Ballooning instabilities in the solar corona - Conditions for stability

A method for analyzing the stability of cylindrical loops and arcades to ballooning modes is presented. Using a WKB method, simple tests for instability (or stability to localized modes) are obtained for the two commonly used, line tying, conditions. In addition, when instabilities are present, the physical growth rate and the radial structure of the least stable can be computed from the solution of a 4th order system of ordinary differential equations. The detailed analysis for a particular field is presented in an Appendix