Velocity-space divergence (${\nabla }_{\mathbf{v}}\cdot \mathbf{A}$)

The divergence with respect to velocity coordinates, with position held fixed. In $d$ dimensions, $\mathbf{A}(\mathbf{x},\mathbf{v})=\mathbf{B}(\mathbf{x})-a(\mathbf{x})\mathbf{v}$ has ${\nabla }_{\mathbf{v}}\cdot \mathbf{A}=-da$. A kinetic conservation law must retain this term for velocity-dependent forces.