Multipole imaging of an elongated magnetic source

This paper describes a mathematical method for modeling the magnetic field from an elongated source, a method that is relevant to the reduction of the magnetic signature of a marine vessel. We seek the magnetic multipole image (MMI), the set of coefficients in a pr olate spheroidal harmonic expansion of magnetic scalar potential U, which d escribes the magnetic source, The MMI is useful for efficient and accurate modeling of the magnetic field outside the source and for developing method s of reducing the magnetic signature. We model an elongated complex source by consideration of elementary interna l sources, which consist of concentrated eccentric dipoles (located away fr om the origin) inside the spheroidal boundary and coils on the spheroidal s urfaces (bounded by longitudes and latitudes). For the internal dipole sources, the scaler magnetic potential U is expande d in prolate spheroidal coordinates in terms of associated Legendre functio ns, The Green function F = 1/R, R being the distance between the source and evaluation point, is also expressed in terms of Legendre functions of the first and second kind, Since U of an elementary dipole is proportional to t he gradient of F, comparison of the expansion coefficients is used to deter mine the MMI of the source, In the same way, an integration of the gradient of F over the virtual surface dipoles inside the coil boundaries is used t o determine the MMI of each elementary coil.