Surface Current Method Research Articles

In the case of a nearly perfect conductor, i.e., when the skin depth δ (in ordinary conductors) or the London penetration depth δ L (in superconductors) is much smaller than the other physical scales, the current flows only on the surface. Hence, the three-dimensional distribution of the magnetic field is fully specified by the two-dimensional current distribution (boundary elements) on the surface. The specific BEM (boundary element method) is called SCM (surface current method). In SCM, the surface is partitioned into N small areas, each with a looping current I i (1 ≤ i ≤ N). I i 's are determined by solving N simultaneous linear equations so as to eliminate the normal component of the magnetic field at the center of each area. The inductance is given in terms of the magnetic energy among N current loops. Thus, the problem is reduced to a two-dimensional one in SCM. To obtain the final results, the error estimate as a function of N is made and they are obtained as the extrapolation for N tending to infinity. Calculations for some examples including a fully three-dimensional object are presented. The effect of non-zero δ and δ L can be, in the present SCM, made by thinning the object by the amount δ (if the width of the conductor is larger than δ) but the more rigorous treatment is left for future study.

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