ASYMPTOTIC FORMS FOR THE ENERGY OF FORCE-FREE MAGNETIC-FIELD CONFIGURATIONS OF TRANSLATIONAL SYMMETRY

It is known from computer calculations that if a force-free magnetic f ield configuration is stressed progressively by footpoint displacement s, the configuration expands and approaches the open configuration wit h the same surface flux distribution and the energy of the field incre ases progressively. For configurations of translational symmetry, it h as been found empirically that the energy tends asymptotically to a ce rtain functional form. It is here shown that analysis of a simple mode l of the asymptotic form of force-free fields of translational symmetr y leads to and therefore: justifies this functional form. According to this model, the field evolves in a well-behaved manner with ho indica tion of instability or loss of equilibrium.