Holes needed for B-coils (sensors of flux density B) cause errors in measured B

What is it about?

Local B-coils require holes to be drilled in the sample. Such holes are magnetic discontinuities and lead to measurement errors proportional to the ratio between the hole size and the distance between the holes. The relationship is almost direct because for the hole with diameter h and distance between the holes d the ratio R=h/d has the same order of magnitude as the systematic error caused by the presence of the holes. For example for h = 1 mm and d = 10 mm the ratio would be R = 1/10 = 10% and hence 10% error can be expected in the worst case.

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Why is it important?

This effect is widely known, but it has not be quantified before. This paper quantifies the percentage value so that an appropriate uncertainty budget can be constructed for a given system. There are also further implications. If the flux density B is to be controlled (in terms of shape) and an incorrect value is detected (due to presence of the holes) then not only the B measurement is affected, but also the H measurement, because the operating point will be controlled to be erroneously different from the ideal one.