Figure 13.

Cross-section of a non-axisymmetric equilibrium. The curved grey line towards the right is the surface of the star and the centre of the star is on the left; the coordinate system used for the plot is cylindrical. The blue/red shading represents the toroidal field component (out of/into the page) multiplied by the cylindrical radius. The poloidal component (in the plane of the page) is represented by the arrows and by contours of its scalar potential, calculated by ignoring spatial derivatives perpendicular to the plane. In fact, it can be seen that the arrows are very nearly parallel to the contours of the scalar potential, showing that the length scale of variation in the direction perpendicular to the page is much greater than the length scale in the plane of the page, i.e. that the flux tubes meander around the star over scales much greater than their width. Note also that neighbouring flux tubes can have toroidal field in either the same or opposite directions: as the toroidal field is absent from the space between the tubes, one tube is not ‘aware’ of the direction of toroidal field in its neighbours, so the equilibrium and stability properties are independent of its direction. Figure from Braithwaite [93].