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.