Cylindrical tokamak

For a large aspect-ratio, circular cross section tokamak, the $R$ on a magnetic surface is nearly constant, $R \approx R_0$. The poloidal angle dependence of the magnetic field can be neglected, i.e., $B_{\phi} (r, \theta) \approx B_{\phi} (r)$, and $B_p (r, \theta) \approx B_p (r)$. Using these, the safety factor in Eq. (29) is approximated to

$$q = \frac{1}{2 \pi} \oint \frac{1}{R} \frac{B_{\phi}}{B_p} d \ell... ...)}{B_p (r)} \frac{1}{R_0} 2 \pi r = \frac{r}{R_0} \frac{B_{\phi} (r)}{B_p (r)},$$ (503)

where $r$ is the minor radius of the magnetic surface.