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Copy file name to clipboardExpand all lines: docs/src/scatterer.md
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# Sphere Dimensions
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!!! note
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In all of the following setups the sphere is embedded in a homogeneous background medium with permeability ``\mu`` and permittivity ``\varepsilon`` defined by [`Medium(ε, μ)`](@ref). The values [`μ0`](@ref) and [`ε0`](@ref) are provided containing the free space values.
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In all of the following setups the sphere is embedded in a homogeneous background medium with permeability ``\mu`` and permittivity ``\varepsilon``.
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This medium is defined only by the chosen excitation as a [`Medium(ε, μ)`](@ref).
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---
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---
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## Dielectric Sphere
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The dielectric sphere has radius ``r`` and is assumed to be located in the origin. It is defined by [`DielectricSphere`](@ref). In addition to the embedding [`Medium(ε, μ)`](@ref) a filling [`Medium(εᵢ, μᵢ)`](@ref) with permeability ``\mu_\mathrm{i}`` and permittivity ``\varepsilon_\mathrm{i}`` has to be defined.
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The dielectric sphere has radius ``r`` and is assumed to be located in the origin. It is defined by [`DielectricSphere`](@ref), where the filling [`Medium(εᵢ, μᵢ)`](@ref) with permeability ``\mu_\mathrm{i}`` and permittivity ``\varepsilon_\mathrm{i}`` has to be defined.
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```@docs
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DielectricSphere
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```
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Here `radius` is a Float and `filling` of type [`Medium(εᵢ, μᵢ)`](@ref).
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Here `radius` is a Float and `filling`is of type [`Medium(εᵢ, μᵢ)`](@ref).
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---
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## Layered Dielectric Sphere
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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`](@ref). In addition to the embedding [`Medium(ε, μ)`](@ref) a vector of fillings [[`Medium(ε₁, μ₁)`](@ref), [`Medium(ε₂, μ₂)`](@ref), ..., [`Medium(εN, μN)`](@ref)] with permeability ``\mu_n`` and permittivity ``\varepsilon_n`` has to be defined.
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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`](@ref), where the vector of fillings [[`Medium(ε₁, μ₁)`](@ref), [`Medium(ε₂, μ₂)`](@ref), ..., [`Medium(εN, μN)`](@ref)] with permeability ``\mu_n`` and permittivity ``\varepsilon_n`` has to be defined.
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`](@ref). In addition to the embedding [`Medium(ε, μ)`](@ref) a vector of fillings [[`Medium(ε₁, μ₁)`](@ref), [`Medium(ε₂, μ₂)`](@ref), ..., [`Medium(εN, μN)`](@ref)] with permeability ``\mu_n`` and permittivity ``\varepsilon_n`` has to be defined.
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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`](@ref), where the vector of fillings [[`Medium(ε₁, μ₁)`](@ref), [`Medium(ε₂, μ₂)`](@ref), ..., [`Medium(εN, μN)`](@ref)] with permeability ``\mu_n`` and permittivity ``\varepsilon_n`` has to be defined.
## [Dielectric Sphere with Thin Impedance Layer](@id dielecimped)
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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`](@ref). 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]](@ref refs)). This leads to a potential drop across the thin layer, while the displacement field is constant in radial direction. In addition to the embedding [`Medium(ε, μ)`](@ref) and filling [`Medium(εᵢ, μᵢ)`](@ref), the impedance layer must be specified, both the [`Medium(εₜ, μₜ)`](@ref) and its `thickness`.
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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`](@ref). 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]](@ref refs)). 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)`](@ref), the impedance layer must be specified, both the [`Medium(εₜ, μₜ)`](@ref) and its `thickness`.
sphere.embedding == excitation.embedding ||error("Excitation and sphere are not in the same medium.") # verify excitation and sphere are in the same medium
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F =zeros(fieldType(quantity), size(quantity.locations))
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# --- compute field in Cartesian representation
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sphere::DielectricSphere, excitation::UniformField, point, quantity::ElectricField; parameter::Parameter=Parameter()
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)
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ε0 =sphere.embedding.ε
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ε0 =excitation.embedding.ε
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ε1 = sphere.filling.ε
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E0 =field(excitation, point, quantity)
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sphere::DielectricSphere, excitation::UniformField, point, quantity::ScalarPotential; parameter::Parameter=Parameter()
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)
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ε0 =sphere.embedding.ε
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ε0 =excitation.embedding.ε
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ε1 = sphere.filling.ε
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Φ0 =field(excitation, point, quantity)
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E =scatteredfield(sphere, excitation, point, ElectricField(quantity.locations); parameter=parameter)
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ifnorm(point) > sphere.radius
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D =sphere.embedding.ε * E
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D =excitation.embedding.ε * E
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else
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D = sphere.filling.ε * E
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end
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R = sp.radius
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Δ = sp.thickness
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εₘ = sp.thinlayer.ε
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εₑ =sp.embedding.ε
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εₑ =ex.embedding.ε
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εᵢ = sp.filling.ε
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E₀ = ex.amplitude
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Copy file name to clipboardExpand all lines: src/dipoles/scattered.jl
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T =typeof(excitation.frequency)
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sphere.embedding == excitation.embedding ||error("Excitation and sphere are not in the same medium.") # verify excitation and sphere are in the same medium
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excitation.orientation × excitation.position ==SVector{3,T}(0, 0, 0) ||error("The dipole is not perpendicular to the sphere.")
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F =zeros(SVector{3,Complex{T}}, size(quantity.locations))
sphere.embedding == excitation.embedding ||error("Excitation and sphere are not in the same medium.") # verify excitation and sphere are in the same medium
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T =typeof(excitation.frequency)
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F =zeros(SVector{3,Complex{T}}, size(quantity.locations))
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Copy file name to clipboardExpand all lines: src/ringCurrent/scattered.jl
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T =typeof(excitation.frequency)
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sphere.embedding == excitation.embedding ||error("Excitation and sphere are not in the same medium.") # verify excitation and sphere are in the same medium
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