Ideal magnetohydrodynamic equilibrium expansion about a magnetic axis in a non-symmetric torus

A variant (weitzner Phys.Plasmas 2014) equilibrium representation is employed to construct a a formal expansion of a MHD equilibrium in a topological torus with a given magnetic axis. The lowest order terms are given explicitly and the description of the higher order terms is given. Additionally an examination of the ability to extend the expansion to all orders is presented. The expansion is in terms of the distance from the given magnetic axis. The conditions of quasisymmetry and omnigenity are given in terms of the expanded quantities. Comparison with results of other approaches is also given.