J. Appl. Phys. Vol. 68, p. 3818 (1990) (PDF)
The general approach to cylindrically symmetric force-free magnetic fields first introduced by Lust and Schluter [Z. Astrophys. Vol. 34, 263 (1954)], is restricted to cylindrically symmetric fields, and subsequently used to determine a set of solutions to the force-free field equations with non-constant alpha. The first element of the set is the well known constant a solution of Lundquist [Ark. Fys. Vol. 2, 361 (1951)]. These solutions may have practical applications with respect to high-temperature superconductors.
A Class of Cylindrically Symmetric Solutions to the Force-Free Magnetic Field Equations with Non-Constant Alpha