Turbulent magnetic pumping (${\mathcal{E}}_{\mathrm{pump}}=\mathbf{\gamma }\times \overline{\mathbf{B}}$)

Turbulent magnetic pumping is an effective transport of the mean magnetic field produced by correlations in inhomogeneous or anisotropic turbulence. Its contribution to the mean-field electromotive force is ${\mathcal{E}}_{\mathrm{pump}}=\mathbf{\gamma }\times \overline{\mathbf{B}}$. In the mean induction equation this enters as $\nabla \times (\mathbf{\gamma }\times \overline{\mathbf{B}})$, the same algebraic form as advection by a velocity $\mathbf{\gamma }$. Thus it supplements the mean material velocity without requiring an equal mean mass flow. Downward pumping can help retain or couple fields in a solar dynamo.