 Cartesian magnetic flux function

For a $y$-independent solenoidal magnetic field, the transverse components can be written $B_x=-{\psi }_z$ and $B_z={\psi }_x$. Contours of $\psi$ are transverse magnetic field lines. The independent axial component $B_y$ can twist the flux tube. Under the MHD induction equation, an additive time-dependent gauge can be chosen so that $D\psi /Dt=0$.