We construct exact, non-linear, solutions for an horizontal, cylindrical, current-carrying, prominence supported against solar gravity by the action of a Lorentz force. The solutions incorporate the photosphere boundary condition, proposed by van Tend and Kuperus (1978), and analyzed by them for line filaments. Our solutions have finite radius for the prominence material and, as well as satisfying the equations of magnetostatic equilibrium, they allow for the continuity of gas pressure, and of the normal and tangential components of magnetic field across the circular prominence boundary. We show that an infinity of solutions is possible and we illustrate the basic behavior by investigation of a special case.
We also give a prescription for constructing equilibrium fields for any horizontal prominence with arbitrary cross-section and with an arbitrary external magnetic field. The prescription is ideally suited for numerical codes and we suggest that both the equilibrium of such shapes can easily be accomplished numerically together with their evolutionary history. * In doing preliminary calculations prior to this paper, we at one stage computed the energy of a circular cylinder of current. In so doing we had to make use of several integrals recorded by Gradshteyn and Ryzhik (1965). It turned out that two of the recorded integrals are in error and we report here the corrections. On p. 568, 4.317, integral (3) a factor 'In' should be inserted after ~r cot(t); on p. 538, 4.253 integral (4), the upper limit should be ~, not unity.