Configurations of axisymmetric quasi-force-free magnetic systems. II

Three methods for obtaining equilibrium configurations, which are prototypes of quasi-force-free windings, are considered using the zero-thickness model. These methods include the formation of an equilibrium figure by iterations, application of diamagnetic shields, and poloidal current drainage from the end part of the magnet to its external zone. Combination of these methods makes it possible to construct configurations of thin-wall quasi-force-free magnets and to determine the limiting size of the end parts of windings, on which the magnetic pressures of the poloidal and toroidal fields on both sides of the current-carrying layer are balanced. The possibilities of constructing the outer zone of a thin-wall magnet with cylindrical reinforcements are considered. It is shown that it is possible to avoid the emergence of axial forces in the entire volume of the magnet in magnetic systems with an aspect ratio of two and smaller. A two-module configuration is considered and the possibility of additional reduction of stresses in this system as compared to a single balanced module is demonstrated. An equilibrium configuration of a three-layer magnet with zero-thickness layers is constructed. It is shown that the transition from this configuration to real finite-thickness layers does not introduce significant changes in the results of calculation of stresses in the most loaded parts of the magnet.