Wave Equation, Electric
The Wave Equation, Electric node is the main node for the Electromagnetic Waves, Transient interface. The governing equation can be written in the form
for transient problems with the constitutive relations B = μ0μrH and D = ε0εrE. Other constitutive relations can also be handled for transient problems. The Divergence Constraint subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
Electric Displacement Field
Select an Electric displacement field model — Relative permittivity (the default), Refractive index, Polarization, Remanent electric displacement, or Drude-Lorentz dispersion model.
Relative Permittivity
When Relative permittivity is selected, the default Relative permittivity εr (dimensionless) takes values From material. For User defined select Isotropic, Diagonal, Symmetric, or Full and enter values or expressions in the field or matrix. If Effective medium is selected, the Effective medium subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
Refractive Index
When Refractive index is selected, the default Refractive index n (dimensionless) takes the value From material. To specify the refractive index and assume a relative permeability of unity and zero conductivity, for one or both of the options, select User defined then choose Isotropic, Diagonal, Symmetric, or Full. Enter values or expressions in the field or matrix.
Notice that only the real part of the refractive index is used for the transient formulation.
Polarization
For Polarization enter coordinates for the Polarization P (SI unit: C/m2).
Remanent Electric Displacement
For Remanent electric displacement enter coordinates for the Remanent electric displacement Dr (SI unit: C/m2). Then select User defined or From Material as above for the Relative permittivity εr.
Drude–Lorentz Dispersion Model
For Drude-Lorentz Dispersion Model select User defined or From Material for the Relative permittivity, high-frequency ε∞ and enter a value for the Plasma frequency ωp (SI unit: rad/s).
When Drude-Lorentz Dispersion Model is selected, the Drude-Lorentz Polarization subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu. Each Drude-Lorentz Polarization subnode adds another polarization term Pn to the electric displacement field D, defined by
,
where the polarization is the solution to the ordinary differential equation
.
For more information, see the Drude–Lorentz Polarization feature.
Magnetic Field
This section is available if Relative permittivity, Polarization, or Remanent electric displacement are chosen as the Electric displacement field model.
Select the Constitutive relation — Relative permeability (the default), Remanent flux density, or Magnetization.
Relative Permeability
For Relative permeability the relative permeability μr uses values From material. For User defined select Isotropic, Diagonal, Symmetric, or Full based on the characteristics of the magnetic field, and then enter values or expressions in the field or matrix. If Effective medium is selected, the Effective medium subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
Remanent Flux Density
For Remanent flux density the relative permeability μr uses values From material. For User defined select Isotropic, Diagonal, Symmetric, or Full based on the characteristics of the magnetic field, and then enter values or expressions in the field or matrix. Then enter coordinates for the Remanent flux density Br (SI unit: T).
Magnetization
For Magnetization enter coordinates for M (SI unit: A/m).
B-H Curve
Select B-H curve |B| (SI unit: T) to use a curve that relates magnetic field H and the magnetic flux density B as |B| = f(||H||)H/||H||. The Magnetic field norm setting can take the values From material or User defined.
Material properties from Nonlinear Magnetic Materials Library can be used for B-H curve that are generally provided as interpolation functions for the magnetization curve without hysteresis effects.
Nonlinear simulations with the B-H curve magnetic field constitutive relation may require customized time-stepping settings in the Time-Dependent Solver for stability. The BDF method, with constant maximum step constraint, user-defined maximum step, and low maximum BDF order such as 2, would provide better convergence.
Conduction Current
This section is available if Relative permittivity, Polarization, or Remanent electric displacement are chosen as the Electric displacement field model.
By default, the Electrical conductivity σ (SI unit: S/m) uses values From material.
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For User defined select Isotropic, Diagonal, Symmetric, or Full based on the characteristics of the current and enter values or expressions in the field or matrix.
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For Linearized resistivity the default values for the Reference temperature Tref (SI unit: K), Resistivity temperature coefficient α (SI unit: 1/K), and Reference resistivity ρ0 (SI unit: Ωm) use values From material. For User defined enter other values or expressions for any of these variables.
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If Effective medium is selected, the Effective medium subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.
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If Archie’s Law is selected, the Archie’s Law subnode is available from the context menu (right-click the parent node) or from the Physics toolbar, Attributes menu.