Resistive ballooning line-tied boundary conditions

Ideal and resistive ballooning modes are investigated for different ratios of a two-layer stratified density region representing a model for the photospheric/coronal boundary. Construction of the ballooning equations using a WKB approach is justified by comparison between the values of the growth rate obtained using Hain-Luest and ballooning equations together with a WKB integral relation. Different values of the density ratio, radius, and resistivity are considered. Sausage-type and kink-type instabilities are found. One of these, depending on the value of r, remained unstable for large density ratios. The other instability tended to marginal stability as the density ratio was increased, and allowed parallel and perpendicular flows across the boundary. This is contrary to the predictions of both the 'rigid-wall' and 'flow-through' conditions