Singular lines of one-dimensional force-free magnetic field

The behavior of adiabatically slow deformations of the force-free field is investigated. Using the linear approximation it is shown that for a rather wide class of boundary perturbations of one-dimensional force-free field there appear singular magnetic force lines or surfaces. Hence the problem of quasi-steady deformation of frozen-in magnetic field has no solution. Relating to the problem of magnetic field in the solar corona it means that there will appear discontinuities (current sheets), when the magnetic field is deformed, for example, due to photospheric motion.