Low-Frequency Electromagnetic Shielding and Scattering of Multiple Cylindrical Shells

Emerging additive manufacturing methods facilitate the creation of enclosures with tailor-made shielding and scattering performance by using multiple conductive and dielectric layers. For a first analysis an elongated housing, with a cross-section small compared to the wavelength of the impinging electromagnetic field is replaced by an infinitely long multilayered cylinder. In a previous paper, we concluded that existing solutions of the Maxwell equations for this configuration are not accurate in calculating scattering. This also negatively impacts results for multilayer shielding. This article proposes a fast, time-harmonic formulation based on a combination of Bessel and Hankel functions as solution to the Helmholtz equation. Both electric and magnetic fields are considered and solutions are obtained independently for transversal and longitudinal source fields. These can be superpositioned to describe arbitrary source fields. The system of equations defined by the boundary conditions of the multilayer problem is solved via Gaussian elimination which can easily be automated with standard MATLAB or Octave functions. Results are compared to known approaches and applied to a dual-layer use case. The latter shows that shielding and scattering performance improves significantly with multiple layers compared to a single layer with equivalent thickness both for transversal and longitudinal fields.