A small electrically conducting sphere contains a dynamo source of magnetic field which externally has quadrupolar symmetry. It is surrounded by a force-free medium of finite electrical conductivity. Differential rotation of the sphere, together with a 'solar wind' blowing offit, can maintain a twisted force-free external field despite the ohmic dissipation; differential rotation alone cannot do so. Increasing differential rotation can lead to a rotating almost radial field that extends to ever greater distances, coupled with a strongly dissipative conical current sheet separating regions of outgoing and incoming field. Dissipation in the sheet prevents the field from reaching the critical twist angle (flashpoint) at which all the flux would extend to infinity. A thin current sheet of this kind is susceptible to resistive instabilities; possible consequences are discussed in the concluding section.
Lynden-Bell, D., & Moffatt, H. K. (2015). Flashpoint. Monthly Notices of the Royal Astronomical Society, 452(1), 902–909. https://doi.org/10.1093/mnras/stv1255