Magnetic Field of Hollow Triaxial Ellipsoids

A prolate spheroidal model of axisymmetric hollow ellipsoid is usually used for the analytical estimation of magnetic signature of ships and vessels. To overcome several limitations of the model such as the rotational symmetry, a general solution of the problem for a triaxial ellipsoid without the rotational symmetry is presented. The true analytical solution is derived in terms of elliptic integrals of the first and second kind. The presented solution is validated by the comparison with the results from a finite element analysis. The ellipsoidal system of coordinates implies that the outer and inner surfaces of a hollow ellipsoid are confocal. This leads to the analytical model of vessel hull with a variable wall thickness. The thickness variation depends on the hull aspect ratio, and it may lead to an inaccurate estimation of the magnetic signature. To overcome this limitation, the hollow ellipsoidal body with the non-confocal outer and inner surfaces is also considered, so that the thickness of the vessel hull is the same in all directions. The magnetic signature in this case can be significantly different from the case of the hollow ellipsoid with the confocal surfaces. In addition to the magnetic field outside the ellipsoid, the field inside the wall and in the cavity is analyzed. As a result of this analysis the formulas for the shielding effectiveness and magnetic moment are derived and validated. Also, cases of an axial symmetry when the triaxial ellipsoid transforms into the sphere, prolate or oblate spheroids are considered.