HYDROMAGNETIC EQUILIBRIA AND FORCE-FREE FIELDS

Solutions of the equilibrium equations of a perfectly conducting fluid (1) div B = 0, grad p = J x B = curl B x B/u are corsidered. The special case p = constant is a force-free field. These equations are formally identical to those of incompressible fluid flow if B is identified with the fluid velocity and -p with the Bernoulli constant. The solutions of (1) are described by formulating initial and boundary value problems, by integrating the equations in terms of arbitrary functions, and by showing the equivalence with a variational formulation. The situation is complicated by the nonlinearity of the equations. First, one can compute the characteristic normals which are four in number (the system is essentially fourth order). The magnetic lines (analoguestream lines) are counted twice and there are two pure imaginary roots as for the potential equation. On this basis a number of existence theorems are conjectured (and in some special cases proved). (auth)