Tokamak βaB/Ilimit and its dependence on the safety factor

It is shown that, for a given tokamak cross-sectional shape and arbitrary values of the magnetic axis safety factor ${\mathit{q}}_0$, the first stability condition against pressure-driven magnetohydrodynamic modes has the form 40πβ${\mathit{aB}}_0$/I≤${\mathit{C}}_{\mathit{R}}$(${\mathit{q}}_0$)/${\mathit{q}}_0$. Moreover, in the limit of large ${\mathit{q}}_0$, ${\mathit{C}}_{\mathit{R}}$(${\mathit{q}}_0$) becomes independent of ${\mathit{q}}_0$ and independent of the toroidal mode number.