Curvature drift (${\mathbf{v}}_c=m{v}_{\parallel }^2\mathbf{b}\times \mathbf{\kappa }/(qB)$)

For a curved field direction $\mathbf{b}=\mathbf{B}/B$, define the curvature vector $\mathbf{\kappa }=(\mathbf{b}\cdot \nabla )\mathbf{b}$. Motion along curved field lines produces a gyroaveraged drift perpendicular to both field and curvature. In a purely toroidal field this and magnetic gradient drift cause opposite vertical drifts for opposite charge signs.