiting case with the use of ideal hydromagnetic equations. The m-th mode of radial displacement δr_m of the plasma boundary is subject to the equation δ\ddotr_m−(S⁄V)δ\dotr_m+m(P⁄V)δr_m=0, where the dots indicate the time derivatives and the coefficients are some averages of the state of the flow along the entire line of force. The reactive force is due to the Corioli’s force on the flowing plasma within a moving flux tube, and the potential force is due to the plasma pressure and the centrifugal force of the flow. Solutions of the equation show that the system is stabilized by the plasma outside the ends, in good agreement with experiments.