a non-perturbative manner.

It should be noted that the twisted-torus magnetic configuration that appears during the evolutionary computations by [@Braithwaite_Spruit_2004] is qualitatively the same as one of the exact axisymmetric and stationary solutions obtained in [@Yoshida_Yoshida_Eriguchi_2006]. Moreover, stable configurations of stellar magnetic fields must have a twisted-torus structure according to [@Braithwaite_2009]. Concerning the stability analysis, this type of configurations is expected to be stable, while magnetic fields with purely [*poloidal*]{} configurations or purely [*toroidal*]{} configurations have been shown to be unstable (see e.g. @Tayler_1973_mnras; @Wright_1973_mnras; @Markey_Tayler_1973_mnras; @Flowers_Ruderman_1977_apj).

In this paper, we apply the formulation developed by [@Tomimura_Eriguchi_2005], [@Yoshida_Eriguchi_2006] and [@Yoshida_Yoshida_Eriguchi_2006] in order to find out how strong and localized [*poloidal*]{} magnetic fields can exist inside stars, as far as equilibrium configurations are concerned. In this formulation, the electric current density consists of several terms with different physical significances which contain arbitrary functionals of the magnetic flux function. These arbitrary functions correspond to the degrees of freedom in magnetized equilibria. One of the arbitrary functionals in the expression for the electric current density corresponds to the current in the [*toroidal*]{} direction. By choosing this functional form properly, we would be able to obtain equilibrium configurations of axisymmetric barotropic stars with highly 