\psfig{figure=periodic-sphere.ps,width=10cm,bbllx=74pt,bblly=206pt,bburx=565pt,bbury=690pt,clip=}

GdfidL v3.5: Syntax and Semantics

Warner Bruns


Contents


List of Figures

  1. The real Part of the frequency dependent Muer(f).
  2. The imaginary Part of the frequency dependent Muer(f).
  3. The analytical Reflection from a finite Slab of dispersive Material.
  4. The numerical Reflection from a Slab of finite Thickness.
  5. The real Part of the frequency dependent epsr.
  6. The imaginary Part of the frequency dependent epsr.
  7. The analytical Reflection from a finite Slab of dispersive Material.
  8. The numerical Reflection from a Slab of finite Thickness.
  9. The real Part of the frequency dependent Muer.
  10. The imaginary Part of the frequency dependent Muer.
  11. The analytical Reflection from a Slab of dispersive Material.
  12. The numerical Reflection from a Slab of dispersive Material.
  13. A simple Brick, and the same Brick-Data translated and rotated.
  14. A simple gccylinder, with its Axis directing towards (-0.4, 1.5, 0.4).
  15. A Chain of simple circular Cylinders. Each Cylinder has its Axis pointing in a different Direction.
  16. A simple ggcylinder
  17. A simple ggcylinder, with a Pitch.
  18. A simple ggcylinder, with different Growthfactors for x and y.
  19. A simple ggcylinder, with zprimedirection different from the Footprints Plane Normal.
  20. The Discretisation of a Cosine-Taper, specified as a ggcylinder with zxscale.
  21. A simple gbor.
  22. The Intersection of two circular Cylinders, where whichcells and taboo were specified.
  23. A complicated gbor
  24. Two complicated gbors (Glasses).
  25. A discretisation of a Wagner Bust, described as a STL-file.
  26. A Discretisation of a Dipole Chamber. The Arc-like Beam-Pipe has been de-bended to allow the Computation of Wakepotentials.
  27. Part of a RF-Quadrupole, where the Electrodes are described by an Algorithm.
  28. Discretisation of some Bricks, translated and rotated.
  29. A twisted Waveguide. Only the Material Boundaries behind the Plane y=0 are shown.
  30. A twisted Waveguide. The Plot is rotated slightly around the y-Axis.
  31. A Device with three Planes of Symmetry. The Planes of Symmetry at x=0 and y= 0 could be used with a Computation with Linecharges. This is not used here. Four Charges are specified such that mainly quadrupole-Wakefields are excited.
  32. The Wakepotential as a Function of (x,y) near s=0. The Input for gd1.pp was: -gen, inf @last, -wakes, watsi= 0, doit
  33. Above: Resulting Plot, with Field Arrows, and Material Patches coloured according to the Field Strength at Material Boundaries. Below: The same Plot, without Field Arrows.
  34. The coloured Material-Patches encode the absorbed Energy in the Materials with type=impedance.
  35. The Time Domain electric Field at an early Time.
  36. The computed Reflection when a Window has been applied.
  37. A computed Transmission when a Window has been applied.
  38. A computed Transmission when a Window has been applied.
  39. A computed Transmission when a Window has been applied.
  40. The computed Reflection when no Window has been applied.
  41. A computed Transmission when no Window has been applied.
  42. A computed Transmission when no Window has been applied.
  43. A computed Transmission when no Window has been applied.
  44. The Sum of the Squares of the computed scattering Parameters when a Window has been applied.
  45. The Sum of the Squares of the computed scattering Parameters when no Window has been applied.
  46. The Time Domain electric Field at an early Time.
  47. The computed Amplitude of the sixth Mode at the lower Beam-Pipe.
  48. The computed Amplitude of the sixth Mode at the lower Beam-Pipe, the time Data while the Beam passes through the Port is replaced by Zeros.
  49. The integrated Power of all Modes at the lower Beam-Pipe.
  50. The integrated Power of all Modes at the lower Beam-Pipe, the time Data while the Beam passes through the Port is replaced by Zeros.
  51. The computed Amplitude of the sixth Mode at the upper Beam-Pipe.
  52. The computed Amplitude of the sixth Mode at the upper Beam-Pipe, the time Data while the Beam passes through the Port is replaced by Zeros.
  53. The integrated Power of all Modes at the lower Beam-Pipe.
  54. The integrated Power of the all Modes at the upper Beam-Pipe, the time Data while the Beam passes through the Port is replaced by Zeros.
  55. The integrated Power of all Modes at the BeamPositionMonitor-Port.
  56. A Part of the STL-Data generated with deflection set to 1e-4
  57. A Part of the STL-Data generated with deflection set to 1e-5
  58. This Volumeplot shows the discretised Device. Although gd1 allows an inhomogeneous Mesh even when a particle Beam is present, this is not explicitely used here.
  59. The z-Component of the Wakepotential at the (x,y)-Position where the exciting Line-Charge was travelling. For Reference, the Shape of the exciting Charge is plotted as well.
  60. The two transverse Components of the Wakepotential at the (x,y)-Position where the exciting Line-Charge was travelling. For Reference, the Shape of the exciting Charge is plotted as well. The transverse Wakepotentials are computed as the Average of the transverse Wakepotentials nearest to the Position where the Line-Charge was travelling. The y-Component of the Wakepotential vanishes, as it should be.
  61. This Volumeplot shows the discretised Geometry.
  62. The Data of the Excitation. Above: The time History of the Amplitude that was excited in the Port with Name 'Input'. Below: The Spectrum of this Excitation.
  63. The Data of the scattered Mode '1' in the Port with Name 'Input'. Above: The time History of its Amplitude. This was computed by gd1. Below: The scattering Parameter as Amplitude Plot, and in a Smith-Chart. These Data are computed by gd1.pp by Fourier-Transforming the time History of this Mode, and dividing by the Spectrum of the Excitation.
  64. The Data of the scattered Mode '1' in the Port with Name 'Output'. Above: The time History of its Amplitude. This was computed by gd1. Below: The scattering Parameter as Amplitude Plot, and in a Smith-Chart. These Data are computed by gd1.pp by Fourier-Transforming the time History of this Mode, and dividing by the Spectrum of the Excitation.
  65. The Sum of the squared scattering Parameters. Since the Device is loss-free, this Sum should ideally be identical to '1' above the cut-off Frequency. The Sum of the computed Parameters is only very near the cut-off Frequency of the Modes unequal '1'.
  66. The four Parts of the Brillouin-Diagram.
  67. The four Parts of the Brillouin-Diagram combined.

Introduction

Features: GdfidL consists of 5 separate Programs that work together. These Programs are: mymtv2 was not written by us. It is a (slightly) modified Version of the Program plotmtv written by Kenny Toh. The original Sources for plotmtv can be found on the Internet: plotmtv can be found at ftp.x.org: /contrib/applications/Plotmtv.1.3.2.tar.Z

gd1

Typical Usage of gd1

gd1 reads its Information from the Standard Input Unit. You will normally use two or more xterms to operate gd1. In one of the xterms you edit an Inputfile that describes your Device, in the other xterm you iteratively start gd1 and try out how gd1 reacts to your Input.

gd1 reads the Description of the Device that you are interested in from stdin or from a File that you specify via include(filename). gd1 generates the Mesh and computes the resonant Fields or time dependent Fields. The Results are written to a Database that can be read by gd1.pp.

Input for gd1

gd1's Input is pure Text. You give gd1 the Information about the Problem to be analysed in distinct Sections.

The required Information that you have to give gd1 is The Symbols in the above Brackets indicate in which Section of gd1 you specify the required Parameters.

Behind the Scenes: When the Mesh is generated

There is no standalone Meshgenerator. When you define a geometric Primitive, the only Thing that happens immediately is that the Information about the geometric Primitive is stored in an internal Database. When you say doit in the Section -eigenvalues, in the Section -fdtd or in the Section -windowwake, the Mesh is generated on the Fly. When you display the Mesh-Filling via the Section -volumeplot, the Mesh is also generated on the Fly.

General Sections

These are the Sections where you specify Parameters that are required for every Field Computation.

In the Section -general, you specify the Name of the File where the Results shall be written to.

In the Section -mesh, you have to specify the Borderplanes of the computational Volume, and the default Mesh Spacing. You also define the boundary Conditions at the Borderplanes here.

In the Section -material, you specify the electric Properties of the Materials.


Entry Section

This is the Section you are in when you start gd1.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # gdfidl (32) (V 3.5) (compiled Mon Apr  3 12:37:17 GMT 2017 on Host wb027a) #
 #  VshzpnIb 2017.04.03                                                       #
 ##############################################################################
 # -general        -- Output File, Annotations.                               #
 # -mesh           -- Bounding Box, Spacing, fixed Meshplanes,                #
 #                 -- Boundary Conditions.                                    #
 # -material       -- Material Properties.                                    #
 # -lgeometry      -- Load a previously used Geometry.                        #
 # ***** Geometric primitives ****                                            #
 # -brick          -- Simple rectangular Brick.                               #
 # -gccylinder     -- Circular Cylinder in general Direction.                 #
 # -ggcylinder     -- General Cylinder in general Direction.                  #
 # -gbor           -- Body of Revolution in general Direction.                #
 # -stlfile        -- CAD Import via STL-File.                                #
 # -geofunction    -- Analytic Function.                                      #
 # -transform      -- Rotations etc                                           #
 #     ( -translate, -rotate )                                                #
 # ***** Solver Sections ****                                                 #
 #  -eigenvalues   -- Resonant Fields                                         #
 #     ( -ports, -linitialfields )                                            #
 #  -fdtd          -- Time dependent Fields                                   #
 #     (-time, -ports, -pexcitation, -lcharges, -voltages, -dipole, -clouds   #
 #      -storefieldsat, -linitialfields, -fexport, -fmonitor, -smonitor       #
 #      -pmonitor, -windowwake, -decaytime )                                  #
 #  -magnetostatic -- Magnetostatic Fields (rudimentary)                      #
 #     ( -lcurrent )                                                          #
 # *******                                                                    #
 #  -volumeplot    -- Displays Mesh Filling.                                  #
 #  -cutplot       -- Displays Mesh Filling in a single Plane                 #
 # ***** Miscellanea ******                                                   #
 #  -debug         -- Specify Debug Levels                                    #
 #                                                                            #
 ##############################################################################
 # ?, end, help, __mdoit                                                      #
 ##############################################################################
The Menu shows all Sections. There are some Subsections, which you may also enter from within any Section, these are shown in Brackets (). You enter a Section by specifying its Name.
Example To enter the Section -general, you say:
   -general
As all Commands may be abbreviated, you may also say:
   -ge


-general : Annotations, filenames

Here you specify where the Results shall be stored and where Scratchfiles shall be written to. You may also document your Project by putting descriptive Text to the Plots.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -general                                                          #
 ##############################################################################
 # outfile    = /tmp/--username--/--SomeDirectory--/Results                   #
 # scratchbase= /tmp/UserName/bla                                             #
 # restartfiles= -none-                                                       #
 #   t1restartfiles=  1440         -- Minutes. When to write the first Set.   #
 #   dtrestartfiles=  1440         -- Minutes. Distance between writing.      #
 #   stopafterrestartfiles=1000000000   -- Stop after writing so often.       #
 #   singlesetofrestartfiles= no        -- Write always the same Set.         #
 # text( 1)= ' '                                                              #
 # text( 2)= ' '                                                              #
 # text( 3)= ' '                                                              #
 # text( 4)= ' '                                                              #
 # text( 5)= ' '                                                              #
 # text( 6)= ' '                                                              #
 # text( 7)= ' '                                                              #
 # text( 8)= ' '                                                              #
 # text( 9)= ' '                                                              #
 # text(10)= ' '                                                              #
 # text(11)= ' '                                                              #
 # text(12)= ' '                                                              #
 # text(13)= ' '                                                              #
 # text(14)= ' '                                                              #
 # text(15)= ' '                                                              #
 # text(16)= ' '                                                              #
 # text(17)= ' '                                                              #
 # text(18)= ' '                                                              #
 # text(19)= ' '                                                              #
 # text(20)= ' '                                                              #
 # ndpw  = auto          -- PVM/MPI: Number of Dice per Worker                #
 # iodice= no            -- PVM    : yes: Each Worker writes its own Results. #
 # nrofthreads= 32       -- SMP and PVM/MPI: Nr of Threads per Worker.        #
 # affinity= yes         -- SMP: yes: Enforce Core Affinity.                  #
 # spinwait= yes         -- SMP: yes: Do not release CPU when a Thread waits. #
 # hyperthreading= yes     -- SMP: no: Schedule on real Cores.                #
 ##############################################################################
 # 2dplotopts   = -geometry 690x560+10+10                                     #
 #   plotopts   = -geometry 800x668+310+40 -noclip                            #
 # showtext     = yes         -- (yes | no)                                   #
 # onlyplotfiles= no          -- (yes | no)                                   #
 ##############################################################################
 # ?, return, help                                                            #
 ##############################################################################

Example The following specifies that the Results of the Computation shall be stored in the Database named '/Data/UserName/resultdirectory'. The Names of Scratchfiles that gd1 generates shall start with '/tmp/UserName/delete-me-'. Restartfiles shall be written every 24 hours, and the Names of the Restartfiles shall start with /Data/UserName/restartfile.
Together with the Plots that gd1.pp will produce, the Text 'Parameter is 45' and '2*Parameter is 90' shall appear.
 -general
     outfile= /Data/UserName/resultdirectory
     scratch= /tmp/UserName/delete-me-
     restartfiles= /Data/UserName/restartfile

 define(PARAMETER, 45)
     text(1)= Parameter is PARAMETER
     text(2)= 2*Parameter is eval(2*PARAMETER)


Example Tell GdfidL that every XX Minutes, all Data describing the current State of Computation shall be written to Files. From these Data, a Computation can be restarted. There is an Option, that after eg. two Datasets written, the Computation shall stop.1.2 A Script, which restarts as long as GdfidL has not yet signalled that the Job is finished, is:

#!/bin/sh
#
# The Input for GdfidL shall contain a Specification
# for Restartfiles. In this Example, we do that
# via creating the './gdfidl.solver-profile', which is
# read and interpreted at the Start of Run.
 (cat > ./gdfidl.solver-profile) << UntilThisMarker
   -general
     # Write a Set of Restartfiles every 60 Minutes.
     restartfiles= /Data/UserName/restartfiles  # Where to write the Restartfiles
     t1restart= 60        # When to write the first Set of Restartfiles
     dtrestart= 60        # Wall Clock Time Difference between writing Restartfiles
     stopafterrestart= 2  # Stop after writing the second Set of Restartfiles.
UntilThisMarker
#
# The initial Run.
# Use '>' instead of '| tee Logfile' to get the Returncode of GdfidL.
# If 'tee' is used the Recturncode would be the Returncode of 'tee'.
 gd1 -DWhateverYourOptions=... \
        < Inputfile > Logfile-restart
 RETURNCODE=$?
 echo RC ist $RETURNCODE
#
# While GdfidL signals that a Restart is useful, restart.
 while [ "$RETURNCODE" -eq "1" ]
 do
    gd1 -restartfiles=/Data/UserName/restartfiles.iMod-2 \
        >> Logfile-restart
    RETURNCODE=$?
 echo RC ist $RETURNCODE
    if [ "$RETURNCODE" -eq "0" ]; then
       exit 0
    fi
 done
#
 exit 0
 #######
Writing Restartfiles is useful anyway. If Restartfiles are written, one has the Chance to restart a crashed Computation which crashed because of some Failure of the Computersystem. To restart a Computation, the Restartfiles must be accessible, of course. So the Restartfiles should not be written to /tmp, or some other Filesystem which might be cleaned at System Boot Time or so.

When writing Restartfiles for the Possibility of recovering from some Failure of the System, you would not specify

    -general, stopafterrestart= 2
The writing of the Restartfiles takes some Time, Minutes or so. So the '-general, dtrestart= XX' Parameter should be significantly larger than '1'. We suggest '-general, dtrestart= 24*60'. That says: Write Restartfiles once per 24 Hours.

If such a Computation crashed, inspect the Logfile. You shall find Lines similar to:

 ###############
 # Restartfiles are to be written.
 #########################################################################
 # A Set of Restartfiles has been written.
 # To restart this Computation, start with the same Command,
 # on the same Computer System, but with the additional Parameter
 #    -restartfiles=/Data/UserName/restartfiles.iMod-1
 #########################################################################
This 'start with the same Command, on the same Computer System,' is for Safety. A Restart will work as long as the same Executables are used, the same PVM/MPI-Parameters are used, and the Restartfiles are accessible from every used Node.


