On the action of magnetic gradient forces in micro-structured copper deposition

In order to shed more light on the role of magnetic gradient forces and Lorentz forces on the deposition pattern found recently at copper electrodes, experiments and numerical simulations have been performed in a generic geometry that consists of a single small cylindrical permanent magnet which is placed behind the cathode. The cylinder axis coincides with the magnetization direction and points normal to the electrode surface. The electrode is oriented vertically which allows a separate discussion of the influence of both forces.

Experiments and numerical simulations are found to give very good agreement with respect to the deposition pattern. Our analysis clearly shows that the major influence is due to the action of the magnetic gradient force. Numerical simulations prove that the separate action of the Lorentz force does not reproduce the deposition structure. A detailed analytical discussion of the motion forced by the different magnetic forces in superposition with natural convection is given.