Inflexional disequilibrium of magnetic flux-tubes

In this paper, we prove that magnetic flux-tubes in inflexional configuration are in disequilibrium and evolve to an inflexion-free state. The magnetic field is defined in a tube of circular cross-section and is chosen so as to have toroidal and poloidal components contributing to the internal twist of the flux-tube. By using orthogonal curvilinear coordinates, we derive the equations for the Lorentz force associated with the magnetic flux-tube and use them to study the generic behaviour associated with passage through inflexional configuration. Inflexional state is attained when local curvature vanishes as the tube axis changes concavity. We check that the conditions for the equilibrium of the flux-tube in inflexional configuration are not satisfied and hence we prove disequilibrium. Inflexional disequilibrium makes magnetic flux-tubes evolve to an inflexion-free state. As a consequence, inflexional flux-tubes in free space evolve naturally to an inflexion-free configuration. This mechanism has important implications for the energetics of solar coronal loops and astrophysical flows.