-mesh : Outer Boundary Conditions, Spacings

gd1 needs to know You specify these Values in this Section.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section -mesh                                                              #
 ##############################################################################
 ## Bounding Box:                                                             #
 #   pxlow = undefined      , pylow = undefined      , pzlow = undefined      #
 #   pxhigh= undefined      , pyhigh= undefined      , pzhigh= undefined      #
 #  volume= (undefined, undefined, undefined, undefined, undefined, undefined)#
 #      __zlowref = undefined                                                 #
 #      __zhighref= undefined                                                 #
 ## Boundary Conditions:                                                      #
 #   cxlow = electric, cylow = electric, czlow = electric                     #
 #   cxhigh= electric, cyhigh= electric, czhigh= electric                     #
 ## Periodic BC's for loss-free Eigenvalues:                                  #
 #   xperiodic= no , xphase= undefined                                        #
 #   yperiodic= no , yphase= undefined                                        #
 #   zperiodic= no , zphase= undefined                                        #
 #  fillfrom= (undefined, undefined, undefined)                               #
 # # # # #                                                                    #
 # xspacing= undefined, xminspacing= undefined                                #
 # yspacing= undefined, yminspacing= undefined                                #
 # zspacing= undefined, zminspacing= undefined                                #
 # graded  = no                                                               #
 #   xgraded= no , ygraded= no , zgraded= no                                  #
 # xqfgraded= 1.20, xdmaxgraded= undefined                                    #
 # yqfgraded= 1.20, ydmaxgraded= undefined                                    #
 # zqfgraded= 1.20, zdmaxgraded= undefined                                    #
 # perfectmesh= yes                                                           #
 # geoscale= 1.0                                                              #
 ## Commands: # # # # # # # # # #                                             #
 # xfixed(N, X0, X1)  -- N fixed Meshplanes between X0 and X1                 #
 # yfixed(N, Y0, Y1)  -- N fixed Meshplanes between Y0 and Y1                 #
 # zfixed(N, Z0, Z1)  -- N fixed Meshplanes between Z0 and Z1                 #
 ##############################################################################
 # listplanes, return, help                                                   #
 ##############################################################################

Example
 -mesh
     spacing= 1e-3
     pxlow= 1e-2, pxhigh= 0
     pylow= 2e-2, pyhigh= 0
     pzlow= 3e-2, pzhigh= 0
     
     cxlow= ele, cxhigh= mag
     cylow= ele, cyhigh= mag
     zperiodic= yes, zphase= 120


-material : electric / magnetic Properties

This Section is about specifying the Material Parameters. Materials may be perfect electric conducting (type= electric), perfect magnetic conducting (type= magnetic), electric conducting with Impedance Boundary Conditions applied (type= impedance), or may be loss-free 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.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -material                                                          #
 ##############################################################################
 # 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            #
 ##############################################################################
 # flow  =  undefined                   -- Plot feps(f) & fmue(f) from this f #
 # fhigh =  undefined                   -- upto this f.                       #
 #  thickness=       100.0              -- .. assuming this Thickness.        #
 #   xlog= no                           -- f-Axis logarithmic.                #
 # 2dplotopts= -geometry 690x560+10+10                                        #
 # showtext     = yes         -- (yes | no)                                   #
 # onlyplotfiles= no          -- (yes | no)                                   #
 ##############################################################################
 # return, showfeps, help                                                     #
 ##############################################################################

Frequency dependent Materialparameters are taken into account by directly simulating the Dynamics of the Electron Hull of Molecules. For each Fieldcomponent in a dispersive Material with N Poles, the Equations of Motion ($v$ Velocity, $Q$ Charge, $k$ Spring-constant, $R$ Damping Term, $m$ Mass of the electron Hull) are solved

\begin{eqnarray*}
\frac{d}{dt} v_i &=& \frac{Q}{m} E - \frac{k}{m} x_i - \frac{...
...a \times }H - \frac{1}{\varepsilon } \sum\limits_{i=1}^N Q_i v_i
\end{eqnarray*}


The Parameters $Q$ Charge, $k$ Spring-constant, $R$ Damping Term, $m$ Mass of the electron Hull, are computed from the User-Specified Values epsr, aeps(n), feps(n), fegm(n).

The Permittivity for an $N$.th Order LORENTZ Medium with resonant Frequencies $\omega_n$ and damping Frequencies $\gamma_n$ reads

\begin{displaymath}
\varepsilon_r(\omega) = \varepsilon_\infty
+ \varepsilon_\...
...mega_n^2 }
{ \omega_n^2 + {\rm j}\omega \gamma_n - \omega^2 }
\end{displaymath} (1.1)

Such a Permittivity is described with the Parameters
$\displaystyle \verb ... $\textstyle :=$ $\displaystyle \varepsilon_\infty$ (1.2)
$\displaystyle \verb ... $\textstyle :=$ $\displaystyle A_n$ (1.3)
$\displaystyle \verb ... $\textstyle :=$ $\displaystyle \omega_n \frac{1}{ 2 \pi }$ (1.4)
$\displaystyle \verb ... $\textstyle :=$ $\displaystyle \gamma_n$ (1.5)


Note: Three Materials are predefined:
Note: While a Time Domain Computation with type= impedance Materials is performed, every 500 Timesteps the absorbed Energy in that Materials is written to GdfidL's stdout. For a Computation with four such Materials (3,5,6,8) that Output is similar to
     1.61138828e-9     1.53411444e-9  <= Time [s], IntegratedSumPowerAll [J]
     1.61138828e-9   303.51498474e-12 <= Time [s], IntegratedSumPowerMat003 [J]
     1.61138828e-9     4.27840722e-12 <= Time [s], IntegratedSumPowerMat005 [J]
     1.61138828e-9    15.01830736e-12 <= Time [s], IntegratedSumPowerMat006 [J]
     1.61138828e-9     1.21130274e-9  <= Time [s], IntegratedSumPowerMat008 [J]
The Format is such that one can grep for IntegratedSumPowerMatXXX and create without much Hassle a Datafile for further Inspection.
Example The following specifies that the Material with Number 3 shall be treated as a perfect magnetic conducting Material, the Material with Number 4 shall be a lossy Dielectric.
 -material
    material= 3
       type= magnetic
    material= 4
       type= normal, epsr= 3, kappa= 1, muer= 1

Example The following specifies that the Material with Index 10 shall be treated as a dispersive Dielectric with one LORENTZ Resonance. The frequency Dependence of the $\mu$ and the S11 of a 1/10 of a Metre thick Slab of such a Material shall be plotted.
 -material
# Dispersive Materials and Losses.
   material= 10, type= normal
  define(MUR, 1.36)
   muer= MUR, epsr= 12, kappa= 1e-6, mkappa=0
   fmue(1)= 0.61e9, amue(1)= 460/MUR/MUR, fmgm(1)= 116e9
       flow= 0.1e9, fhigh= 10e9, thickness= 0.1, xlog= yes,
       showfeps # Show the resulting fEps & fMue

To compute the Time Domain Field with dispersive Materials:

 gd1 < /usr/local/gd1/examples-from-the-manual/dispersiveMue-TEM.gdf | tee logfile
We get three Plots. Figure 1.1 shows the real Part, figure 1.2 shows the imaginary Part of the frequency dependent Muer(f). Figure 1.3 shows the Reflection that a Slab of finite Thickness L=0.1 Metres of such a Material gives for a perpendicular incident TEM-wave. The numerically computed Reflection of a such a Slab is given in Figure 1.4.
Figure 1.1: The real Part of the frequency dependent Muer(f).
\begin{figure}\epsfig{figure=dispersivMue-Re.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.2: The imaginary Part of the frequency dependent Muer(f).
\begin{figure}\epsfig{figure=dispersivMue-Im.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.3: The analytical Reflection from a finite Slab of dispersive Material.
\begin{figure}\epsfig{figure=dispersivMue-S11-analytisch.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.4: The numerical Reflection from a Slab of finite Thickness.
\begin{figure}\epsfig{figure=dispersivMue-S11-numerisch.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}


Example The following specifies that the Material with Index 3 shall be treated as a dispersive Dielectric with four LORENTZ Resonances. The frequency Dependence of the epsr and the S11 of a 0.1 Metres thick Slab of such a Material shall be plotted.

 -material
# Dispersive Materials and Losses.
# To have Re(epsr) about 10 and Im(epsr) about 1 in 10-40GHz:
 define(EPSQ, 10**2)
     material= 3, type= normal, epsr= 10, muer= 1, kappa= 1
 kappa= 0
 define(i, 0)
 define(i, i+1) feps(i)= 10e9, aeps(i)= 1.1/EPSQ, fegm(i)= 100e9
 define(i, i+1) feps(i)= 20e9, aeps(i)= 0.42/EPSQ, fegm(i)= 100e9
 define(i, i+1) feps(i)= 30e9, aeps(i)= 0.26/EPSQ, fegm(i)= 100e9
 define(i, i+1) feps(i)= 40e9, aeps(i)= 0.28/EPSQ, fegm(i)= 100e9

     flow= 1e9, fhigh= 70e9, showfeps

To compute the Time Domain Field with dispersive Materials:

 gd1 < /usr/local/gd1/examples-from-the-manual/dispersiveEps-TEM.gdf | tee logfile
We get three Plots. Figure 1.5 shows the real Part, figure 1.6 shows the imaginary Part of the frequency dependent epsr(f). Figure 1.7 shows the Reflection that a 0.1 Metres thick Slab of such a Material would produce for a perpendicular incident TEM-wave. The numerically computed Reflection of a thick Slab of such a Material is given in Figure 1.8.
Figure 1.5: The real Part of the frequency dependent epsr.
\begin{figure}\epsfig{figure=dispersiv-Re.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.6: The imaginary Part of the frequency dependent epsr.
\begin{figure}\epsfig{figure=dispersiv-Im.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.7: The analytical Reflection from a finite Slab of dispersive Material.
\begin{figure}\epsfig{figure=dispersiv-S11-analytisch.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.8: The numerical Reflection from a Slab of finite Thickness.
\begin{figure}\epsfig{figure=dispersiv-S11-numerisch.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}


Example The following specifies that the Material with Index 10 shall be treated as a dispersive Dielectric with two LORENTZ Resonances. The frequency Dependence of the muer and the S11 of a 20 mm Slab of such a Material shall be plotted.

 -material
# Dispersive Materials and Losses.
   material= 10, type= normal
  define(MUR, 1.36)
   muer= MUR, epsr= 1, kappa= 0, mkappa=0

   fmue(1)= 1e9, amue(1)= 200/MUR/MUR, fmgm(1)= 800.0e9
   fmue(2)= 2e9, amue(2)= 30/MUR/MUR, fmgm(2)= 80.0e9
    flow= 1e6, fhigh= 1400e6, xlog= yes, showfeps # Show the resulting fEps, fMue

To compute the Time Domain Field with dispersive Materials:

 gd1 < /usr/local/gd1/examples-from-the-manual/dispersiveMue2-TEM.gdf | tee logfile
We get three Plots. Figure 1.9 shows the real Part, figure 1.10 shows the imaginary Part of the frequency dependent Muer(f). Figure 1.11 shows the Reflection that a Slab of such a Material would produce for a perpendicular incident TEM-wave. The numerically computed Reflection of a 20 mm Slab of such a Material is given in Figure 1.12.
Figure 1.9: The real Part of the frequency dependent Muer.
\begin{figure}\epsfig{figure=Oscar-Frasciello-Re.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.10: The imaginary Part of the frequency dependent Muer.
\begin{figure}\epsfig{figure=Oscar-Frasciello-Im.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.11: The analytical Reflection from a Slab of dispersive Material.
\begin{figure}\epsfig{figure=Oscar-Frasciello-S11-analytisch.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 1.12: The numerical Reflection from a Slab of dispersive Material.
\begin{figure}\epsfig{figure=Oscar-Frasciello-S11-numerisch.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}


-lgeometry : Load a previously used Geometry

This Section enables the Loading of the Grid and Material Filling of a previous Computation to be used for the current Computation.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -lgeometry                                                        #
 ##############################################################################
 # infile = -none-                                                            #
 # xmirror= none              -- [none,low,high]                              #
 # ymirror= none              -- [none,low,high]                              #
 #                                                                            #
 #                                                                            #
 ##############################################################################
 # ?, doit, return, end, help                                                 #
 ##############################################################################

Note: If you load a Geometry via -lgeometry, all previous defined Geometric items are lost. You should only redefine Material Parameters after loading a Grid via -lgeometry.

Geometric Primitives


-brick: A rectangular Brick

A Brick is a rectangular Box, with its Edges parallel to the cartesian Coordinate Axes. If you need to model a Brick with Edges in other Directions, you can use the -rotate Section to rotate the Brick in any Direction.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -brick                                                             #
 ##############################################################################
 # material=  1, sloppy= no                                                   #
 # whichcells= all, taboo= none                                               #
 #     show= off    -- [off|now|later|all]                                    #
 #     name= brick-000000000                                                  #
 # xlow = undefined     , ylow = undefined     , zlow = undefined             #
 # xhigh= undefined     , yhigh= undefined     , zhigh= undefined             #
 # # # # #                                                                    #
 # volume= (undefined, undefined, undefined, undefined, undefined, undefined) #
 ##############################################################################
 # doit, return, help                                                         #
 ##############################################################################

Example
 # /usr/local/gd1/examples-from-the-manual/brick-example.gdf
 -general
     outfile= /tmp/UserName/example
     scratch= /tmp/UserName/scratch

 -mesh
     pxlow= -1e-2, pxhigh= 3e-2
     pylow= -1e-2, pyhigh= 2e-2
     pzlow= -0.1e-2, pzhigh= 2e-2
     
     cxlow= ele, cxhigh= mag
     cylow= ele, cyhigh= mag
     czlow= ele, czhigh= mag

     spacing= 1e-3

 -brick
     material= 1, sloppy= no
        xlow= 0, xhigh= 1.1e-2
        ylow= 0, yhigh= 1.5e-2
        zlow= 0, zhigh= 0.8e-2
     doit

 -transform,
      -translate, offset= ( 1.5e-2, 0, 0 ), doit
      -rotate, axis= ( 1, 0, 0 ), angle= -45, doit
 -brick, material= 3, sloppy= yes, doit

 -volumeplot
     scale= 3
     doit
Figure 1.13: A simple Brick, and the same Brick-Data translated and rotated.
\begin{figure}\begin{center}\quad \quad
\psfig{figure=brick-example.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
\end{center}
\end{figure}


-gccylinder: A circular Cylinder in general Direction

A gccylinder is a circular Cylinder, with its Axis in some arbitrary Direction.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -gccylinder                                                        #
 ##############################################################################
 # material  =  1                                                             #
 # whichcells= all, taboo= none                                               #
 #     show= off    -- [off|now|later|all]                                    #
 #     name= gccyl-000000000                                                  #
 # radius    = undefined                                                      #
 # length    = undefined                                                      #
 # origin    = ( undefined, undefined, undefined )                            #
 # direction = ( undefined, undefined, undefined )                            #
 ##############################################################################
 # doit, return, help                                                         #
 ##############################################################################

Note: You can revert the Direction of the Cylinder by negating the direction, or (easier) by negating the length.
Note: If you want eg. a Quarter of a circular Cylinder, you have to use -gbor, see Pages [*] ff.
Example
 # /usr/local/gd1/examples-from-the-manual/gccylinder-example.gdf

 -general
     outfile= /tmp/UserName/example
     scratch= /tmp/UserName/scratch-

 -mesh
     pxlow= 0, pxhigh= 1e-2
     pylow= 0, pyhigh= 2e-2
     pzlow= 0, pzhigh= 1.5e-2
     
     cxlow= ele, cxhigh= mag
     cylow= ele, cyhigh= mag
     czlow= ele, czhigh= mag

     spacing= 0.2e-3

 -gccylinder
     material= 5, radius= 3e-3, length= 7e-3
     origin= ( 0.5e-2, 0.3e-2, 0.6e-2 )
     direction= ( -0.4, 1.5, 0.4 )
     doit
        
 -volumeplot
     scale= 3
     doit
Figure 1.14: A simple gccylinder, with its Axis directing towards (-0.4, 1.5, 0.4).
\begin{figure}\centerline{
\psfig{figure=gccylinder-example.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}


Example

 # /usr/local/gd1/examples-from-the-manual/gccylinder-example2.gdf

 define(VeryLarge, 10000)

 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch

    text()= A Chain of circular Cylinders
    text()= The Cylinders are partly outside of the bounding Box.

