Generation of maximum magnetic fields using permanent magnets

A general approach to the problem of optimization of magnetic systems of permanent magnets is formulated. The potential of the method is illustrated using the example of systems producing a maximum magnetic, field in a given point of space. For two types of geometry, a solution is obtained that gives an optimum distribution of magnetization and an optimum shape of the region occupied by a magnetically hard material. The possibility of creating, in a local region of space, a magnetic field several times as great as the residual induction of the material of the magnet is shown.