Boundary-coupled generalization of the Newcomb stability criterion

In magnetohydrodynamic problems in which there are boundaries in the axial or azimuthal symmetry directions, the energy principle involves multiple nonorthogonal trial perturbations. The subsequent Euler--Lagrange coupling of these allowed excitations necessitates a generalization of the Newcomb necessary-and-sufficient stability criterion. This extension, in which the absence of a conjugate point (instead of a simple zero) provides stability, is described in this paper. An important aspect of the proof involves the treatment of certain asymmetries which arise in the presence of the anisotropy caused by the magnetic field. The general method described here has applications to finite-length axial laboratory pinches and to astrophysical plasmas with rooted magnetic fields