 -mesh
    pxlow= -0.8, pxhigh= 10
    pylow= -2, pyhigh= 2
    pzlow= -0, pzhigh= 1.8

    spacing= 8e-2

 -brick
    material= 0
    volume= ( -VeryLarge, VeryLarge, \
              -VeryLarge, VeryLarge, \
              -VeryLarge, VeryLarge )
    doit

 define(RADIUS, 0.6)
 -gccylinder
    length= 1.7
    radius= RADIUS
    do jj= 0, 9, 1
       material= jj+3
       origin= ( jj*1.5*RADIUS, 0, 0 )
 define(PHI, jj*22.5*@pi/180 )
       direction= ( 0, cos(PHI), sin(PHI) )
       doit
    end do

 -volumeplot
    eyeposition= ( 1.0, 2.30, 2 )
    scale= 5
    doit
Figure 1.15: A Chain of simple circular Cylinders. Each Cylinder has its Axis pointing in a different Direction.
\begin{figure}\centerline{
\psfig{figure=gccylinder-example2.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}


-ggcylinder: A general Cylinder in general Direction

A ggcylinder is a general Cylinder with a Footprint (Cross-Section) described as a general Polygon. This Footprint is swept along an Axis in a general Direction, additionally, this Footprint can shrink or expand along this Axis, additionally, this Footprint can be rotated along the Axis, additionally, only Parts of the ggcylinder that fulfill some additional Condition will be filled.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -ggcylinder                                                        #
 ##############################################################################
 # material   =  1                                                            #
 # whichcells = all, taboo= none                                              #
 #     show   = off                     -- (off | all | later | now)          #
 #     name   = ggcyl-000000000                                               #
 #   fixpoints= no                      -- (yes|no)                           #
 #     inside = yes                     -- (yes|no)                           #
 # originprime    = ( 0.0, 0.0, 0.0 )                                         #
 # xprimedirection= ( 1.0, 0.0, 0.0 )                                         #
 # yprimedirection= ( 0.0, 1.0, 0.0 )                                         #
 #   zprimedirection= ( 0.0, 0.0, 1.0 )                                       #
 #   usezprimedirection= no             -- (yes|no)                           #
 # range      = ( undefined, undefined )                                      #
 # pitch      = 0.0                     -- [Degs/m]                           #
 # xexpgrowth = 0.0                                                           #
 # yexpgrowth = 0.0                                                           #
 # xslope     = 0.0                     -- (x2/x1-1)/len [1/m]                #
 # yslope     = 0.0                     -- (y2/y1-1)/len [1/m]                #
 # xscaleprime= 1.0                                                           #
 # yscaleprime= 1.0                                                           #
 # zxscaletablefile= -none-
 # zyscaletablefile= -none-
 #    deltaphi= 4.0                     -- Arc and Ellipse Resolution [Degs]  #
 ##############################################################################
 ## Syntax:                                                                   #
 #  point= (Xi, Yi)                                                           #
 #  arc, radius= RADIUS, type= [clockwise | counterclockwise]                 #
 #       size= [small | large ]                                               #
 #       deltaphi= 5                                                          #
 #  ellipse, center= (X0, Y0), size= [small | large ]                         #
 #       deltaphi= 5                                                          #
 ##############################################################################
 # doit, return, help, list, reset, clear                                     #
 ##############################################################################


Example The following decribes a Cavity with rounded Corners.

 # /usr/local/gd1/examples-from-the-manual/ggcylinder-example.gdf

 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch

    text()= We use 'fixpoints= yes'
    text()= to ensure Meshplanes at the Points of the Polygon.
    text()=
    text()= We use a graded Mesh.

 -mesh
    spacing= 100e-6
    graded= yes, dmaxgraded= 263.3e-6
    pxlow= -5e-3, pxhigh= 5e-3
    pylow= -4.34e-3, pyhigh= 0
    pzlow= -1.6665e-3, pzhigh= 1.6665e-3

    cxlow= ele, cxhigh= mag
    cylow= ele, cyhigh= mag
    czlow= ele, czhigh= ele

 -ggcylinder

    material= 7
    originprime= ( 0, 0, 0 )
    xprimedirection= ( 1, 0, 0 )
    yprimedirection= ( 0, 0, 1 )
    range= ( -4.2e-3, 4.2e-3 )

    clear  # Clear the Polygon-List, if any
    point= ( -3.3405e-3, -816.5e-6 )
       arc, radius= 500.0e-6, type= counterclockwise, size= small
    point= ( -2.8405e-3, -1.3165e-3 )
    point= (  2.8405e-3, -1.3165e-3 )
       arc
    point= (  3.3405e-3, -816.5e-6 )
    point= (  3.3405e-3,  816.5e-6 )
       arc
    point= (  2.8405e-3, 1.3165e-3 )
    point= ( -2.8405e-3, 1.3165e-3 )
       arc
    point= ( -3.3405e-3,  816.5e-6 )

    fixpoints= yes # Ensure Mesh-Planes at the Points of the Polygon.
    doit

 -volumeplot
    scale= 4
    doit
Figure 1.16: A simple ggcylinder
\begin{figure}\centerline{ \psfig{figure=ggcylinder-example.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=} }
\end{figure}


Example The following decribes a twisted rectangular Waveguide.

 # /usr/local/gd1/examples-from-the-manual/ggcylinder-twisted.gdf

 define(LargeNumber, 10000)

 define(LENGTH, 10e-3)
 define(WGW, 2.54e-3 )
 define(WGH, WGW/2 )

 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch

    text()= A Waveguide-Twist
    text()= Waveguide-Width : WGW
    text()= Waveguide-Height: WGH

 -mesh
    spacing= WGW/40
    pxlow= -1e-3, pxhigh= LENGTH+1e-3
    pylow= -WGW*0.6, pyhigh= 0.6*WGW
    pzlow= -WGW*0.6, pzhigh= 0.6*WGW


 define(EL, 10)
 -material, material= EL, type= electric 
 -brick
    #
    # Fill the Universe with Metal:
    #
    material= EL
       volume= ( -LargeNumber, LargeNumber, \
                 -LargeNumber, LargeNumber, \
                 -LargeNumber, LargeNumber )
    doit

 -ggcylinder
    #
    # The twisted Waveguide.
    # We use a rectangular Footprint,
    # and specify a Pitch.
    # The Footprint shall rotate by -90 Degrees, over a length of LENGTH.
    #


    material= 0
    originprime= ( 0, 0, 0 )
    xprimedirection= ( 0, 1, 0 )
    yprimedirection= ( 0, 0, 1 )
    range= ( 0, LENGTH )
    pitch= -90/LENGTH

    clear  # Clear the previous Polygon-List, if any.
    point= ( -WGW/2, -WGH/2 )
    point= (  WGW/2, -WGH/2 )
    point= (  WGW/2,  WGH/2 )
    point= ( -WGW/2,  WGH/2 )
    doit

 -volumeplot
    eyeposition= ( 1, 2, 1.3 )
    scale= 4.5
    doit
Figure 1.17: A simple ggcylinder, with a Pitch.
\begin{figure}\centerline{ \psfig{figure=ggcylinder-twisted.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=} }
\end{figure}


Example The following decribes a Transition from a circular Waveguide to an elliptical Waveguide.

 # /usr/local/gd1/examples-from-the-manual/ggcylinder-circular-to-elliptic.gdf

 define(LargeNumber, 10000)

 define(LENGTH, 10e-3)
 define(RADIUS1, 2.54e-3 ) define(RADIUS2, 5.0e-3  )
 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch

    text()= A Transition from a circular Waveguide to an elliptical One.
    text()= The Bounding box is specified such,
    text()= that only the Part below the Plane z=0 is discretised.

 -mesh
    spacing= RADIUS1/20
    pxlow= -1e-3, pxhigh= LENGTH+1e-3
    pylow= -RADIUS2*1.0, pyhigh= RADIUS2*1.0
    pzlow= -RADIUS1*1.1, pzhigh= 0


 define(EL, 10)
 -material, material= EL, type= electric 
 -brick
    #
    # Fill the Universe with Metal:
    #
    material= EL
       volume= ( -LargeNumber, LargeNumber, \
                 -LargeNumber, LargeNumber, \
                 -LargeNumber, LargeNumber )
    doit

 -ggcylinder
    #
    # The Waveguide.
    # We use a circular Footprint,
    # and specify a Slope, different in x- and y
    #
    material= 0
    originprime= ( 0, 0, 0 )
    xprimedirection= ( 0, 1, 0 )
    yprimedirection= ( 0, 0, 1 )
    range= ( 0, LENGTH )
# xlingro 1+(RADIUS2/RADIUS1-1)/LENGTH
    xslope= (RADIUS2/RADIUS1-1)/LENGTH
    yslope= 0

    clear  # Clear the previous Polygon-List, if any.
    point= ( -RADIUS1, 0 )
      arc, radius= RADIUS1, size= large, type= counterclockwise
    point= (  RADIUS1, 0 )
      arc
    point= ( -RADIUS1, 0 )
    doit

 -volumeplot
    eyeposition= ( 2, 1, 1.8 )
    scale= 3
    doit
Figure 1.18: A simple ggcylinder, with different Growthfactors for x and y.
\begin{figure}\centerline{ \psfig{figure=ggcylinder-circular-to-elliptic.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=} }
\end{figure}


Example The following decribes a elliptical Wedge where the Axis of the ggcylinder is in the z-Direction, while the Plane Normal of the Wedge is tilted.

 # /usr/local/gd1/examples-from-the-manual/ggcylinder-usezprimedirection.gdf

 #
 # Some helpful Symbols:
 #
 define(EL, 1) define(MAG, 2)
 define(INF, 1000)

 define(STPSZE, 0.5e-3)       # Define the transverse Mesh Step Size, 0.5 mm
 
 #
 # Description of the Flange Geometry.
 #
 define(FlangeGap, 10e-3 )     # Gap of the Flange Joint
 define(FlangeD0, 80e-3)      # Diameter of Gasket Seal
 define(Width, FlangeGap/2 )  # 1/2 Width of Flange Gap in z-Axis.
 define(FlangeRadius, FlangeD0/2 )
 define(AxisA  , 70e-3/2 )    # 1/2 *major Diameter of interior Ellipse.
 define(AxisB  , 32e-3/2 )    # 1/2 *minor Diameter of interior Ellipse.

  #--- Parameters related to a tilted Flange Joint ---
 define(ZW, 10e-3)                      # z-Deviation from the y-Axis 
 define(Theta, atan(ZW/FlangeRadius) )  # Angle between y-Axis and y'-Axis
 define(RR, FlangeRadius/cos(Theta) )   # Radius of the tilted Cylinder.
 define(LL, Width/cos(Theta) )          # Half Length of tilted Cylinder.


 ###
 ### We enter the Section "-general"
 ### Here we define the Name of the Database where the
 ### Results of the Computation shall be written to.
 ###    (outfile= )
 ### We also define what Names shall be used for Scratchfiles.
 ###    (scratchbase= )
 ###
 -general
    outfile= /tmp/UserName/bla
    scratch= /tmp/UserName/scratch-

    text()= Flange Gap= FlangeGap
    text()= Mesh= STPSZE m
    text()= tilt Angle of Flange= eval(Theta*180/@pi) [Degrees]

 ###
 ### We define the default Mesh-Spacing,
 ### we define the Borders of the computational Volume.
 ###
 define(Zmin, -4e-2)
 define(Zmax,  4e-2)
 -mesh
   spacing= STPSZE
   pxlow= -5e-2, pxhigh= 0
   pylow= -4e-2, pyhigh= 4e-2
   pzlow= Zmin, pzhigh= Zmax

 #####
 # Specify that the Material Index '3'
 # describes a perfect conducting Material.
 -material
   material= 3
   type= electric

## 
## fill the Universe with Metal.
##
 -brick
   material= 3
     xlow= -INF, xhigh= INF
     ylow= -INF, yhigh= INF
     zlow= -INF, zhigh= INF
   doit


 ##
 ## Step 1: Carve out a tilted circular Box.
 ##
  -ggcylinder         # A Parallelogram Gap with a tilt Angle.
     material= 0
     origin= (0,0,0)
     xprimedirection= (1,0,0)
     yprimedirection= (0, cos(Theta), sin(Theta) )
 zprimedirection= ( 0, 0, 1 )
 usezprimedirection= yes
     range= ( -LL, LL )

     clear
     point= ( -RR, 0 )
       arc, radius= RR,type= counterclockwise, size= small
     point= (  RR, 0 )
       arc, radius= RR,type= counterclockwise, size= smal 
     point= ( -RR, 0 )
     show= later
     doit
 usezprimedirection= no # Switch back to the Default, 'no'.

##
## Step 2: Creating the interior Footprint of elliptic Beampipe(hollow)
##
-ggcylinder
   material= 0
   origin= (0, 0, 0)
   xprimedirection= (1, 0, 0)
   yprimedirection= (0, 1, 0)
   range= (Zmin-2*STPSZE, Zmax+STPSZE)
   xslope= 0, yslope= 0

   clear  # Clear any old Polygon-Description of the Footprint.
    # point= (x', y')
   point= (0, -AxisB),
     ellipse, center= (0,0),
   point= (AxisA, 0),
     ellipse,
   point= (0, AxisB),
     ellipse,
   point= (-AxisA, 0),
     ellipse,
   point= (0, -AxisB),
# show= all
   doit

 ############

 -volumeplot
    eyeposition= ( 1, -0.5, 0.5 )
    scale= 3
    doit
Figure 1.19: A simple ggcylinder, with zprimedirection different from the Footprints Plane Normal.
\begin{figure}\centerline{ \psfig{figure=ggcylinder-usezprimedirection.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=} }
\end{figure}


Example The following decribes a Cosine-Taper. The Cross-Section is specified as a ggcylinder, the Cross Section is circular. The xscale and yscale are specified via tables.

 # /usr/local/gd1/examples-from-the-manual/zxscale-example.gdf

 define(R1, 1 )
 define(R3, 3 )

 define(DR, 0.1*R1)

 -general
    outfile= /tmp/UserName/bla
    scratch= /tmp/UserName/scratch-

 -mesh
    spacing= R1 / 10
    pxlow=  -16, pxhigh= 5
    pylow = -(R3+DR), pyhigh= R3+DR
    pzlow = -(R3+DR), pzhigh= R3+DR

 # Compile the program which creates the Table.
 system( $FC Two-Cosine-Table.f90 )
 # Run the program which creates the table.
 system( ./a.out >  Two+Cosine-Table )

# The source Code looks like:
#    Pi= 4*ATAN(1.0)
#    z0= 0
#    zN= 10
#    N= 100
#    DO i= 1, N
#       z= z0 + (i-1)*(zN-z0) / (N-1)
#       WRITE (*,*) z, 2 - COS((z-z0) * Pi/(zN-z0))
#    END DO
#    END
#

##
## Create the tapered Beampipe.
##
 -ggcylinder
    material= 3
    origin= ( 0, 0, 0 )
    xprime= ( 0, 0, 1 )  # The x'-Direction.
    yprime= ( 0, 1, 0 )  # The y'-Direction.
                         # The z'-Direction is then implicitely the
                         # ( -1, 0, 0 ) Direction.
                         #    z' = x' cross y'
    range= ( -3, 14 )  # The Range of the z'-Values.

