Frozen mirror image method

Fig. 1. Illustration of the frozen mirror image method for a simplest case of the magnetic dipole over the flat superconducting surface.

Frozen mirror image method (or method of frozen images) is a modification of the method of images for magnet-superconductor systems that has been introduced to take into account the magnetic flux pinning phenomenon. The method gives a simple representation of the magnetic field distribution generated by a magnet (a system of magnets) outside an infinitely flat surface of a perfectly hard (with infinite pinning force) type-II superconductor in a most general field cooled (FC) case, i.e. when the superconductor goes into superconducting state been already exposed to the magnetic field.

The name originates from the replacement of certain elements in the original layout with imaginary magnets, which replicates the boundary conditions of the problem (see Dirichlet boundary conditions). In a simplest case of the magnetic dipole over the flat superconducting surface (see Fig. 1), the magnetic field, generated by a dipole moved from its initial position (at which the superconductor is cooled to the superconducting state) to a final position and by the screening currents at the superconducting surface, is equivalent to the field of three magnetic dipoles: the original one (1), its mirror image (3), and the magnetization inversed mirror image of it in its initial position (2). The method has been shown to work for the bulk high temperature superconductors (HTSC), which are characterized by a strong pinning and is useful for calculation of the interaction in magnet-HTSC systems such as magnetic bearings, superconducting flywheels, MAGLEV, etc.

See also

• Method of images
• Ideally hard superconductor
• Magnetic levitation
• Bean's critical state model
• High temperature superconductors