Stability of a diffuse linear pinch with axial boundaries

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Abstract
A formulation of the stability behavior of a finite‐length pinch is presented. A general initial perturbation is expressed as a uniformly convergent sum over a complete discrete k set. A variational calculation is then performed, based on the energy principle, in which the end‐boundary conditions appear as constraints. The requisite Lagrange multipliers mutually couple the elemental periodic excitations. The resulting extended form of δW still admits a proper second‐variation treatment so that the minimization and stability considerations of Newcomb remain applicable. Comparison theorems are discussed as is the relevance of this end‐effect model to the stability of solar coronal loops.

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