    # Filenames of the Tables.
    zxscale= Two+Cosine-Table
  ##  zyscale= -none-

    clear  # Clear any old Polygon-Description of the Footprint.
    #
    # This decribes a circular Footprint.
    #
     # point= (x', y')
    point= ( 0, -R1 )
      arc, radius= R1, type= clockwise, size= small
    point= ( 0,  R1 )
      arc
    point= ( 0, -R1 )
 # show= now
    doit

 -volumeplot, scale= 4, doit
Figure 1.20: The Discretisation of a Cosine-Taper, specified as a ggcylinder with zxscale.
\begin{figure}\centerline{
\psfig{figure=zxscale-example.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}


-gbor: A general Body of Revolution in general Direction

A gbor is a Body of Revolution with a Cross Section described as a general Polygon. This Cross Section is swept around some Axis in a general Direction. Moreover, only Volume that fulfills some additional Condition will be filled.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -gbor                                                              #
 ##############################################################################
 # material       =  1                                                        #
 # whichcells     = all, taboo= none                                          #
 #     show       = off                 -- (off | all | later | now)          #
 #     name       = gbor-000000000                                            #
 # inside         = yes                 -- (yes|no)                           #
 # originprime    = ( 0.0, 0.0, 0.0 )                                         #
 # zprimedirection= ( 0.0, 0.0, 1.0 )                                         #
 # rprimedirection= ( 1.0, 0.0, 0.0 )                                         #
 # range          = ( 0.0, 360.0 )                                            #
 # xscaleprime    = 1.0                 -- Elliptic Coordinates.              #
 # yscaleprime    = 1.0                 -- Elliptic Coordinates.              #
 ##############################################################################
 ## Syntax:                                                                   #
 #  point= (Zi, Ri)                                                           #
 #  arc, radius= RADIUS, type= [clockwise | counterclockwise]                 #
 #       size= [small | large ]                                               #
 #       deltaphi= 5                                                          #
 #  ellipse, center= (Z0, R0), size= [small | large ]                         #
 #       deltaphi= 5                                                          #
 ##############################################################################
 # doit, return, help, list, reset, clear                                     #
 ##############################################################################


Example The following describes something like a Tuning-Plunger.
 # /usr/local/gd1/examples-from-the-manual/plunger0.gdf

 define(PlungerInnerRadius, 100e-3/2 )
 define(PlungerCurvature, 16e-3 )
 define(PlungerAngle, -67.5*@pi/180 )

 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch-

    text()= A Plunger, modelled as a body of revolution.
    text()= Curvature     : PlungerCurvature
    text()= Radius        : PlungerInnerRadius
    text()= Angle of Axis : eval(PlungerAngle * 180 / @pi) Degrees

 -mesh
    spacing= 0.2e-2
    pxlow= -0.12, pxhigh= 0.05
    pylow= -0.02, pyhigh= 0.18
    pzlow= -6e-2, pzhigh= 6e-2

 -gbor
     material= 4
     originprime= ( 0, 0, 0 )
     zprimedirection= ( cos(PlungerAngle), sin(PlungerAngle), 0 )
     rprimedirection= ( 0, 0, 1 )
     range= ( 0, 360 )

     clear
        # point= ( z, r )
     point= ( 0, 0 )
     point= ( 0, PlungerInnerRadius-PlungerCurvature )
        arc, radius= PlungerCurvature, size= small, type= counterclockwise
     point= ( -PlungerCurvature, PlungerInnerRadius )
     point= ( -170e-3, PlungerInnerRadius )
     point= ( -170e-3, 0 )
# show= now
     doit

 -volumeplot, eyeposition= ( 1, -0.5, 0.6 )
     scale= 3
     doit
Figure 1.21: A simple gbor.
\begin{figure}\centerline{
\psfig{figure=gbor-example0.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}

Example The following discretises the Connection of two circular Waveguides, meeting at an Angle of 90 Degrees.
 # /usr/local/gd1/examples-from-the-manual/gbor-example1.gdf
define(LargeNumber, 10000)       # some big number

define(MAXCELLS, 1e+5)

define(XLOW, 0) define(XHIGH, 5e-2)
define(YLOW, 0) define(YHIGH, 6e-2)
define(ZLOW, -1.1e-2) define(ZHIGH, 0)

define(STPSZE, ((XHIGH-XLOW)*(YHIGH-YLOW)*(ZHIGH-ZLOW)/MAXCELLS)**(1/3) )

 -mesh
    volume= ( XLOW, XHIGH, \
              YLOW, YHIGH, \
              ZLOW, ZHIGH )

    spacing= STPSZE

 -general
    outfile= /tmp/UserName/example
    scratch= /tmp/UserName/scratch
 define(R, 1.0e-2)
    text()= Intersection of two circular Cylinders with Radius R
    text()= generated as general Cylinders
    text()= where 'taboo' is specified.
    text()= stpsze= STPSZE, maxcells= MAXCELLS

#
# Fill the Universe with Metal.
#
 -brick
    material= 1
    volume= ( -LargeNumber, LargeNumber, \
              -LargeNumber, LargeNumber, \
              -LargeNumber, LargeNumber )
    doit

#
# First Step,
# fill Cells above the Diagonal with Material 3.
# these Cells will not be filled by the first circular Cylinder,
# since we will specify 'taboo= 3'.
#
#
 -ggcylinder
    material= 3,
    origin= ( 0, 0, 0 ), xprime= ( 1, 0, 0 ), yprime= ( 0, 1, 0 ),
    range= ( ZLOW, ZHIGH ),

    clear
    point= ( XLOW, YLOW ), point= ( XLOW, YHIGH ),
    point= ( XLOW+(YHIGH-YLOW), YLOW )

    doit

#
# Second Step:
# Fill a circular Cylinder in x-Direction,
# but NOT Cells with Material Index 3 (taboo=3).
#
 -ggcylinder
    material= 0, taboo= 3,
    xprime= ( 0, 1, 0 ), yprime= ( 0, 0, 1 ),  # So the Axis will be in +x.
    origin= ( 0, 4e-2, 0 ),                    # Shift of Origin.
    range= ( XLOW, XHIGH ),

    clear
       point= ( -R, 0 ),
         arc, radius= R, type= counterclockwise,
       point= ( 0, -R ),
         arc, radius= R,
       point= ( R, 0 ),
    doit

#
# Third Step:
# Fill a circular Cylinder in y-Direction,
# but ONLY Cells with Material Index 3 (whichcells=3).
#
 -ggcylinder
    material= 0, whichcells= 3, taboo= none
    xprime= ( 1, 0, 0 ), yprime= ( 0, 0, -1 ),  # So the Axis will be in +y.
    origin= ( 2.e-2, 0, 0 ),                    # Shift of Origin.
    range= ( YLOW, YHIGH ),

    clear
       point= ( -R, 0 ),
          arc, radius= R, type= clockwise,
       point= ( 0, R ),
          arc, radius= R,
       point= ( R, 0 ),
    doit

 -volumeplot
    eyeposition= ( 1, 2, 1 )
    scale= 3.5
    doit
Figure 1.22: The Intersection of two circular Cylinders, where whichcells and taboo were specified.
\begin{figure}\centerline{
\psfig{figure=gbor-example1.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}

Example The following describes a reentrant Cavity.
 # /usr/local/gd1/examples-from-the-manual/gbor-example.gdf
 define(MaxCells, 2e+6)

 #
 # define the geometry parameters
 #
 define(RBeamTube, 4.7625e-2)
 define(RCurve,  1.0e-2)
 define(ZGapNose, 10.9e-2)
 define(RLarge, 25.0e-2)  define(RSmall, 15.0e-2)  define(RCenter, 10.0e-2)

 define(INF, 10000) define(EL, 1) define(MAG, 2)

 define(XLOW, -0.250) define(XHIGH, 0.250)
 define(YLOW, -0.250) define(YHIGH, 0.250)
 define(ZLOW, -0.200) define(ZHIGH, 0.200)

 define(STPSZE, ((XHIGH-XLOW)*(YHIGH-YLOW)*(ZHIGH-ZLOW)/MaxCells)**(1/3) )

 #
 # gdfidl can evaluate sin(), cos(), atan() and X**Y
 # definition of functions degsin() and degcos()
 #
 sdefine(degsin, [sin((@arg1)*@pi/180)])
 sdefine(degcos, [cos((@arg1)*@pi/180)])
 sdefine(degtan, [sin((@arg1)*@pi/180)/cos((@arg1)*@pi/180)])

-general
   outfile= /tmp/UserName/example
   scratch= /tmp/UserName/scratch-

   text(3)= A Quarter of a reentrant Cavity.
   text()= The Cavity is described as a Body of Revolution.
   text()=
   text()= maxcells= MaxCells, stpsze= STPSZE

-mesh
   pxlow= 0*XLOW, pxhigh= 1*XHIGH
   pylow= 0*YLOW, pyhigh= 1*YHIGH
   pzlow= 1*ZLOW, pzhigh= 1*ZHIGH

   cxlow= mag, cxhigh= mag
   cylow= mag, cyhigh= mag
   czlow= ele, czhigh= ele

   spacing= STPSZE

 -material
   material= 3, type= electric

 -brick
    #
    # We fill the Universe with Metal.
    #
    material= 3
       volume= ( -INF,INF, -INF,INF, -INF,INF )
    doit

 #
 # We carve out the Cavity.
 #
 -gbor
     material= 0, range= ( 0, 360 )
     origin= ( 0, 0, 0 )
     show= later,      # Do not show now, but show later.

     clear   # Clear a previous Polygon List.
        point= (     0          , 0 ),
        point= ( ZHIGH+2*STPSZE , 0 ),
        point= ( ZHIGH+2*STPSZE , RBeamTube ),
        point= ( ZGapNose+RCurve, RBeamTube ),
           arc, radius= RCurve, size= small, type= clockwise,
           deltaphi= 10
define(rdum, RBeamTube+(1+degcos(30))*RCurve)
define(zdum, ZGapNose +(1-degsin(30))*RCurve)
        point= ( zdum, rdum )
define(deltaz, RSmall-zdum)
define(deltar, deltaz*degtan(30))
 define(ffac, 0.85)   ## adjust this for a smooth transition
define(zdum2, zdum+ffac*deltaz)
define(rdum2, rdum+ffac*deltar)
        point= ( zdum2, rdum2 )
          arc, radius= RCurve, size= small, type= counterclockwise,
          deltaphi 10
        point= ( RSmall, RCenter-0.8*RCurve ),
        point= ( RSmall, RCenter ),
           arc, radius= RSmall, size= small, type= counterclockwise,
           delta= 3
        point= ( -RSmall, RCenter ),
        point= ( -RSmall, RCenter-0.8*RCurve ),
           arc, radius= RCurve, size= small, type= counterclockwise,
           deltaphi= 10
        point= ( -zdum2, rdum2 )
        point= ( -zdum, rdum )
           arc, radius= RCurve, size= small, type= clockwise, delta 10
        point= ( -(ZGapNose+RCurve), RBeamTube ),

        point= ( ZLOW-2*STPSZE, RBeamTube ),
        point= ( ZLOW-2*STPSZE, 0 )
     list
     doit
#
# Enforce some Meshplanes:
#
-mesh
   zfixed( 2, -(ZGapNose+RCurve), -ZGapNose ) # At the Noses.
   zfixed( 2,  (ZGapNose+RCurve),  ZGapNose ) # At the Noses.

   zfixed( 2, -RSmall, RSmall)                # At the z-Borders of the Cavity.

-volumeplot
   scale= 3
   doit
Figure 1.23: A complicated gbor
\begin{figure}\centerline{
\psfig{figure=gbor-example.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}


Example The following describes two Bodies of Revolution that look similiar to Glasses. The Shape is only specified once, but two different Glasses are generated by varying 'zprime' and 'rprime'

 # /usr/local/gd1/examples-from-the-manual/gbor-glasses.gdf

define(MAXCELLS,1e+6)

define(XLOW,-5e-2) define(XHIGH,18e-2)
define(YLOW,-0e-2) define(YHIGH,17e-2)
define(ZLOW,-3e-2) define(ZHIGH,18e-2)
define(STPSZE, ((XHIGH-XLOW)*(YHIGH-YLOW)*(ZHIGH-ZLOW)/MAXCELLS)**(1/3) )

 -general
    outfile= /tmp/UserName/glasses
    scratch= /tmp/UserName/glasses-scratch-

 -mesh
    spacing= STPSZE
    volume= ( XLOW, XHIGH, \
              YLOW, YHIGH, \
              ZLOW, ZHIGH )

# Fill the Universe with Vacuum.
 define(LargeNumber,10000)
 -brick
     material= 0
        volume= ( -LargeNumber, LargeNumber, \
                  -LargeNumber, LargeNumber, \
                  -LargeNumber, LargeNumber )
     doit

 #
 # The Glasses:
 #
  -gbor

     #
     # Definition of the Cross-Section:
     #
     clear
     point= (  0.7e-2,      0 ),
     point= (       0, 4.0e-2 ),
       arc, radius=0.25e-2, size= large, type= clockwise
     point= (  0.3e-2, 4.0e-2 ),
     point= (  1.0e-2, 1.0e-2 ),
     point= (  8.0e-2, 0.8e-2 ),
     point= ( 10.0e-2, 1.4e-2 ),
     point= ( 15.0e-2, 6.0e-2 ),
       arc, radius= 0.4e-2, type= clockwise
     point= ( 15.2e-2, 5.4e-2 ),
     point= ( 10.0e-2,      0 )

     #
     # That Cross-Section is used twice,
     # with different Parameters for origin, zprime etc..
     #

     material= 1,
     origin= ( -2e-2, 0, 4e-2 ),
     zprimedir= ( 1, 0, 0 ),
     rprimedir= ( 0, 1, 0 ),
     range= ( -90, 90 ),
 ##    show= now
     doit                 # This 'doit' generates the first 'glass'.


     material= 3
     origin= ( 0, 12e-2, 4e-2 ),
     zprimedir= ( 1, -0.5, 0.7 ),
     rprimedir= ( 0, 1, 0 ),
     range= ( 0, 360 ),
 ##    show= all
     doit                 # This 'doit' generates the second 'glass'

 -volumeplot
     eyeposition= ( 0.7, 1, 0.5 )
     scale= 4
    doit
Figure 1.24: Two complicated gbors (Glasses).
\begin{figure}\centerline{
\psfig{figure=gbor-glasses.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}


-stlfile: CAD Import via STL-File

This Section is about importing a Geometry Description from a CAD System1.3 via a STL-file (STereo-Lithography). A STL-file describes a closed Body via a Set of Triangles.

The so described Body can be rotated, shrunk or expanded and shifted.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -stlfile                                                           #
 ##############################################################################
 # file= /usr/local/gd1/examples/woman.stl                                    #
 # material  =  1                                                             #
 # whichcells= all, taboo= none, nboundaries=  1                              #
 # originprime    = ( 0.0, 0.0, 0.0 )                                         #
 # xprimedirection= ( 1.0, 0.0, 0.0 )                                         #
 # yprimedirection= ( 0.0, 1.0, 0.0 )                                         #
 # xscale = 1.0                                                               #
 # yscale = 1.0                                                               #
 # zscale = 1.0                                                               #
 # debend = no                          -- debend description around uaxis    #
 #    uaxis= z                          -- [xyz] : direction of debend-axis   #
 #    radius= 0.0                                                             #
 #    v0    = 0.0                       -- v0,w0: coordinates of the axis.    #
 #    w0    = 0.0                                                             #
 # show   = no                          -- ( yes | no )                       #
 #    plotbbox= ( -1.0e+30, 1.0e+30,  \                                       #
 #                -1.0e+30, 1.0e+30,  \                                       #
 #                -1.0e+30, 1.0e+30 )                                         #
 ##############################################################################
 # doit, return, help                                                         #
 ##############################################################################


Example

 # /usr/local/gd1/examples-from-the-manual/stl-example2.gdf

 -mesh
     spacing= 2.2
 perfectmesh= yes
     volume= ( 0,200, 0,130, -200,0 )

 -stlfile
     file= /usr/local/gd1/examples/wagner60kASTL.stl
     xprime= ( 1, 0, 0 )
     yprime= ( 0, 0, -1 )
     material= 1, taboo= none
##     show= yes,
     doit

 -volumeplot, scale= 2.5, eyepos= ( 1, 2, 0.5), doit
Figure 1.25: A discretisation of a Wagner Bust, described as a STL-file.
\begin{figure}\centerline{
\psfig{figure=stl-example2.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}

Example
 # /usr/local/gd1/examples-from-the-manual/stl-example-debend.gdf
 
 define(FILE, dipchamSTL00)
 define(INF, 10000)

 define(SIGMA, 5e-3)
define(SIGMA, 10e-3) # 8 times less gridcells.
 define(STPSZE, SIGMA/5 )
 define(TRAILER, 68*SIGMA)
 define(OFFSET,20e-3)

 define(A,    300.0e-3)
 define(B,    400.0e-3)

 define(ZYL1, 120e-3)

###############################################################

 -general
   outfile= /tmp/UserName/bla
   scratch= /tmp/UserName/scratch-
   text()= stpsze= STPSZE
   text()= sigma= SIGMA, sigma/stpsze= eval(SIGMA/STPSZE)
   text()= charge= CHARGE, RDV
   text()= offset= OFFSET	

###############################################################         
 -mesh
   pxlow= -ZYL1+40e-3, pxhigh= ZYL1+100e-3
   pylow= -ZYL1,     pyhigh= ZYL1
   pzlow= 2e-3,     pzhigh= 398e-3
   pzhigh= 1.59

   spacing= STPSZE

#########################################################################
-material
  material= 3, type= electric

-brick
  #
  # Fill the universe with metal.
  #
  material= 1, name= Background
     volume= (-INF,INF, -INF,INF, -INF,INF)
  doit
################################################################

-stlfile
   file= /usr/local/gd1/examples-from-the-manual/DP_VAC_Xapa.stl
   material= 0, whichcells= all, taboo= none
    #
    # The stl-file does not describe the volume filled with vacuum,
    # but the metal body.
    # To model the vacuum part, we use a trick:
    # We say that the number of triangles that are to be crossed
    # when going from inside the body to outside of the body
    # (to infinity) has to be a multiple of two.
    #
   nboundaries= 2

