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5.5.9. Technical Reference

MS2p and MS3p are based on the following formulation. The total energy in the fields is given by

Now express H in terms of a field that satisfies Ampere's Law in the volume and an irrotational part, i.e.,

and the basic functional (with Neumann boundary conditions) is given by

For permanent magnet sources you can write


Therefore you have


and M0 is the remanent magnetization, R is the rotation matrix to bring the susceptibility into the lab frame, and χ is the magnetic susceptibility defined by

Note that in general, μ is a function of the magnetic field, leading to a nonlinear equation for the potential. The functional now becomes

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