SOME PROPERTIES OF FINITE-ENERGY CONSTANT-ALPHA FORCE-FREE MAGNETIC-FIELDS IN A HALF-SPACE

Some useful properties of a finite energy, constant-alpha, force-free magnetic field B-alpha occupying a half-space D are presented. In particular: (a) Fourier and Green representations of B(alpha) are obtained and used to derive conditions for the existence and uniqueness of a B(alpha) having a given normal component B(z) on the boundary partial derivative D. (b) The asymptotic behaviour of B(alpha) at infinity as well as stability results against changes in the boundary condition on partial derivative D and in the value of alpha are established. (c) The energy of B(alpha) is shown to be smaller than the energy of the open field having the same B(z) on partial derivative D, thus confirming an earlier conjecture (Aly, 1984). (d) B(alpha) is proved to not be a Taylor-Heyvaerts-Priest state, in spite of the fact that its relative helicity H is finite and that it is the only solution of the Lagrange-Euler equation associated with the problem of minimizing the energy among all the fields having the same value of H and the same B(z) on partial derivative D.