QUASI-STATIC EVOLUTION OF A FORCE-FREE MAGNETIC-FIELD

We consider in the half-space {z > 0} a simple-topology force-free magnetic field B embedded in a highly conducting plasma (resistivity σ) and its quasi-static evolution driven by motions imposed to the feet of its lines on the boundary {z = 0}. We first study the case when B is an x-invariant arcade, discussing in particular: (i) for σ = 0, the existence of stable equilibria corresponding to arbitrarily large shearing, and the qualitative time behaviour of the field (in particular in the limit t → ∞); (ii) for σ ≠ 0, the possibility of a fast transition by reconnection from an arcade to a complex topology configuration having a lower energy, but the same "distribution of magnetic fluxes". We thus consider a fully three-dimensional field (having an "arcade" or a "tube" topology), showing in particular how it is possible to extend to that situation some of the results obtained for an x-invariant arcade when σ = 0. © 1990.