The Mathematical Institute, University of Oxford, Eprints Archive

Homogenized boundary conditions and resonance effects
in Faraday cages

Hewett, D. P. and Hewitt, I. J. (2016) Homogenized boundary conditions and resonance effects
in Faraday cages.
Technical Report. Unspecified. (Submitted)



We present a mathematical study of two-dimensional electrostatic and electromagnetic shielding by a cage of conducting wires (the so-called `Faraday cage effect'). Taking the limit as the number of wires in the cage tends to infinity we use the asymptotic method of multiple scales to derive continuum models for the shielding, involving homogenized boundary conditions on an effective cage boundary. We show how the resulting models depend on key cage parameters such as the size and shape of the wires, and, in the electromagnetic case, on the frequency and polarisation of the incident field. In the electromagnetic case there are resonance effects, whereby at frequencies close to the natural frequencies of the equivalent solid shell, the presence of the cage actually amplifies the incident field, rather than shielding it. By appropriately modifying the continuum model we calculate the modified resonant frequencies, and their associated peak amplitudes. We discuss applications to radiation containment in microwave ovens and acoustic scattering by perforated shells.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1922
Deposited By: Helen Taylor
Deposited On:27 Jan 2016 07:28
Last Modified:09 Feb 2016 10:16

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