# define(UA, 1)
 define(UA, 2)
# define(UA, 3)
   if (UA == 2) then
      originprime = ( 0, 0, -6093e-3 )
      xprimedirection= ( 0, 0, 1 )
      yprimedirection= ( 1, 0, 0 ) # axis= +y
   elseif (UA == 1) then
      originprime = ( 0, -6093e-3, 0 )
      xprimedirection= ( 0, 1, 0 )
      yprimedirection= ( 1, 0, 0 ) # axis= -z
   else
      originprime=  ( 0, -6093e-3, 0 )
      xprimedirection= ( 0, 1, 0 )
      yprimedirection= ( 0, 0, 1 ) # axix= +x
   end if
   xscale= 1e-3
   yscale= 1e-3
   zscale= 1e-3
   if (1) then
      #
      # The geometry is a dipole chamber.
      # The charge in reality travels over a circular path.
      # As GdfidL can only compute wakepotentials when the
      # exciting charge and the witness charges are traveling
      # in + z-direction, we de-bend the geometry such that the
      # originaly arc-like beampipe is straight.
      #
      debend= yes
      if (UA == 2) then
         uaxis= y # (u,v,w) = (y,z,x)
         radius= 8.25
         v0= 0
         w0= -8.25
      elseif (UA == 1) then
         uaxis= z # (u,v,w) = (z,x,y)
         radius= 8.25
         v0= -8.25
         w0= 0
      else
         uaxis= x # (u,v,w)= (x,y,z)
         radius= 8.25
         v0= 0
         w0= -8.25
      end if
   end if
   
##   show= yes
   doit

#########################################################################
-volumeplot
      scale= 4
  roty= 90
  bbylow= 0.
      doit
# end

##########################################################################

#
# Wake-Parameters.
#
 -fdtd
  -ports
    name= lower_end, plane= zlow,   modes= 0, npml= 20, doit
    name= upper_end, plane= zhigh,  modes= 0, npml= 20, doit

 -lcharge 
    xpos    = OFFSET
    ypos    = 0
    charge  = 1e-12
    sigma   = SIGMA
    shigh   = 12*SIGMA +TRAILER
##    showdata= yes

# -fdtd, doit
Figure 1.26: A Discretisation of a Dipole Chamber. The Arc-like Beam-Pipe has been de-bended to allow the Computation of Wakepotentials.
\begin{figure}\centerline{ \psfig{figure=stl-example-debend.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=} }
\end{figure}


-geofunction: Analytic Description

This Section allows the Specification of the Parameters of an analytic Function which describes a Body. The analytic Function must be programmed in some external Binary which is loaded at run Time.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -geofunction                                                       #
 ##############################################################################
 # material  =  1                                                             #
 # whichcells= all, taboo= none                                               #
 # fdescriptionsubroutine=-none-
 # a1= 0.0,                             b1= 0.0                               #
 # a2= 0.0,                             b2= 0.0                               #
 # a3= 0.0,                             b3= 0.0                               #
 # a4= 0.0,                             b4= 0.0                               #
 # a5= 0.0,                             b5= 0.0                               #
 # a6= 0.0,                             b6= 0.0                               #
 # a7= 0.0,                             b7= 0.0                               #
 # a8= 0.0,                             b8= 0.0                               #
 # a9= 0.0,                             b9= 0.0                               #
 ##############################################################################
 # doit, return, help                                                         #
 ##############################################################################


Example
 # /usr/local/gd1/examples-from-the-manual/geofunction-example.gdf
 -general
    outfile= /tmp/UserName/geofunction
    scratch= /tmp/UserName/scratch

 -mesh
    perfectmesh= yes
    spacing= 0.1e-3
    pxlow= -3e-3, pxhigh= 3e-3
    pylow= -3e-3, pyhigh= 3e-3
    pzlow= 0, pzhigh= 5e-3
  czlow= magnetic, czhigh= magnetic
  pylow= 0, cylow= magnetic

 -brick
    material= 0, whichcells= all, taboo= none
    volume= ( -INF,INF, -INF,INF, -INF,INF )
    doit

    # Fill Parts of the Universe which shall later be described
    # by the 'geofunction'.
 -brick
    material= 10
    xlow= -1e-3, xhigh= 1e-3
    ylow= -INF, yhigh= INF
    zlow= -INF, zhigh= INF
  sloppy= yes
    doit
    xlow= -INF, xhigh= INF
    ylow= -1e-3, yhigh= 1e-3
    doit
  sloppy= no

 system( ifort -O3 -fPIC -auto -c \
            ./PointInsideFunction.f90 )
 system( gcc -fPIC -shared -Wl,-soname,PointInsideFunction.so \
           -o /tmp/PointInsideFunction.so PointInsideFunction.o )
    
 define(VAL, 1)
 -geofunction
    #
    # If this Inputfile is to be used with PVM/MPI,
    # each Task will try to load the Shared Object.
    # We assume here, /tmp/ is accessible by each Task.
    #
    fdescriptionsubroutine= /tmp/PointInsideFunction.so
    material= 3, whichcells= 10, taboo= none
## whichcells= all
    a1= 1              # Key
    a2= 1825283, a3= 692618, a4= 0.7 * 3.28e-3, a5= 0,
    a8= 1              # Key: Pot gt val
    a9= VAL            # Aequipotential-Value
   doit

    material= 4
    a8= -1              # Key Pot lt val
    a9= -VAL            # Aequipotential-Value
   doit

 -brick, material= 0, whichcells= 10
         volume= ( -INF,INF, -INF,INF, -INF,INF ), doit

 -material
    material= 3, type= electric
    material= 4, type= electric
    material= 10, type= electric

 -volumeplot, scale= 4, eyepos ( -1, -2, 3 ), doit

 -eigenvalues
    estimation= 100e9
#    doit

The Sourcecode PointInsideFunction.f90:

 
 SUBROUTINE fgeosub( Point, A, In )
 
 DOUBLE PRECISION, INTENT(IN), DIMENSION(1:3)  :: Point
 DOUBLE PRECISION, INTENT(IN), DIMENSION(1:20) :: A
 INTEGER,          INTENT(INOUT) :: In
 
 DOUBLE PRECISION :: Pi, Phi, P
 DOUBLE PRECISION :: x, y, z, z0, z1, zz, az, rmz, oodL, a01, a10

    Pi= 4*ATAN(1.0d0)

    IF (NINT(A(1)) == 1) THEN
       x= Point(1)
       y= Point(2)
       z= Point(3)
       P = A(4)+A(5)*z
       Phi= A(2)*(x**2-y**2) &
          + A(3)*(x**2+y**2+(P/Pi)**2)*wbCos(2*Pi*z/P)

       IF (A(8) > 0) THEN
          IF (Phi > A(9)) THEN
             In= 1
          ELSE
             In= 0
          END IF
       ELSE
          IF (Phi < A(9)) THEN
             In= 1
          ELSE
             In= 0
          END IF
       END IF
    ELSE IF (NINT(A(1)) == 2) THEN
 
! a1,a2,a3,a4,a5,a6,a7,a8,a9 => A( 1: 9)
! b1,b2,b3,b4,b5,b6,b7,b8,b9 => A(11:19)
 
!      Period described as a Polinomial
!      Amplitude described as a Polinomial
 
       x= Point(1)
       y= Point(2)
       z= Point(3)
       z0= A(2)
       z1= A(3)
!c      write (*,*) ' a(1:9):', a(1:9)
!c      write (*,*) ' a(11:19):', a(11:19)
       IF ((z < z0) .OR. (z > z1)) THEN
          In= 0
          RETURN
       END IF
       zz= z-z0
       oodL= 1 / (z1-z0)
       P = A(4) +zz*(A(5)-A(4))*oodL
       az= A(6) +zz*(A(7)-A(6))*oodL
       rmz= A(8)+zz*(A(9)-A(8))*oodL
       a10= (rmz**2-1) &
          / (2*(rmz*az)**2+(rmz**2+1)*(P/Pi)**2)
       a01= ((rmz**2+1)*az**2+2*(P/Pi)**2) &
          / (2*(rmz*az)**2+(rmz**2+1)*(P/Pi)**2) &
          / az**2
       Phi= a01*(x**2-y**2) &
          + a10*(x**2+y**2+(P/Pi)**2)*wbCos(2*Pi*zz/P)

       IF (A(11) > 0) THEN
          IF (Phi > A(12)) THEN
             In= 1
          ELSE
             In= 0
          END IF
       ELSE
          IF (Phi < A(12)) THEN
             In= 1
          ELSE
             In= 0
          END IF
       END IF
 
    ELSE
       In= 0
    END IF

 CONTAINS

    DOUBLE PRECISION FUNCTION wbCos( x )
    DOUBLE PRECISION, INTENT(IN) :: x

    DOUBLE PRECISION :: xx
    INTEGER :: iSign

       xx= ABS(x)
       DO WHILE (xx > 2*Pi)
          xx= xx - 2*Pi
       END DO

       IF (xx > Pi) THEN
          iSign= -1
          xx= xx - Pi
       ELSE
          iSign= 1
       END IF

       IF (xx > Pi/2) THEN
          iSign= -iSign
          xx= Pi - xx
       END IF


       wbCos= iSign* &
           (1 - xx**2/2 + xx**4/(2*3*4) - xx**6 / (2.*3.*4.*5.*6.) )
       !!       + xx**8 / (2.*3.*4.*5.*6.*7.*8.) &
       !!       - xx**10 / (2.d0*3.d0*4.d0*5.d0*6.d0*7.d0*8.d0*9.d0*10.d0) )

    END FUNCTION wbCos

 END SUBROUTINE fgeosub
Figure 1.27: Part of a RF-Quadrupole, where the Electrodes are described by an Algorithm.
\begin{figure}\begin{center}\quad \quad
\psfig{figure=geofunction-example.ps,wi...
...m,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
\end{center}
\end{figure}


-transform: Rotations, Translations

All geometric Items are transformed by a Transformation Matrix. Initially, that Transformation Matrix is the unity Matrix. The Specification of a Translation or Rotation modifies the transformation Matrix accordingly. The Transformations are applied one after the other.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -transform                                                        #
 ##############################################################################
 # -translate                                                                 #
 # -rotate                                                                    #
 #                                                                            #
 # Matrix:                                                                    #
 #     1.00000000    ,    0.00000000    ,    0.00000000    ,    0.00000000    #
 #     0.00000000    ,    1.00000000    ,    0.00000000    ,    0.00000000    #
 #     0.00000000    ,    0.00000000    ,    1.00000000    ,    0.00000000    #
 #     0.00000000    ,    0.00000000    ,    0.00000000    ,    1.00000000    #
 ##############################################################################
 # reset, ?, return, help                                                     #
 ##############################################################################

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -translate                                                        #
 ##############################################################################
 # offset= ( 0.0, 0.0, 0.0 )                                                  #
 #                                                                            #
 ##############################################################################
 # doit, ?, return, help                                                      #
 ##############################################################################

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -rotate                                                           #
 ##############################################################################
 # axis= ( 0.0, 0.0, 1.0 )                                                    #
 # angle= 90.0                                                                #
 # Matrix:                                                                    #
 #     1.00000000    ,    0.00000000    ,    0.00000000    ,    0.00000000    #
 #     0.00000000    ,    1.00000000    ,    0.00000000    ,    0.00000000    #
 #     0.00000000    ,    0.00000000    ,    1.00000000    ,    0.00000000    #
 #     0.00000000    ,    0.00000000    ,    0.00000000    ,    1.00000000    #
 ##############################################################################
 # doit, ?, return, help                                                      #
 ##############################################################################


Example

 -general
     outfile= /tmp/UserName/bla
     scratch= /tmp/UserName/scratch

 -mesh
     spacing= 0.01
     pxlow= -0.3, pxhigh= 0.3
     pylow= -0.3, pyhigh= 0.3
     pzlow= -0.1, pzhigh= 0.4

 -transform, reset

 -brick
     material= 1
     volume= ( -BIG,BIG, -BIG,BIG, -BIG,BIG )
     doit

 #
 # Translate all subsequent Items by (0.1, 0, 0).
 #
 -translate, offset= ( 1/10, 0, 0 ), doit

 -brick
    material= 0
    name= brick1
    xlow= 0, xhigh= 0.1
    ylow= 0, yhigh= 0.2
    zlow= 0, zhigh= 0.3
    doit

 #
 # Additionally to the initial Translation,
 # rotate by 90 Degrees around the (0,0,1)-Axis,
 # then rotate 20 Degrees around the (0,1,0)-Axis,
 #
 -rotate,
     axis= ( 0, 0, 1 ), angle= 90, doit
     axis= ( 0, 1, 1 ), angle= 20, doit

 #
 # Next Brick, same Parameters as the first One,
 # but additionally to the Translation now also rotated.
 #
 -brick, name= brick2, doit

 #
 # Next Rotation, same Parameters.
 # Because the Rotations etc are all performed,
 # subsequent Items are translated once and rotated four times.
 #
 -rotate,
     axis= ( 0, 0, 1 ), angle= 90, doit
     axis= ( 0, 1, 1 ), angle= 20, doit

 # Next Brick, same Parameters as the previous One.
 -brick, name= brick3, doit

 -volumeplot, doit
Figure 1.28: Discretisation of some Bricks, translated and rotated.
\begin{figure}\centerline{
\psfig{figure=Transformierte-Bricks.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}


-volumeplot: Shows the resulting Mesh

This Section enables the Generation of the Grid and shows the discretised Material Boundaries as generated from the geometric Primitives specified so far.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -volumeplot                                                       #
 ##############################################################################
 # onlyplotfile  = no         -- Do not display Plot                          #
 # showpartition = no         -- Show MPP-Partioning                          #
 # showlines = no                                                             #
 # text     = yes                                                             #
 # scale    = 1.80                                                            #
 # 2dplotopts = -geometry 690x560+10+10                                       #
 #   plotopts = -geometry 800x668+310+40 -noclip                              #
 # eyeposition  = ( -1.0, -2.30, 0.50 )                                       #
 # bbxlow =    -1.0000e+30, bbylow =    -1.0000e+30, bbzlow =    -1.0000e+30  #
 # bbxhigh=     1.0000e+30, bbyhigh=     1.0000e+30, bbzhigh=     1.0000e+30  #
 # rotx   =     0.0000    , roty   =     0.0000    , rotz   =     0.0000      #
 #                                                                            #
 ##############################################################################
 # doit, ?, return, help                                                      #
 ##############################################################################


Example The following shows the Material Distribution of a Waveguide Twist again, this Time, the Parameter bbyhigh is specified such, that only the Material Boundaries behind the Plane y=0 are shown.
 include(/usr/local/gd1/examples-from-the-manual/ggcylinder-twisted.gdf)
 -volumeplot
    eyeposition= ( 1, 2, 1.3 )
    scale= 4.5
 bbyhigh= 0
    doit
Figure 1.29: A twisted Waveguide. Only the Material Boundaries behind the Plane y=0 are shown.
\begin{figure}\centerline{
\psfig{figure=volumeplot-bbzhigh-eq-ZZ.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}


Example The following shows the Material Distribution of a Waveguide Twist again, this time, the Parameter roty is specified nonzero.

 include(/usr/local/gd1/examples-from-the-manual/ggcylinder-twisted.gdf)
 -volumeplot
    eyeposition= ( 1, 2, 1.3 )
    scale= 4.5
 roty= 20
    doit
Figure 1.30: A twisted Waveguide. The Plot is rotated slightly around the y-Axis.
\begin{figure}\centerline{
\psfig{figure=volumeplot-roty-eq-YY.ps,width=18cm,bbllx=-2pt,bblly=-2pt,bburx=716pt,bbury=556pt,clip=}
}\end{figure}


-cutplot: Shows the resulting Mesh in a selected Meshplane

This Section enables the Generation of the Grid and shows only in a selected gridplane the discretised Material Boundaries as generated from the geometric Primitives specified so far.

