Ballooning modes on open magnetic field lines

The ballooning instability on open magnetic field lines is given a thorough mathematical analysis. It is shown that resistive bounding ends (endplates) induce the same stability properties as insulating ends. When unstable, the maximal growth rate increases monotonically with boundary resistivity. An interchange instability may be present, and one necessary condition for its stability is that ∫dl/B be constant on pressure surfaces. (This is an equilibrium existence condition for systems with closed magnetic field lines.) Another necessary condition for interchange stability has the same form as in the closed line case. Precise necessary and sufficient stability criteria are given for various types of bounding ends, including insulating, resistive, and perfectly conducting.