Magnetic curvature

The magnetic curvature is defined by

${\vec {\kappa }}={\vec {b}}\cdot {\vec {\nabla }}{\vec {b}}$

where

${\vec {b}}={\frac {\vec {B}}{|B|}}$

is a unit vector along the magnetic field. When B is locally a circle section, then κ points towards the centre of the circle.

A plasma is stable against curvature-driven instabilities (e.g., ballooning modes) when

${\vec {\kappa }}\cdot {\vec {\nabla }}p<0$

(good curvature) and unstable otherwise (bad curvature). Here, p is the pressure.