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Sphere Dimensions

Note

In all of the following setups the sphere is embedded in a homogeneous background medium with permeability $\mu$ and permittivity $\varepsilon$. This medium is defined only by the chosen excitation as a Medium(ε, μ).

PEC/PMC Sphere

The perfectly electrically conducting (PEC) or perfectly magnetically conducting (PMC) sphere has radius $r$ and is assumed to be located in the origin. It is defined by PECSphere.


API

Dielectric Sphere

The dielectric sphere has radius $r$ and is assumed to be located in the origin. It is defined by DielectricSphere, where the filling Medium(εᵢ, μᵢ) with permeability $\mu_\mathrm{i}$ and permittivity $\varepsilon_\mathrm{i}$ has to be defined.


API

Here radius is a Float and filling is of type Medium(εᵢ, μᵢ).

Layered Dielectric Sphere

The layered dielectric sphere has radii $[r_1, r_2, \dots, r_N]$ and is assumed to be located in the origin. It is defined by LayeredSphere, where the vector of fillings [Medium(ε₁, μ₁), Medium(ε₂, μ₂), ..., Medium(εN, μN)] with permeability $\mu_n$ and permittivity $\varepsilon_n$ has to be defined.


API

SphericalScattering.LayeredSphere — Type
LayeredSphere( 
    radii   = error("Missing argument `radii`"), 
    filling = error("`missing argument `filling`")
)

Constructor for the layered dielectric sphere.

source

with, e.g., radii = SVector(0.25, 0.5, 1.0) and filling = SVector(Medium(ε1, μ1), Medium(ε2, μ2), Medium(ε3, μ3)).

Layered Dielectric Sphere with PEC Core

The layered dielectric sphere has radii $[r_1, r_2, \dots, r_{N+1}]$ and is assumed to be located in the origin. It is defined by LayeredSpherePEC, where the vector of fillings [Medium(ε₁, μ₁), Medium(ε₂, μ₂), ..., Medium(εN, μN)] with permeability $\mu_n$ and permittivity $\varepsilon_n$ has to be defined.

API

with, e.g., radii = SVector(0.25, 0.5, 1.0) and filling = SVector(Medium(ε1, μ1), Medium(ε2, μ2)).

Dielectric Sphere with Thin Impedance Layer

The dielectric sphere with a thin impedance layer of thickness $t$ has radius $r$ and is assumed to be located in the origin. It is defined by DielectricSphereThinImpedanceLayer. Unlike the LayeredSphere model, the solution is obtained by using an approximation: it is assumed that the impedance is so high that the displacement field is purely radial (see [6, pp. 230ff]). This leads to a potential drop across the thin layer, while the displacement field is constant in radial direction. In addition to the filling Medium(εᵢ, μᵢ), the impedance layer must be specified, both the Medium(εₜ, μₜ) and its thickness.


Note

This configuration is (at least so far) only intended for the uniform static field excitation.

API

SphericalScattering.DielectricSphereThinImpedanceLayer — Type
DielectricSphereThinImpedanceLayer(
    radius    = error("missing argument `radius`"),
    thickness = error("missing argument `thickness` of the coating"),
    thinlayer = error("missing argument `thinlayer`"),
    filling   = error("missing argument `filling`")
)

Constructor for the dielectric sphere with a thin impedance layer. For this model, it is assumed that the displacement field is only radial direction in the layer, which requires a small thickness and low conductivity. For details, see for example T. B. Jones, Ed., “Models for layered spherical particles,” in Electromechanics of Particles, Cambridge: Cambridge University Press, 1995, pp. 227–235. doi: 10.1017/CBO9780511574498.012.

source

Here radius and thickness are a Floats, filling and thinlayer are of type Medium.