Force-free foliations

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.

Figure 1

Poloidal field lines of force-free solutions found by the foliation-searching algorithm. The X point, dipolar, and bent solutions appear to be new (in the first two cases, when rotation of the field lines is considered).