## Influence of Magnetic Fields

When an electrical charge moves in a magnetic field, the magnetic field itself exert a force on the moving charge.

In the alumina reduction cells we have strong magnetic fields, generated by the high intensity electrical currents used for the electrolysis (now going beyond 350000 Amps and in some test cell 500000 Amps), and electrical charges (electrons in the metal pad and ions inside the electrolyte) moving in these magnetic fields.

The force exerted by the magnetic field on the electrical charges moving is calculated by a vectorial product: Where B is the magnetic field while j is the current density. The direction of the force F will be perpendicular to the magnetic field B and the current density j. The direction of F follows the right-hand rule and its unit measure is N/m3.

As a result, these forces induce in the electrolyte and in the molten metal complex movements, in terms of vortexes and bath/metal interface waves. All these movements have a detrimental effect on the current efficiency and the specific energy consumption therefore it is of paramount importance to design pots with good magnetic compensation in order to decrease to a minimum all the bath and metal movements.

Let’s consider one cell in a side by side configuration. To help studying the forces that develop inside the electrolyte and metal, it is useful to refer to a right hand coordinate system with the origin O at the cathode center, the plane defined by the origin O and the axes X and Y parallel to the cathode, the X axis aligned as the line current, and the Z axis going out of the cell through the molten metal and then the electrolyte: Taking this coordinate system as reference, we can split the magnetic field B and the current density j in their components Bx, By and Bz and jx, jy and jz and list in the following table the various components of the forces generated by each B,j components couple:

 Magnetic Field Component Current Density Component Horizontal Transverse Jx Horizontal Longitudinal Jy Vertical Jz Horizontal Transverse Bx 0 Vertical Force Fz (-) Longitudinal Force Fy (+) Horizontal Longitudinal By Vertical Force Fz (+) 0 Transverse Force Fx (-) Vertical Bz Longitudinal Force Fy (-) Transverse Force Fx (+) 0

Inside the electrolyte and/or the molten metal, it is possible to have vortexes only if the following integral: (where w are the forces arising from the gravity) calculated in a closed path is greater than zero.

To avoid any movement in the molten medias the forces need to be balanced point by point per cell quarter as in the drawing below: To achieve the force equilibrium as outlined in the picture above, for every set of four points K1, K2, K3 and K4 (symmetrical respect to the XZ and YZ planes) the magnetic field components must be antisymmetric, or, in other terms:

Bx(K1) = -Bx(K2) = Bx(K3) = -Bx(K4)      (1)

By(K1) = -By(K2) = By(K3) = -By(K4)      (2)

Bz(K1) = -Bz(K2) = Bz(K3) = -Bz(K4)      (3)

These equations imply that along the X and Y axis the magnetic field components are equal to 0.

For the usual arrangement of a side by side cell the current conductor and the ferromagnetic masses are arranged in a way that the Bx and By components are antisymmetric, hence automatically fulfilling the conditions (1) and (2).

This means that the vortexes generation depends mainly on the value of the Z component of the magnetic field. To avoid any vortexes the current conductors and ferromagnetic masses should be arranged in a way that the Bz component is antisymmetric point by point as expressed by the (3) or at least antisymmetric in average in the four quadrants.

If any of the magnetic field components do not satisfy the (1) and/or (2) and/or (3) then the electrolyte and the metal start to move.

Because the Bz component acts together with the horizontal components of the current density, to limit the forces that set movement into the molten medias it is important to reduce as much as possible the jx and jy current density components.

Inside the electrolyte jx and jy are close to zero, and the current is mainly vertical, while in the molten metal the following causes:

• Unbalanced currents between the different anodes
• Muck and/or crust in the bottom
• Cryolite ledge too much thin or terminating below the anodes

lead to horizontal current density components with subsequent set up of an oscillating wave in the metal pad.