Determination of a flow generating a neutral magnetic mode

The problem of the reconstruction of a flow of conducting incompressible fluid generating a given magnetic mode is considered. We use the magnetic induction equation to derive ordinary differential equations along the magnetic field lines, which gives an opportunity to determine the generating flow if additional data is provided on a two-dimensional manifold transversal to magnetic field lines, and show that an arbitrary solenoidal vector field cannot be a neutral magnetic mode sustained by any flow of conducting fluid, unless a scalar consistency condition is satisfied at every point within the fluid volume.