Magnetic-history constant in an undamped plasma (${\partial }_t(\nabla \times \mathbf{j}+{ϵ}_0{\omega }_p^2\mathbf{B})=0$)

The linear carrier acceleration equation $\dot{\mathbf{j}}={ϵ}_0{\omega }_p^2\mathbf{E}$ and Faraday's law imply this conserved local quantity. Setting its initial value to zero gives the second London equation and London screening. An undamped response alone does not select that initial value, so it must not be used to infer expulsion of a pre-existing magnetic field for every magnetic history.^[ref]