-material : electric / magnetic properties

This section is for specifying the material parameters. Materials may be perfect electric conducting (type= electric), perfect magnetic conducting (type= magnetic), or may be lossyfree or lossy dielectrics with anisotropic values for $\mu$ and $\varepsilon$ (type= normal). Dielectrics may have up to 10 LORENTZ-resonances in their permittivity and permeability functions.

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 # section -material                                                          #
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 # material=  3        epsr    = undefined      kappa    =       0.0          #
 # type= undefined        xepsr= undefined        xkappa =       0.0          #
 #                        yepsr= undefined        ykappa =       0.0          #
 #                        zepsr= undefined        zkappa =       0.0          #
 #                     muer    = undefined      mkappa   =       0.0          #
 #                        xmuer= undefined        xmkappa=       0.0          #
 #                        ymuer= undefined        ymkappa=       0.0          #
 #                        zmuer= undefined        zmkappa=       0.0          #
 # # Dispersion parameters.                                                   #
 #                 feps(1)   = undefined     fmue(1)   = undefined            #
 #                   xfeps(1)= undefined       xfmue(1)= undefined            #
 #                   yfeps(1)= undefined       yfmue(1)= undefined            #
 #                   zfeps(1)= undefined       zfmue(1)= undefined            #
 #                 aeps(1)   = undefined     amue(1)   = undefined            #
 #                   xaeps(1)= undefined       xamue(1)= undefined            #
 #                   yaeps(1)= undefined       yamue(1)= undefined            #
 #                   zaeps(1)= undefined       zamue(1)= undefined            #
 #                 fegm(1)   = undefined     fmgm(1)   = undefined            #
 #                   xfegm(1)= undefined       xfmgm(1)= undefined            #
 #                   yfegm(1)= undefined       yfmgm(1)= undefined            #
 #                   zfegm(1)= undefined       zfmgm(1)= undefined            #
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 # return, help                                                               #
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• material
  The material index of the material whose parameters are to be changed. This number must be between 0 and 50 inclusive.
• type
  The type of the material. Possible values are "electric", "magnetic", "normal". An "electric" material is treated as perfect electric conducting for the field computation, a "magnetic" material is treated as perfect magnetic conducting in the field computation.
  • For eigenvalue computations:
    • When the parameter lossy= no in the section -eigenvalues is selected, only the "epsr" and "muer" of a "normal" material are used for the field computation, ie. no losses, and no dispersive parameters are modeled for eigenvalue computations. The parameters "kappa" and "mkappa" of materials with "type= normal" may be used by the postprocessor, gd1.pp, to compute dielectric losses via a perturbation formula.
    • When the parameter lossy= yes in the section -eigenvalues is selected, losses due to finite electric and magnetic conductivities, and the dispersive parameters are taken into account.
  • For time domain computations, "epsr", "muer", "kappa" and "mkappa" as well as the dispersive parameters of a "type= normal" material are used for the field computation.
  • Both for time domain and for eigenvalue computations, materials with
    "type= electric" are considered perfectly conducting, and materials with "type= magnetic" are considered perfectly magnetic conducting. Any specified electric conductivities for materials with "type= electric" are used in the postprocessor, gd1.pp, to compute wall losses via a perturbation formula.
• epsr
  The relative permittivity of the material. If you specify eg. epsr= 3, all three epsr values xepsr, yepsr and zepsr are set to the value 3.
• xepsr, yepsr, zepsr
  The x-, y-, z-value of an anisotropic material. Only diagonal epsr matrices can be specified.
• muer
  The relative permeability of the material. If you specify eg. muer= 4, all three muer values xmuer, ymuer and zmuer are set to the value 4.
• xmuer, ymuer, zmuer
  The x-, y-, z-value of an anisotropic material. Only diagonal muer matrices can be specified.
• kappa
  The electric conductivity of the material in MHO/m (1/Ohm/m). If you specify eg. kappa= 5, all three kappa values xkappa, ykappa and zkappa are set to the value 5.
• xkappa, ykappa, zkappa
  The x-, y-, z-value of an anisotropic material. Only diagonal kappa matrices can be specified.
• mkappa
  The magnetic conductivity of the material in Ohm/m. If you specify eg. mkappa= 6, all three kappa values xmkappa, ymkappa and zmkappa are set to the value 6.
• xmkappa, ymkappa, zmkappa
  The x-, y-, z-value of an anisotropic material. Only diagonal mkappa matrices can be specified.
• feps(I)
  The $I$.th LORENTZ-frequency of a dispersive material. If you specify eg. feps(1)= 3e9, all three feps(1) values xfeps(1), yfeps(1) and zfeps(1) are set to the value 3 GHz.
• xfeps(I), yfeps(I), zfeps(I)
  The x-, y-, z-value of an anisotropic material.
• aeps(I)
  The $I$.th $\varepsilon$-amplitude of a dispersive material.
• fegm(I)
  The $I$.th $\gamma_e$-value of a dispersive material.
• fmue(I), amue(I), fmgm(I)
  The corresponding resonant frequency, amplitude and $\gamma_m$ values for a material with LORENTZ-resonance in the permeability.

The permittivity for an $N$.th order LORENTZ medium with resonant frequencies $\omega_n$ and damping frequencies $\gamma_n$ reads

$$\varepsilon_r(\omega) = \varepsilon_\infty + \sum\limits_{... ...mega_n^2 } { \omega_n^2 + {\rm j}\omega \gamma_n - \omega^2 }$$ (1.1)

Such a permittivity is described with the parameters

$$:= \varepsilon_\infty$$ (1.2)

$$:= A_n$$ (1.3)

$$:= \omega_n$$ (1.4)

$$:= \gamma_n$$ (1.5)

Note: Three materials are predefined:

• Material '0' is a dielectric whose default values of epsr and muer are 1. This is vacuum. You can change the parameters epsr, muer, kappa and mkappa of the material '0', but you cannot change its type= normal.
• Material '1' is treated as a perfect electric material for the field computations. You can change its kappa values, but this only effects the wall-loss computations of gd1.pp. You cannot change its type= electric.
• Material '2' is treated as a perfect magnetic conducting material. You cannot change its type= magnetic.

Example The following specifies that the material with number 3 shall be treated as a perfect magnetic conducting material, the material with number 4 is a lossy dielectric.

 -material
    material= 3
       type= magnetic
    material= 4
       type= normal, epsr= 3, kappa= 1, muer= 1