Tokamak beta aB/I limit and its dependence on the safety factor.

Abstract

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 40\ensuremath{\pi}\ensuremath{\beta}${\mathit{aB}}_{0}$/I\ensuremath{\le}${\mathit{C}}_{\mathit{R}}$(${\mathit{q}}_{0}$)/${\mathit{q}}_{0}$. 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.