Magnetic field-line curvature ($\mathbf{\kappa }=\mathbf{b}\cdot \nabla \mathbf{b}$)

The curvature vector of a magnetic field line parametrized by arc length. For circular lines, it points towards their center and has magnitude $1/R$. The curvature contribution to magnetic tension is $B^2\mathbf{\kappa }/(4\pi )$ in Gaussian units.