  Electromagnetic field configurations with vanishing Lorentz force density are
known as force-free and appear in terrestrial, space, and astrophysical
plasmas. We explore a general method for finding such configurations based on
formulating equations for the field lines rather than the field itself. The
basic object becomes a foliation of spacetime or, in the stationary
axisymmetric case, of the half-plane. We use this approach to find some new
stationary and axisymmetric solutions, one of which could represent a rotating
plasma vortex near a magnetic null point.
