Steps to construct a straight-line flux coordinate system

In Sec. 6, we have provided the steps to construct the magnetic surface coordinate system $(\psi , \theta , \phi )$. Only one additional step is needed to construct the straight-line flux coordinate system $(\psi , \theta , \zeta )$. The additional step is to calculate the generalized toroidal angle $\zeta$ according to Eq. (235), where $\delta$ is obtained from Eq. (). This step introduces the new toroidal angle $\zeta$ and thus introduces a new magnetic surfaces coordinate system $(\psi , \theta , \zeta )$, which is a straight-line flux coordinate system. Also note that the Jacobian of $(\psi , \theta , \zeta )$ coordinates happens to be equal to that of $(\psi , \theta , \phi )$ coordinates.