A similar Effect can be achieved with the Section -volumeplot with the aid of the Parameters bb?low, bb?high.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -cutplot                                                          #
 ##############################################################################
 # onlyplotfile= no                     -- don't display Plot                 #
 # draw  = both                         -- both | approximated | input        #
 # grid  = yes                          -- yes|no                             #
 # normal= z                            -- Plane Normal of the Cut-Plane      #
 # cutat = undefined                    -- The Coordinate of the Cut-Plane    #
 #                                                                            #
 # plotopts= -geometry 800x668+310+40 -noclip                                 #
 # eyeposition= ( -1.0, -2.30, 0.50 )                                         #
 ##############################################################################
 # doit, ?, return, help                                                      #
 ##############################################################################

Solver sections: Eigenvalues and driven Time Domain Problems


-eigenvalues

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -eigenvalues                                                       #
 ##############################################################################
 # solutions    = 15                                                          #
 # estimation   = undefined                                                   #
 # storeallmodes= no                                                          #
 #    flowsave  = 0.0                                                         #
 #    fhighsave = 1.0e+30                                                     #
 # passes       =  2                                                          #
 # pfac2        = 1.0e-3                                                      #
 # lossy          = no                  -- Lossy or dispersive Computation    #
 #     flowsearch = undefined           -- Edges of the search Region...      #
 #     fhighsearch= undefined           -- ...when "lossy= yes"               #
 #   -ports                             -- ...when "lossy= yes"               #
 #   -linitialfields                    -- ...when "lossy= yes"               #
 #                                                                            #
 #                                                                            #
 # compressed   = no                    -- Minimal RAM, more CPU and IO Time  #
 ##############################################################################
 # return, doit, help, ?                                                      #
 ##############################################################################


Example The following specifies that we want to compute with 15 Basisvectors, we want to perform two Passes to search for the Eigenvalues, and we estimate that the highest resonant Frequency of the 15 to be found will be about 1.3 GHz. The final doit starts the Eigenvalue Computation.
 -eigenvalues
   solutions= 15
   passes= 2
   estimation= 1.3e9
   doit


-fdtd: Compute time dependent Fields

This Section shows the Subsections that only make Sense for Time Domain Computations. The "doit" in this Section starts the Time Domain Computation.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -fdtd                                                             #
 ##############################################################################
 # -ports                     -- Absorbing Boundary Conditions.               #
 # -pexcitation               -- Excited Port Modes.                          #
 # -lcharges                  -- One or more relativistic Line Charges.       #
 # -windowwake                -- Wakes in a moving Mesh Window.               #
 # -clouds          -- not yet finished.                                      #
 # -linitialfields            -- Loads initial Fields at t=0.                 #
 # -voltages                  -- Enforce Voltages between Points.             #
 # -decaytime                 -- z-dependent Damping.                         #
 # -time                      -- Timestep etc.                                #
 # -storefieldsat             -- When to store Fields.                        #
 # -fexport                   -- When to store Fields.                        #
 # -smonitor                  -- What Flux Quantities to store.               #
 # -fmonitor                  -- What Field Quantities to store.              #
 # -pmonitor                  -- What Power Quantities to store.              #
 #                                                                            #
 # hfdtd= yes                 -- Use higher Order Curl-Operators.             #
 ##############################################################################
 # doit, ?, return, help                                                      #
 ##############################################################################


-fdtd,-ports/ -eigenvalues,-ports

The Section -time,-ports is the same as -eigenvalues,-ports.

A "Port" is a Part of the Border of the computational Volume that shall be treated as an infinitely long Waveguide. In this Section you specify the Location of Ports. You also specify the Number of Modes whose time Amplitudes shall be written to File.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -ports                                                            #
 ##############################################################################
 # name  = noname-001                                                         #
 # plane = xlow                                                               #
 # modes = 1                                                                  #
 #(pxlow=      -1.0e+30    , pxhigh=       1.0e+30    ) Ignored for plane=xlow
 # pylow=      -1.0e+30    , pyhigh=       1.0e+30                            #
 # pzlow=      -1.0e+30    , pzhigh=       1.0e+30                            #
 # epsmaximum= 2.0                                                            #
 # muemaximum= 1.0                                                            #
 # npml      = 40                  -- No of PML-Planes                        #
 # dampn     = 50.0e-3             -- Damping factor in last Plane            #
 # enforcemesh= yes                -- Enforce translational invariant Mesh    #
 ##############################################################################
 # doit, list, ?, return, help                                                #
 ##############################################################################


Example The following specifies that we want to have attached four Ports: Two are at the lower x-Boundary, the Names are xlow1, xlow2. Two Ports are at the upper x-Boundary of the computational Volume, the Names are xhigh1, xhigh2. The Ports at the same Boundary are distinguished by their pzlow, pzhigh Parameters.
-fdtd
  -ports
     name= xlow1,  plane= xlow , pzlow= 0,  modes= 10, doit
     name= xhigh1, plane= xhigh, pzlow= 0,  modes= 2, doit
     name= xlow2,  plane= xlow , pzhigh= 0, modes= 2, doit
     name= xhigh2, plane= xhigh, pzhigh= 0, modes= 2, doit


-fdtd,-pexcitation: What Port-Mode shall be excited

Here you may specify what Port-Excitation shall be used. The Excitation can be a switched on Sine-signal, a Gaussian Pulse modulated with a Sine, or a user specified Signal.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -pexcitation                                                      #
 ##############################################################################
 # port  =  undefined                                                         #
 # mode  = 1                                                                  #
 # amplitude = 1.0                                                            #
 # phase     = 0.0                                                            #
 # frequency = undefined                                                      #
 # bandwidth = undefined                                                      #
 # risetime  = 0.0                                                            #
 # signalcommand= -none-                                                      #
 ##############################################################################
 # nextport, list, ?, return, help                                            #
 ##############################################################################


Example The following specifies that the fundamental Mode of the Port with Name InputPort shall be excited. Its Amplitude shall be '1', the Centerfrequency of the excited Pulse shall be 1.2 GHz, and the Bandwidth of the excited Pulse shall be 0.7 GHz.
 -fdtd,
    -pexcitation
        port= InputPort
        mode= 1
        amplitude= 1
        frequency= 1.2e+9
        bandwidth= 0.7e+9

Example The following specifies that the fundamental Mode of the Port with Name InputPort1 shall be excited. Its Amplitude shall be '1', the Frequency of the excited Signal shall be 1.2 GHz, and the Risetime until Steady State of the Excitation shall be 10 HF-Periods. In Addition, the fundamental Mode of the Port with Name InputPort2 shall be excited. Its Amplitude shall be '1'.
 -fdtd,
    -pexcitation
        port= InputPort1, mode= 1, amplitude= 1, phase= 0
        frequency= 1.2e9, risetime= 10 / 1.2e9
      nextport
        port= InputPort2, mode= 1, amplitude= 1, phase= 0


Example The following specifies that the fundamental Mode of the Port with Name InputPort shall be excited. The Portmodes Pattern shall be computed for a Frequency of 10 GHz, and the Signal of the Excitation shall be defined by an external Signal-command.

 -fdtd,
    -pexcitation
        port= InputPort
        mode= 1
        amplitude= 1
        frequency= 10e9
 #
 # Compile the Signalcommand.
 #
 system($F90 signal-command.f -o signal-command)
        signalcommand= ./signal-command
This is the Sourcefile signal-command.f:
      PROGRAM SignalCommand
      IMPLICIT DOUBLE PRECISION (a-h,o-z)

      Pi= 4*ATAN(1.0d0)
      Frequency= 10e9
      TRise= 10/Frequency
      TDecay= 20/Frequency
      THold= 50/Frequency
      READ (*,*) iTime1, iTime2, TimeStep
      READ (*,*) Beta, Alpha, DeltaZ
      DO iTime= iTime1, iTime2, 1
         ActualTime= iTime*TimeStep
         IF (ActualTime .LE. TRise) THEN
            Phi= ActualTime * Pi / TRise
            Factor= (1-COS(Phi))/2
         ELSE IF (ActualTime .LE. TRise+THold) THEN
            Factor= 1
         ELSE IF (ActualTime .LE. TRise+THold+TDecay) THEN
            Phi= (ActualTime - (TRise+THold)) * Pi / TDecay
            Factor= (1+COS(Phi))/2
         ELSE
            Factor= 0
         ENDIF
         Factor= Factor * TimeStep / DeltaZ
         WRITE (*,*) Factor*SIN(2*Pi*Frequency*ActualTime)
      ENDDO
      END PROGRAM SignalCommand

-fdtd,-lcharge: Properties of relativistic Line-Charges

In this Section one specifies the Properties of one or several relativistic Line-Charges. When computing with the conventional Scheme, i.e. not with the Windowwake Algorithm, one can specify up to 100 Linecharges, each with a different Charge, different Position, different Distribution and different Direction of Flight. When using the Windowwake Algorithm, all Charges must go in positive z-Direction, and they must have the same Shape. They may differ in their Positions and Charge. Once the Properties of a Linecharge are specified, one switches to the next Linecharge with the Command 'nextcharge'.

The standard Usage of this Section is to compute Wakepotentials. When a nonzero Charge is specified, and a Time Domain Computation is performed, the Wakepotentials are computed as the Potential that is seen by Witness Particles that are traveling in positive z-Direction. When the conventional Scheme is used, Fields and Port Amplitudes may be stored and monitored as well.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -lcharge                                                          #
 ##############################################################################
 # ----- Parameters of a Line Charge: ------                                  #
 # charge    =        0.0               -- [As]                               #
 # shape     = gaussian                 -- gaussian | triangular | table      #
 #    tablefile=  -none-
 #    xtable =        1.0               -- [m]                                #
 # sigma     =  undefined               -- [m]                                #
 # isigma    =  6                       -- Number of Sigmas to use.           #
 # xposition =        0.0               -- [m]                                #
 # yposition =        0.0               -- [m]                                #
 # direction = +z                       -- +z, -z                             #
 # soffset   =        0.0               -- [m]                                #
 # beta  =        1.0                   -- [1], quite a Hack, if not 1.       #
 # ----- Other Parameters: ------                                             #
 # shigh     =       auto               -- [m]                                #
 # showdata  = no                       -- ( yes | no )                       #
 # napoly    = yes                      -- ( yes | no )                       #
 #   naccuracy=      10.0e-6     -- wanted acc for poisson-eq in Napoly alg.  #
 #   ignoretem= yes                     -- should be "yes" for Wx, Wy         #
 ##############################################################################
 # ?, nextcharge, return, help                                                #
 ##############################################################################


Example The following specifies that we want to model a Linecharge travelling with the Speed of Light along the Axis (x,y)=(0,0). The total Charge of the Linecharge shall be 1 pC, and its Gaussian Width sigma shall be 1 mm. We are interested in s-Values up to 100 mm.
 -lcharge
    xpos= 0
    ypos= 0
    charge= 1e-12
    sigma= 1e-3

    shigh= 100e-3


Example An Example for a Table File describing a Charges Shape is given below.

# -lcharge
#    shape= table, tablefile= Bunch1.txt
#    xtable= 1e-6, charge= 1e-12
#
# Everything behind a '#' is ignored.
# Lines in the Tablefile may be empty, or they may
# contain two (or more) Numbers.
# The first Number is a Position, the next number is
# a relative Charge. What follows behind these two Numbers is ignored.
#
# bunch1 (linac entrance)
# s[microns]   No. of macro-particles
# ________________________________________________


0,      0
1       -1.32067
2       -1.10711
3       -0.894051
4       -0.6815
5       -0.469454
6       -0.25791
7       -0.046869
8       0.16367
9       0.373709
10       0.583247


Example An Example how to specify four Line-Charges that excite mostly quadrupole-Wakepotentials:

 define(CHARGE, 1e-12) define(SIGMA, 1e-3)
 define(RADIUS, SomeValue)

 define(RADIUSoSQRT2, RADIUS * (2**0.5) ) # Radius * Cos( 45 Degrees )
 -lcharge
         xposition=  RADIUSoSQRT2, yposition=  RADIUSoSQRT2
         charge= CHARGE, sigma= SIGMA, soffset= 0
      nextcharge
         xposition= -RADIUSoSQRT2, yposition=  RADIUSoSQRT2
         charge= -CHARGE, sigma= SIGMA, soffset= 0
      nextcharge
         xposition= -RADIUSoSQRT2, yposition= -RADIUSoSQRT2
         charge=  CHARGE, sigma= SIGMA, soffset= 0
      nextcharge
         xposition=  RADIUSoSQRT2, yposition= -RADIUSoSQRT2
         charge= -CHARGE, sigma= SIGMA, soffset= 0

Example
 # /usr/local/gd1/examples-from-the-manual/quadrupole.gdf
 #
 # This Device has two Planes of Symmetry.
 # These Planes of Symmetry are NOT used here.
 # Four Charges are specified such that
 # the excited Wakefields are mainly quadrupole Wakefields.

 -general,
     outfile= /tmp/UserName/bla
     scratch= /tmp/UserName/scratch

 define( A , 2*0.038 )
 define( A2, 2*0.016 ) # x-Width

 define( B , 2*0.010 ) # y-Width
 define( B2, 2*0.002 )

 define(RANGE, 0.01)

 define(STPSZE, B/100 )
 -mesh
     spacing= STPSZE
     pxlow= -(A/2+STPSZE), pxhigh= (A/2+STPSZE), cxlow= ele, cxhigh= ele
     pylow= -(B/2+STPSZE), pyhigh= (B/2+STPSZE), cylow= ele, cyhigh= ele
     pzlow= -0.02, pzhigh= 0.02

 ##########
 -material, material= 3, type= electric

 # Fill the Universe with Metal:
 -brick
     material= 3
         xlow= -INF, xhigh= INF
         ylow= -INF, yhigh= INF
         zlow= -INF, zhigh= INF
     doit

 do ii= 1, 2

    # The Device also has a Plane of Symmetry at z=0.
    # Half of the Device is modeled here, and that Half
    # is rotated and translated to the wanted Position
    # and Orientation.

    -transform, reset
    if (ii == 1) then
       -translate, offset= ( 0, 0, -(0.01+RANGE+0.005/2) ), doit
    else
       -rotate, axis= ( 0, 1, 0 ), angle= 180, doit
       -translate, offset= ( 0, 0,  0.01+RANGE+0.005/2 ), doit
    end if

    -ggcylinder
        material= 0
        xprime= ( 1, 0, 0 )
        yprime= ( 0, 1, 0 )
        xslope= 0, yslope= 0  # Re-Set to the Default Values
        xscale= 1, yscale= 1  # Re-Set to the Default Values

        clear
           point= (  0   , -B /2 )
           point= (  A2/2, -B /2 )
           point= (  A /2, -B2/2 )
           point= (  A /2,  B2/2 )
           point= (  A2/2,  B /2 )
           point= ( -A2/2,  B /2 )
           point= ( -A /2,  B2/2 )
           point= ( -A /2, -B2/2 )
           point= ( -A2/2, -B /2 )
     show= later

         origin= ( 0, 0, 0 )
         range= ( 0, 0.01 )
         doit   # The wide and straight Part.

 # Same Cross-section, linear slopes:
         xslope= (0.033/0.038-1)/RANGE
         yslope= (0.011/0.012-1)/RANGE
         origin= ( 0, 0, 0.01 )
         range= ( 0, RANGE )
    show= later
         doit  # The tapered Part.

 # Same Cross-section, scaled
         xslope= 0, yslope= 0
         xscale= 0.033/0.038, yscale= 0.011/0.012
         origin= ( 0, 0, 0.01+RANGE )
         range= ( 0, 0.005 )
    if (ii == 1) then
       show= later
    else
       show= all
    end if
         doit  # The narrow and straight Part.
 end do

 -volumeplot, doit
 -mesh, perfectmesh= no
 ##########
 -ports
      name= Lower, plane= zlow, modes= 0, doit
      name= Upper, plane= zhigh, modes= 0, doit
 ##########
 define(CHARGE, 1e-12) define(SIGMA, 1e-3)
 define(RADIUS, B/10)
 define(RADIUSoSQRT2, RADIUS * (2**0.5) ) # Radius * Cos( 45 Degrees )
 -lcharge
         xposition=  RADIUSoSQRT2, yposition=  RADIUSoSQRT2
         charge= CHARGE, sigma= SIGMA, soffset= 0
      nextcharge
         xposition= -RADIUSoSQRT2, yposition=  RADIUSoSQRT2
         charge= -CHARGE, sigma= SIGMA, soffset= 0
      nextcharge
         xposition= -RADIUSoSQRT2, yposition= -RADIUSoSQRT2
         charge=  CHARGE, sigma= SIGMA, soffset= 0
      nextcharge
         xposition=  RADIUSoSQRT2, yposition= -RADIUSoSQRT2
         charge= -CHARGE, sigma= SIGMA, soffset= 0

    shigh= 10 * SIGMA

 -fdtd, doit
Figure 1.31: A Device with three Planes of Symmetry. The Planes of Symmetry at x=0 and y= 0 could be used with a Computation with Linecharges. This is not used here. Four Charges are specified such that mainly quadrupole-Wakefields are excited.
\begin{figure}\begin{center}% \quad \quad
\psfig{figure=Quadrupole.ps,width=18cm,bbllx=202pt,bblly=174pt,bburx=503pt,bbury=372pt,clip=}
\end{center}
\end{figure}
Figure 1.32: The Wakepotential as a Function of (x,y) near s=0. The Input for gd1.pp was: -gen, inf @last, -wakes, watsi= 0, doit
\begin{figure}\begin{center}\quad \quad
\psfig{figure=QuadrupoleWat0.ps,width=18cm,bbllx=60pt,bblly=160pt,bburx=718pt,bbury=422pt,clip=}
\end{center}
\end{figure}


-fdtd,-windowwake: Wakepotential in a moving computational Window

Here you specify the Properties of a computational Window which flies with the Velocity of Light synchronously with the exciting Charges.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -windowwake                                                       #
 ##############################################################################
 # strangsplitting= yes                                                       #
 # fdtdorder= 31              -- What Order of FDTD Algorithm to take [1,31]  #
 # periodic  = no             -- Assume periodic Geometry.                    #
 #    nperiods=   100         -- Maximum Number of Periods to consider.       #
 #    modstore=    10         -- Store Wakepotentials after simulating        #
 #                            --   Multiples of modstore*(pzhigh-pzlow).      #
 # __xpartition= no           -- PVM/MPI: Enforce Partitioning in x only.     #
 ##############################################################################
 # doit, ?, return, help                                                      #
 ##############################################################################


Note: The Parameters of the exciting Linecharge are taken from the section -lcharge. The moving computational Window has a Length of isigma*sigma + shigh. The used Grid-Spacing in z is the Minimum of all the x-Spacings and y-Spacings and, if the specified "zspacing" in Section "-mesh" is smaller, then that zspacing is used.

