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.In the second part we study the stability of these equilibria in terms of localized displacements. The results indicate some regions of stabilities for configurations characterized by ι0c/2π≈k: A simple example of a straight stellarator is treated and furnished with conditions for equilibrium and stability characterized by some βc's of equilibrium and stability.
A three-dimensional magnetohydrodynamic equilibrium in an axial coordinate with a constant curvature