New developments in magnetostatic cleanliness modeling

The paper describes improvements and extensions of the multiple magnetic dipole modeling method (MDM) for cleanliness verification which had been introduced by the author¹ in 1977 and then applied during 3 decades to numerous international projects. The solutions of specific modeling problems which had been left unsolved so far, are described in the present paper. Special attention is given to the ambiguities of MDM solutions caused by the limited data coverage available. Constraint handling by the constraint-free NLP solver, optimal MDM sizing and multiple-point far-field compensation techniques are presented. The recent extension of the MDM method to field gradient data is formulated and demonstrated by an example. Finally, a complex MDM application (Ulysses) is presented. Finally, a short description of the MDM software GAMAG, recently introduced by the author¹, is given.