Abstract:
The equations for equilibrium of a thin, isolated, axisymmetric, and force-free magnetic flux tube are derived, taking into account the inhomogeneities of the magnetic field, plasma pressure, and plasma density over the tube's cross-section, and the variation of the cross-section diameter, up to the second-order in the parameter representing the tube thinness. It is shown that the two equations of equilibrium and the essential constraints applied form a closed system of equations. Auxiliary assumptions concerning the temperature of the tube plasma are found to be neither necessary nor possible.
