Boundary effects on the magnetohydrodynamic stability of a resistive plasma

A general method for studying the resistive MHD stability of plasma configurations where boundary effects are of crucial importance and can be expressed as additional constraints on a periodic system is presented and applied to the case of line-tied cylindrically symmetric coronal loops. The eigenvalue equations obtained are a generalization of the Freidberg and Hewett equations, to which they reduce when the loop length is made infinite. An application to tearing modes is described which shows that in a finite geometry, tearing takes place at the center of the configuration, corresponding to the vertex of coronal loops. Applications to other configurations of astrophysical interest are described.