Abstract
We present a new complete asymptotic expansion for the low‐frequency time‐harmonic magnetic field perturbation caused by the presence of a conducting (permeable) object as its size tends to zero for the eddy current regime of Maxwell's equations. The new asymptotic expansion allows the characterisation of the shape and material properties of such objects by a new class of generalised magnetic polarizability tensors, and we provide an explicit formula for their calculation. Our result will have important implications for metal detectors since it will improve small object discrimination, and for situations where the background field varies over the inclusion, this information will be useable, and indeed useful, in identifying their shape and material properties. Thus, improving the ability of metal detectors to locate landmines and unexploded ordnance, sort metals in recycling processes, and ensure food safety as well as enhancing security screening at airports and public events.
Highlights
The characterisation of highly conducting objects from low-frequency magnetic field perturbations has important applications in metal detection where the goal is to locate and identify concealed inclusions in an otherwise low conducting background
Metal detectors are used in the search for artefacts of archaeological significance, the detection of landmines and unexploded ordnance, the recycling of metals, and ensuring food safety as well as in security screening at airports and at public events
For a range of electromagnetic and acoustic phenomena, similar findings have been found where, in each case, an asymptotic expansion of the field perturbation caused by the presence of an inclusion as its size, α, tends to zero results in formula that permits the low-cost characterisation of an object
Summary
The characterisation of highly conducting objects from low-frequency magnetic field perturbations has important applications in metal detection where the goal is to locate and identify concealed inclusions in an otherwise low conducting background. The explicit expression for their coefficients is with respect to the standard orthonormal basis rather than the space of harmonic polynomials They are functions of B, α, σ∗, μ∗∕μ0, and ω and can be computed by solving a generalised form of the vectorial transmission problem obtained in Ammari et al[8] and Ledger and Lionheart.[9] the leading order term in our new expansion agrees with our previous result,[9] and here, the GMPT agrees with ̌̌. 6 is concerned with the representation of the asymptotic formula in terms of a new class of higher-order GMPTs
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
