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Context. The understanding of fossil fields origin, topology and stability isone of the corner stones of the stellar magnetism theory. On one hand, sincethey survive over secular time-scales, they may modify the structure and theevolution of their host stars. On the other hand, they must have a complexstable structure since it has been demonstrated by Tayler and collaboratorsthat simplest purely poloidal or toroidal fields are unstable on dynamicaltime-scales. In this context, the only stable configuration which has beenfound today is the one resulting of a numerical simulation by Braithwaite andcollaborators who have studied the evolution of an initial stochastic magneticfield, which is found to relax on a mixed stable configuration (poloidal andtoroidal) that seems to be in equilibrium and then diffuses. Aims. In thiswork, we thus go on the track of such type of equilibrium field in asemi-analytical way. Methods. In this first article, we study the barotropicmagnetohydrostatic equilibrium states; the problem reduces to aGrad-Shafranov-like equation with arbitrary functions. Those latters areconstrained by deriving the lowest-energy equilibrium states for giveninvariants of the considered axisymmetric problem and in particular for a givenhelicity which is known to be one of the main actor of such problems. Then, weobtain the generalization of the force-free Taylor's relaxation states obtainedin laboratory experiments (in spheromaks) that become non force-free in theself-gravitating stellar case. The case of general baroclinic equilibriumstates will be studied in Paper II. Results. Those theoretical results areapplied to realistic stellar cases, namely to the solar radiative core and tothe envelope of an Ap star, and discussed. In both cases we assume that thefield is initially confined in the stellar radiation zone.

Large-Scale Magnetic Fields in Stellar Interiors I. Equilibrium Configurations to Model Fossil Fields