Equilibrium and stability of a toroidal magnetohydrodynamic system in the neighbourhood of a magnetic axis

In this work we study first the most general toroidal equilibria in the neighbourhood of a magnetic axis, characteristic line in toroidal topology. For this purpose we use a system of tri-orthogonal coordinates tied to the magnetic axis, which is defined with the help of its own intrinsic co-ordinates: R(s) and T(s). The results of the equilibrium calculations show that all other things being equal, no further equilibrium is possible in general when the angle ιc0 of rotational transformation on the magnetic axis approaches a whole multiple of 2π. We give the developments of the physical quantities at equilibrium as far as the third order. We deduce from these properties a classification of toroidal equilibria, and some examples are treated.