Field line curvature
The magnetic field line curvature is defined by
is a unit vector along the magnetic field. κ points towards the local centre of curvature of B, and its magnitude is equal to the inverse radius of curvature.
A plasma is stable against curvature-driven instabilities (e.g., ballooning modes) when
(good curvature) and unstable otherwise (bad curvature). Here, p is the pressure. 
The component of the curvature perpendicular to the flux surface is
Here, ψ is a flux surface label (such as the poloidal flux).
The component of the field line curvature parallel to the flux surface is
Flux surface curvature
The tangent plane to any flux surface is spanned up by two tangent vectors: one is the normalized magnetic field vector (discussed above), and the other is
The corresponding perpendicular curvature (the curvature of the flux surface in the direction perpendicular to the magnetic field) is
and one can again define the corresponding normal and geodesic curvature components in analogy with the above.