Napoly-like Integration is performed, and cannot be switched off.

The Memory Requirement is proportional to the Length of the moving computational Window, i.e. proportional to isigma*sigma + shigh. One should not specify a large Value for shigh, in particular not longer than the structure Length, otherwise a conventional Wakepotential Computation is more economic.

The CPU Requirement is proportional to the Length of the moving Window times the Length over which the moving Window must travel. That Length is the z-Extension of the Structure plus the Length of the Window. The CPU Requirement is proportional to (isigma*sigma + shigh) * (pzhigh-pzlow + isigma*sigma + shigh). Any specified Port is ignored. The x- and y-Extension of the computational Volume must be specified large enough that Reflections from the x- and y-Borders cannot change the Wakepotentials. E.g. Waveguides going in x- or y-Direction should be modeled with a Length of "shigh".

The Losses of dielectric Materials are ignored.

Only Fields specified via fexport will be exported.

The only other Result is the Wakepotential.


Example The following specifies that we want to compute the Wakepotential of a Linecharge travelling with the Speed of Light along the axis (x,y)=(0,0). The total charge of the Linecharge shall be 1 pC, and its Gaussian Width Sigma shall be 1 mm. We are interested in s-Values up to 20 mm.

 -lcharge
    xpos= 0, ypos= 0
    charge= 1e-12
    sigma= 1e-3
    shigh= 20e-3
 -windowwake
    doit


-fdtd,-clouds: Properties of nonrelativistic Clouds of Charge

This Section enables the computation with nonrelativistic Cloud Charges. As of today (October 2004) this PIC Computation is not yet fully finished. Since the planned Computations are not yet fully implemented, we do not even document the Usage of what is available. What is available is the Ejection of Clouds of Charge, the Computation of the induced electromagnetic Fields of these Charges, and the integration of the Lorentz-Forces on these Clouds.

If a 'Particle in Cell' Computation is badly needed, contact Warner Bruns Field Computations. It might be that by the Date that you read this, what you need is already available.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -clouds                                                           #
 ##############################################################################
 # box        = no                                                            #
 #   fraction = 0.950                                                         #
 #   bverbose = no                                                            #
 # ejectioncommand= -none-                                                    #
 # ejectionsubroutine= -none-                                                 #
 #                                                                            #
 #                                                                            #
 ##############################################################################
 # ?, return, help                                                            #
 ##############################################################################


-fdtd,-linitialfields/ -eigenvalues,-linitialfields: Specifies the initial Fields

This Section enables the loading of initial Fields for a Time Domain Computation or a lossy Eigenvalue Computation. If no initial Fields are specified, the initial Fields will be assumed to be Zero for Time Domain Fields and random Fields for Eigenvalue Computations.

The initial Field is the Sum of the specified Fields.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -linitialfields                                                   #
 ##############################################################################
 # infile   = ./previous_outfile                                              #
 #    symbol   = e_1                                                          #
 #    quantity = e                                                            #
 #    solution = 1                                                            #
 #    factor   = 1.0                                                          #
 #    torealpart= yes                                                         #
 #    static   = no                                                           #
 #    brz      = no                                                           #
 #      xmirror= none                                                         #
 #      ymirror= none                                                         #
 # abstatic = 0.0                                                             #
 # nbstatic = ( 0.0, 0.0, 1.0 )                                               #
 ##############################################################################
 # doit, ?, return, end, help                                                 #
 ##############################################################################


Example The following specifies that we want to use the Grid of a previous Computation, that we want to load the electric Field of the first Mode of that same previous Computation with a Factor of '1'. In Addition, we want to load the magnetic Field of the same Mode with an Amplitude of '-1'. If the two Fields come from a resonant Field Computation, this has the Effect of loading the Mode with a Phase of -45 Degrees.
 #
 # As the Filename in two Places better be the same,
 # We define the Files Name as a Variable.
 #
 sdefine( INFILE, /tmp/UserName/resonant-computation )
  -lgeometry
     infile= INFILE
  -linitialfields
     infile= INFILE
     symbol= e_1, factor=  1, doit
     symbol= h_1, factor= -1, doit


-fdtd,-voltages: Voltage Sources between selected Points

During a Time Domain Computation (with a static Mesh, i.e. not windowwake), Voltages along Paths can be specified and measured. The recorded Data can by analysed by gd1.pp's -voltages section.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -voltages                                                         #
 ##############################################################################
 # startpoint  = ( 0.0, 0.0, 0.0 )                                            #
 # endpoint    = ( 0.0, 0.0, 0.0 )                                            #
 # resistance  = 0.10                   -- [Ohm]                              #
 # inductance  = 0.0                    -- [Henry]                            #
 # amplitude   = undefined              -- [V]                                #
 # phase       = 0.0                    -- [Degs]                             #
 # frequency   = undefined              -- [1/s]                              #
 # bandwidth   = undefined              -- [1/s]                              #
 # risetime    = undefined              -- [s]                                #
 # logcurrent  = yes                                                          #
 # name        = noname-001                                                   #
 ##############################################################################
 # doit, ?, list, return, help                                                #
 ##############################################################################

If Voltage Sources are specified, the electric Field Strength between the Startpoint and Endpoint is measured while the Time Domain Computation is running. The Difference between the specified Voltage and the so measured Voltage is multplied by the Resistance of the Voltage Source. That Value is used as Current which is enforced to flow between the starting Point and Endpoint. The Current is low pass filtered with a time Constant given by $\tau=R/L$.

The Values of the wanted Voltage, the measured Voltage and the Current can be inspected in the Postprocessor.

No Example yet.


-fdtd,-decaytime: Z-dependent damping Factor

During a Time Domain Computation (with a static Mesh, i.e. not windowwake), the Fields can be damped with a z-dependent damping Factor.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -decaytime                                                         #
 ##############################################################################
 ## syntax:                                                                   #
 #  point= (Z_i, Tau_i)                                                       #
 ##############################################################################
 # clear, show, doit, ?, return, help                                         #
 ##############################################################################


Example

 -fdtd
    define(FREQ, 12e9)
    -decaytime
       clear
       point= ( -INF, 6000 / (@pi*FREQ) )
       point= ( Zmin, 6880 / (@pi*FREQ) )
       point= ( Zmax, 6580 / (@pi*FREQ) )
       point= (  INF, 6000 / (@pi*FREQ) )
      # show
       doit


-fdtd,-time: minimum / maximum Time, when to Store

In this Section one specifies the Time Parameters of a Time Domain Computation. Up to what Time to simulate, when to stop etc.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -time                                                              #
 ##############################################################################
 # firstsaved    = undefined                                                  #
 # lastsaved     = undefined                                                  #
 # distancesaved = undefined                                                  #
 # tminimum      = undefined                                                  #
 # tmaximum      = undefined                                                  #
 # decaytime =       1.0e+30                                                  #
 ##############################################################################
 # amptresh =       3.0e-3                                                    #
 # dtsafety =       0.80                                                      #
 # ndt      = auto                                                            #
 # ___stopafter=       1.0e+30          -- Force Stop after that Time.        #
 # ___evmax    = undefined              -- Dangerous.                         #
 # ___dt       = undefined              -- Dangerous.                         #
 ##############################################################################
 # return, help, ?                                                            #
 ##############################################################################


Example The following specifies that we want to simulate a minimum Timespan of 100 Periods of a Frequency of 1 GHz. We are absolutely shure that after a Timespan of 1000 Periods the Fields have decayed sufficiently, and we want to store the Fields between 10 Periods and 20 Periods, in a Distance of 1/2 Period.
  define(FREQ, 1e9)
  tmin=  100/FREQ, tmax= 1000/FREQ
  firstsaved= 10/FREQ, lastsaved=  20/FREQ
  distance=   1/2/FREQ


-fdtd,-storefieldsat: When to Store

Selected Fields can be stored at selected Times. This Section triggers the writing of full Fields. If you want to monitor selected Components, or selected Fluxes, use -fmonitor or -smonitor.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -storefieldsat                                                    #
 ##############################################################################
 # name  = noname-0001                                                        #
 # whattosave= both                     -- e-fields, h-fields, both, clouds,  #
 #                                      --     jimpedance                     #
 # firstsaved   = undefined                                                   #
 # lastsaved    = undefined                                                   #
 # distancesaved= undefined                                                   #
 ##############################################################################
 # doit, list, ?, return, help                                                #
 ##############################################################################


Example The following specifies that we want to store both the electric and magnetic Fields in the Timespan of 10 Periods to 12 Periods. The Distance shall be 0.1 periods. In the Timespan between 20 Periods and 30 Periods we want to store only the electric Field. The Distance between the saved fields shall be a quarter Period.
 define(FREQ, 1e9)

 -fdtd
    -storefieldsat
      name= a, what= both
         firstsaved= 10/FREQ
         lastsaved=  12/FREQ
         distance=   0.1/FREQ
      doit

      name= b, what= e-fields
         firstsaved= 20/FREQ
         lastsaved=  30/FREQ
         distance=   0.25/FREQ
      doit

Example The following specifies that we want to store the electric Fields every 100 HF-Periods. Every 100 HF-Periods the fields shall be stored with a Time Density of 1/8 Period.
 define(FREQ, 1e9)

 -fdtd
    -storefieldsat
      do ii= 100, 1000, 100
         #
         # This 'name= a-ii' gets expanded to eg. 'name= a-100'
         #
         name= a-ii, what= e-fields
            firstsaved=  ii       /FREQ
            lastsaved=  (ii+1+1/8)/FREQ
            distance=   1/8/FREQ
         doit
      enddo


-fdtd,-fexport: Text-File Export of selected Fields at selected Times

During a Time Domain Computation (also windowwake), the Fields can be stored at selected Times. The written Files can be imported by other Programs, or they can be used to create gif-Files and then mpeg-Files.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -fexport                                                          #
 ##############################################################################
 # outfile= noname-0001
 # whattosave= e                        -- e-fields, h-fields, honmat         #
 # firstsaved   = undefined                                                   #
 # lastsaved    = undefined                                                   #
 # distancesaved= undefined                                                   #
 # bbxlow  =    -1.0000e+30, bbylow =    -1.0000e+30, bbzlow =    -1.0000e+30 #
 # bbxhigh =     1.0000e+30, bbyhigh=     1.0000e+30, bbzhigh=     1.0000e+30 #
 ##############################################################################
 # doit, ?, return, end, help                                                 #
 ##############################################################################

Example The following Inputfile is for performing a Wakepotential Computation with a moving Mesh Window. During the Time Domain Computation, the magnetic Fields on the Boundaries shall be exported as ASCII-Files.
 define(STPF, 0.5) define(NP, 4) define(RADIUS, 1+1) define(GAP, 0.5)
 define(PERIODE, 0.6) define(BEAMR, RADIUS/2) define(STPSZE, SIGMA/10/STPF)

 define(DRADIUS, 2*STPSZE )
 define( ZLOW, -(NP*PERIODE+BEAMR)/2 )
 define( ZHIGH, (NP*PERIODE+BEAMR)/2 )
 -general
    outfile= /tmp/UserName/resultfile
    scratch= /tmp/UserName/scratch

 -mesh
    pxlow= -(RADIUS+DRADIUS), pxhigh= (RADIUS+DRADIUS)
    pylow= -(RADIUS+DRADIUS), pyhigh= (RADIUS+DRADIUS)
    pzlow= ZLOW, pzhigh= ZHIGH
 define(PZLOW, ZLOW)
 define(PZHIGH, ZHIGH)

   pxlow= 0, cxlow= mag
   pylow= 0, cylow= mag
   spacing= STPSZE

 ############
 -brick, material 1, volume (-INF, INF, -INF, INF, -INF, INF), doit

 do ip= -(NP-1)/2, (NP-1)/2, 1
    -gccylinder
       material= 0, radius= RADIUS, length= GAP
       origin= (0,0,ip*PERIODE-GAP/2)
       direction= (0,0,1)
 show= later
       doit
 enddo

 -gccylinder
    material= 0, radius= BEAMR, length= INF
    origin= ( 0, 0, -INF/2 ), direction= ( 0, 0, 1 )
# show= all
    doit

 #####
 -volumeplot, scale 1.8, plotopts -geometry 600x550+10+10, doit

 ####
  -lcharge
    sigma= 0.1, charge= 1e-12, xposition= 0, yposition= 0
    #
    # The following large Value for shigh is chosen for getting a Movie
    # of the full Structure.
    # 
    shigh= ZHIGH-ZLOW

   define(NDT, 0.5 * SIGMA / @clight)
 -fexport
    outfile= /tmp/UserName/H-onmat-
    what= honmat
    firstsaved= 1e-20, lastsaved= 1e20
    distancesaved= NDT
    bbxlow= 0, bbxhigh= INF
    bbylow= 0, bbyhigh= INF
    bbzlow= PZLOW+2*STPSZE, bbzhigh= PZHIGH-2*STPSZE
    doit

 -windowwake,
     doit
 end
#####################

The following is Input for gd1.pp to read the Files and create many gifs from them. From the gifs, a mpeg File is created and displayed.

# Input for gd1.pp:

 -3dmanygifs
   1stinfile= /tmp/UserName/H-onmat--000000001.gz
   outfiles= /tmp/UserName/absh-
## uptonfiles= 10
#   what= abs
   what= logabs
   uptonfiles= 1e9
   xrot= -30, yrot= 40
   doit

 system( mpeg_encode ./gdfidl.3dmanygifs-mpeg_encode-params )
 system( mpeg_play -dither color fexported.mpg )


-fdtd,-smonitor: Monitoring of scalar Quanitities

During a Time Domain Computation (with a static Mesh, i.e. not windowwake), the scalar Field Quantities can be monitored.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -smonitor                                                         #
 ##############################################################################
 # name  = noname-001                                                         #
 # whattosave= convectioncurrent                                              #
 #                       -- convectioncurrent, displacementcurrent            #
 #                       -- magneticflux                                      #
 #                       -- poyntingflux, ppclouds, pnclouds                  #
 #    normal= z, cutat= undefined                                             #
 #    xlow=      -1.0e+30    , xhigh=       1.0e+30                           #
 #    ylow=      -1.0e+30    , yhigh=       1.0e+30                           #
 #    zlow=      -1.0e+30    , zhigh=       1.0e+30                           #
 ##############################################################################
 # doit, list, ?, return, help                                                #
 ##############################################################################


-fdtd,-fmonitor: Monitoring of Field Quanitities

During a Time Domain Computation (with a static Mesh, i.e. not windowwake), selected field Quantities can be monitored.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -fmonitor                                                         #
 ##############################################################################
 # name  = noname-001                                                         #
 # whattosave= ecomponents                                                    #
 #                       -- ecomponents, hcomponents                          #
 #    position= ( 0.0, 0.0, 0.0 )                                             #
 ##############################################################################
 # doit, list, ?, return, help                                                #
 ##############################################################################


-fdtd,-pmonitor: Monitoring of Power Quanitities

During a Time Domain Computation (with a static Mesh, i.e. not windowwake), selected Power Quantities can be monitored.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -PMonitor                                                         #
 ##############################################################################
 # name = noname-001                                                          #
 # whattosave= pdielectrics                                                   #
 #                       -- ( pdielectrics | energy )                         #
 #    xlow=      -1.0e+30    , xhigh=       1.0e+30                           #
 #    ylow=      -1.0e+30    , yhigh=       1.0e+30                           #
 #    zlow=      -1.0e+30    , zhigh=       1.0e+30                           #
 #    stride= 10                                                              #
 ##############################################################################
 # doit, list, ?, return, help                                                #
 ##############################################################################

gd1.pp

gd1.pp is the Postprocessor. gd1.pp loads the Data that is computed by gd1 and displays it. gd1.pp also computes Integrals over Fields, like Wall Losses and Voltages. Together with the Macro Facility, this allows comfortable Computation of Figures of Merit like Q-Values and Shunt-Impedances.
A Special Section (-sparameter) computes Scattering Parameters from the Amplitudes of Port-Modes that were computed and stored by gd1.
Wakepotentials and Impedances are computed in the Section -wakes.
TouchStone-Files containing Scattering Matrices may be created in the Section -totouchstone.

Before you can do anything useful, you have to specify from what Database gd1.pp shall take the Fields from. Therefore the first Thing you do is: enter the Section -general.

-base

This is the Base Section of gd1.pp.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -base                                                             #
 #  VshzpnIb 2017.04.03                                                       #
 ##############################################################################
 # -general         -- Define Database                                        #
 # -3darrowplot     -- Field Plots, Material Plot                             #
 # -lineplot        -- Lineplot of Field Components,                          #
 # -glineplot       -- Lineplot of Field Comp along gline,                    #
 # -2dplot          -- Aquivalue Plot of a Component on a Plane.              #
 # -energy          -- Compute stored Energy                                  #
 # -lintegral       -- Compute Voltages                                       #
 # -wlosses         -- Compute Wall Losses                                    #
 # -dlosses         -- Compute dielectric Losses                              #
 # -flux            -- Compute Fluxes through rectangular Areas               #
 # -clouds          -- Properties of free moving Clouds                       #
 # -sparameters     -- Analyses Time History of Port Mode Amplitudes          #
 # -material        -- Specify Conductivities for Loss Computations           #
 # -wakes           -- Wakepotentials, Impedances                             #
 # ***** Miscellanea ******                                                   #
 #  -totouchstone   -- Convert fri-data to touchstone Form                    #
 #  -combine        -- Combines Scattering Parameters                         #
 #  -pcombine       -- Combines E & H to Poynting Field.                      #
 #  -smonitor       -- Display and fft smonitor Data                          #
 #  -fmonitor       -- Display and fft fmonitor Data                          #
 #  -pmonitor       -- Display pmonitor Data                                  #
 #  -voltages       -- Display and fft Voltages Data                          #
 #  -fexport        -- Export 3D Field Data                                   #
 #  -2dmanygifs     --                                                        #
 #  -3dmanygifs     --                                                        #
 #  -debug          -- Specify Debug Levels                                   #
 #                                                                            #
 ##############################################################################
 # ?, help, end, ls                                                           #
 ##############################################################################


-general

Here you specify what Resultfile shall be processed and where Scratchfiles shall be written to.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -general                                                          #
 ##############################################################################
 # infile     = ./results                                                     #
 # scratchbase= ./scratch.                                                    #
 # text( 1)=                                                                  #
 ##############################################################################
 # 2dplotopts   = -geometry 690x560+10+10                                     #
 #   plotopts   = -geometry 800x668+310+40 -noclip                            #
 # showtext     = yes         -- (yes | no)                                   #
 # onlyplotfiles= no          -- (yes | no)                                   #
 # nrofthreads=  1            -- SMP: Nr of Threads.                          #
 ##############################################################################
 # ?, return, end, help, ls                                                   #
 ##############################################################################

Example The following specifies that we want to work with the Data that is generated by the last Run of gd1. We want to have the Scratchfiles written into the Directory '/tmp/garbage/' and there the Files shall be called 'delete-me-*'. We want to have mymtv2 started with an X11-geometry of 800x600. We want to have gd1.3dplot started with an X11-geometry of 1024x768.
 -general
    infile= @last
    scratchbase= /tmp/garbage/delete-me-
    2dplotopts= -geometry 800x600
    plotopts= -geometry 1024x768


-3darrowplot: Plots 3D Fields together with the Material Boundaries.

This Section plots 3D electric or magnetic Fields. Also Portmodes can be plotted.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -3darrowplot                                                      #
 ##############################################################################
 # symbol      = e_1                                                          #
 # quantity    = e                                                            #
 # solution    = 1                                                            #
 # component   = all                    -- (x|y|z|all)                        #
 #    phase    = 45.0                   -- Only for Portmodes                 #
 # arrows      = 10000                                                        #
 # lenarrows   = 2.0                                                          #
 # maxlenarrows= 2.0                                                          #
 #   fcolour   = 4                                                            #
 # materials   = yes                    -- (yes | no)                         #
 # dielectrics = yes                    -- (yes | no)                         #
 # fonmaterials= yes                    -- (yes | no)                         #
 #    logfonmat= no                     -- (yes | no)                         #
 #    fmaxonmat= auto                                                         #
 # jonmaterials= no                     -- (yes | no)                         #
 # scale       = 2.80                                                         #
 # fscale      = auto                                                         #
 # nlscale     = no, nlexp= 0.30                                              #
 # eyeposition = ( -1.0, -2.30, 0.50 )                                        #
 # bbxlow = -1.0000e+30,    bbylow = -1.0000e+30,    bbzlow = -1.0000e+30     #
 # bbxhigh= 1.0000e+30,     bbyhigh= 1.0000e+30,     bbzhigh= 1.0000e+30      #
 # rotx   = 0.0000,         roty   = 0.0000,         rotz   = 0.0000          #
 # clouds = yes     -- Show Clouds                                            #
 ##############################################################################
 # plotopts= -geometry 800x668+310+40 -noclip                                 #
 # showtext     = yes                   -- (yes | no)                         #
 # showlines    = no                    -- (yes | no)                         #
 # onlyplotfiles= no                    -- (yes | no)                         #
 ##############################################################################
 # @absfmax:  undefined                                                       #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################

Example To generate a Plot of the first electric Field found in the Database, we say:
   symbol= e_1
   doit

Example To generate a Plot of the real Part of the fourtht complex electric Field found in the Database, with the Colours of the material Patches showing the Field strength at the Material Boundaries, we say:
   symbol= ere_4
   fonmat= yes
   doit

 # only the Material Plot, without the Field-Arrows:
 lena 1e-6
   doit
Figure 2.1: Above: Resulting Plot, with Field Arrows, and Material Patches coloured according to the Field Strength at Material Boundaries. Below: The same Plot, without Field Arrows.
\begin{figure}\centerline{ \quad \quad \psfig{figure=fonmat-eq-yes.ps,width=10cm...
...width=10cm,bbllx=20pt,bblly=232pt,bburx=582pt,bbury=802pt,clip=} }\end{figure}

Example A Plot of the absorbed Energy in Materials with type=impedance: In the first Step, we compute the Time Domain Fields with gd1:
 gd1 < DDBA_simple_button_racetrack_no_cavity_no_recess.gdf
That Inputfile specifies all metallic Materials as of type=impedance.
 -material
   material= 3, type= impedance, kappa= 1.3514e6 # button
   material= 5, type= impedance, kappa= 1.82e7   # pin
   material= 6, type= impedance, kappa= 1.3889e6 # anulus
   material= 7, type= impedance, kappa= 4.561e7  # coax pin
   material= 8, type= impedance, kappa= 1.35e6   # block
   material= 9, type= impedance, kappa= 1.59e7   # coax outer
Fields at selected Times are stored.
    # Store the e-Fields at selected Times.
    #     This will then also store the deposited Energy in
    #     'type= impedance'.
    #  gd1.pp: -3darrow, jonmat= yes, symbol= Bla_e_1, doit
    #
    -storefieldsat
        name= Bla, what= e
           firstsaved= 0.1 / @clight
           lastsaved= INF
           distance= 0.1 / @clight
        doit

After the Time Domain Computation has finished, we start gd1.pp with the Input:

    -general, infile= @last
    -3da
        jonmat= yes
        arrows= 1, lena= 1e-7  # No Arrows shown
        symbol= Bla_e_3, doit
The resulting Plot of the absorbed Energy is shown in Figure 2.2.
Figure 2.2: The coloured Material-Patches encode the absorbed Energy in the Materials with type=impedance.
\begin{figure}\epsfig{figure=jonmat-example.ps,width=18cm,bbllx=0pt,bblly=0pt,bburx=747pt,bbury=554pt,clip=}\end{figure}

-lineplot: Plots a Field Component along an Axis.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -lineplot                                                         #
 ##############################################################################
 # symbol    = e_1                                                            #
 # quantity  = e                                                              #
 # solution  = 1                                                              #
 # component = z                                                              #
 #    phase  =       45.0               -- Only for Portmodes                 #
 #                                                                            #
 # direction = z                                                              #
 # startpoint= ( 0.0, 0.0, -1.0e+30 )                                         #
 ##############################################################################
 # 2dplotopts = -geometry 690x560+10+10                                       #
 # showtext   = yes                     -- (yes | no)                         #
 # onlyplotfiles= no                    -- (yes | no)                         #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################

Example To specify the last computed Database as the Database, then to generate a Plot of the x-Component of the electric Field of the third Field in the Database, starting from the lowest z-Coordinate in the Grid, up to the highest z-Coordinate at the Position (x,y)= (0,0), we say (using Abbreviations):
 -gen, i @last
 -linepl, sym e_3, comp x, dir z, sta (0,0,@zmin), do
In full Glory, without Abbreviations, this is:
 -general
    infile= @last
 -lineplot
    symbol= e_3
    component= x
    direction= z
    startpoint= ( 0, 0, @zmin )
  doit

-glineplot: Plots a Field Component along a Line.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -glineplot                                                        #
 ##############################################################################
 # symbol    = e_1                                                            #
 # quantity  = e                                                              #
 # solution  = 1                                                              #
 #                                                                            #
 # startpoint= ( 0.0, 0.0, -1.0e+30 )                                         #
 # direction = ( undefined, undefined, undefined )                            #
 ##############################################################################
 # 2dplotopts= -geometry 690x560+10+10                                        #
 # showtext = yes                       -- (yes | no)                         #
 # onlyplotfiles= no                    -- (yes | no)                         #
 ##############################################################################
 # @gvreal= undefined       @gvimag= undefined      @gvabs= undefined         #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################

-2dplot: Plot a Field Component on a Plane

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -2dplot                                                           #
 ##############################################################################
 # symbol    = e_1                                                            #
 # quantity  = e                                                              #
 # solution  = 1                                                              #
 #                                                                            #
 # component = z                        -- What Component to be plotted.      #
 # normal    = z                        -- The Plane Normal of the Cut-Plane. #
 # cutat     = undefined                -- The Coordinate of the Cut-Plane.   #
 # ncontourlines= 30                    -- The Number of Contourlines.        #
 # fscale    = auto                                                           #
 #                                                                            #
 ##############################################################################
 # 2dplotopts= -geometry 690x560+10+10                                        #
 # showtext = yes                       -- (yes | no)                         #
 # onlyplotfiles= no                    -- (yes | no)                         #
 ##############################################################################
 # doit, ?, return, end, help                                                 #
 ##############################################################################


-energy: Compute Energy in E or H Fields

In this Section you may compute the stored Energy for an electric or magnetic Field. The Result of that Computation is stored in symbolic Variables that may be used e.g. for Computation of user defined figures of Merit.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -energy                                                           #
 ##############################################################################
 # symbol   = h_1                                                             #
 # quantity = h                                                               #
 # solution = 1                                                               #
 # bbxlow =    -1.0000e+30, bbylow =    -1.0000e+30, bbzlow =    -1.0000e+30  #
 # bbxhigh=     1.0000e+30, bbyhigh=     1.0000e+30, bbzhigh=     1.0000e+30  #
 #                                                                            #
 #                                                                            #
 # @henergy : undefined                 (symbol: undefined, m: 1)             #
 # @eenergy : undefined                 (symbol: undefined, m: 1)             #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################
The Energy for a magnetic Field is computed as:
\begin{displaymath}
@henergy = \frac{1}{2m} \int \mu H^2 \; dV
\end{displaymath} (2.1)

The Energy for an electric Field is computed as:
\begin{displaymath}
@eenergy = \frac{1}{2m} \int \varepsilon E^2 \; dV
\end{displaymath} (2.2)

The Time-Averaging Factor m is 2 for resonant Fields, and 1 for nonresonant Rields.

When you are computing resonant Fields without periodic Boundary Conditions, the Fields that gd1.pp processes are the electric Fields at a Time t=0 and the magnetic Fields at a Time t=T/4, where T=1/f. This means, you 'see' both, the electric and magnetic Fields at a Time where they are at a Maximum. To get the total stored Energy for resonant Fields, one has to integrate $ (1/2) \mu H^2 + (1/2) \varepsilon E^2 $ over the Volume at one instant Time. But E and H are not at the same Time. They are offset by T/4. The Factor of 1/m, with m=2 for resonant Fields, accounts for the Effect of integrating both the electric and magnetic Fields at their (time) Peak Values.

When you are computing time dependent Fields, the Fields that gd1.pp (normally) processes are electric and magnetic Fields at (almost) the same Time (almost, because there is a Time-Offset of half of the used Timestep, but the used Timestep is very small). For time dependent Fields, the electric and magnetic Fields are not at their Time-Peak Values, but more important, the electric and magnetic Fields are at the same Time. The stored Energy can therefore be expressed directly by integrating $ (1/2) \mu H^2 + (1/2) \varepsilon E^2 $ over the Volume. No factor 'm' is needed.

You cannot and do not need to specify that 'm'. gd1.pp does this for you.


Example To compute the stored Energy in the first electric Field found in the Database, we say:

 -energy, symbol= e_1, doit


-lintegral: Computes Line Integrals

This Section computes the Integral

\begin{displaymath}
\int F \exp(j \omega s / (\beta c_0)) \; ds.
\end{displaymath}

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -lintegral                                                        #
 ##############################################################################
 # symbol    = e_1                                                            #
 # quantity  = e                                                              #
 # solution  = 1                                                              #
 #                                                                            #
 # direction = z                                                              #
 # component = z                                                              #
 # startpoint= ( 0.0, 0.0, -1.0e+30 )                                         #
 #    (used) : ( @x0: undefined, @y0: undefined, @z0: undefined )             #
 # length    = auto                                                           #
 #    (@length) : undefined                                                   #
 # beta      = 1.0                                                            #
 # frequency = auto                     -- [auto | Real]                      #
 ##############################################################################
 # @vreal= undefined        @vimag= undefined       @vabs= undefined          #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################


-wlosses: Compute Wall Losses from H-fields

In this Section you may compute the Wall Losses that stem from the Induction of Surface Currents from magnetic Fields. This is a Power Loss Perturbation Computation.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -wlosses                                                          #
 ##############################################################################
 # symbol    = h_1                                                            #
 # quantity  = h                                                              #
 # solution  = 1                                                              #
 # frequency = auto                     -- [auto | Real]                      #
 # bbxlow =    -1.0000e+30, bbylow =    -1.0000e+30, bbzlow =    -1.0000e+30  #
 # bbxhigh=     1.0000e+30, bbyhigh=     1.0000e+30, bbzhigh=     1.0000e+30  #
 #                                                                            #
 #                                                                            #
 # @metalpower : undefined         [VA] (symbol: undefined)                   #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################
The Conductivities that are used in the Perturbation Formula may be changed in the Section -material. The Result of the Computation is available as the symbolic Variable @metalpower. The Wall Losses are computed as:

\begin{displaymath}
\int \int \frac{H^2}{2 \kappa \delta} dF \; ; \; \;
\frac{1}{\delta} = \sqrt{ \pi f \mu _0 \kappa }
\end{displaymath}

The Integration is performed over all metallic Surfaces that would appear in a Plot as produced by the Section -3darrowplot. This implies, that Wall Losses are NOT computed for electric Planes of Symmetry, since the Material on the Planes of Symmetry are not shown in -3darrowplot.


-dlosses: Compute dielectric Losses

In this Section you may compute dielectric Losses. The Result of the Computation is available as the symbolic Variables @muepower, @epspower. The dielectric Losses are computed as:

For electric Fields:

\begin{displaymath}
\frac{1}{m} \int \vec{E} \cdot \kappa_e \vec{E} \; dV = {\rm @epspower \; [VA]}
\end{displaymath}

For magnetic Fields:

\begin{displaymath}
\frac{1}{m} \int \vec{H} \cdot \kappa_m \vec{H} \; dV = {\rm @muepower \; [VA]}
\end{displaymath}

The Integration is performed over the specified Volume. The time-averaging Factor m is 2 for resonant Fields, and 1 for nonresonant Fields.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -dlosses                                                          #
 ##############################################################################
 # symbol    = h_1                                                            #
 # quantity  = h                                                              #
 # solution  = 1                                                              #
 # bbxlow =    -1.0000e+30, bbylow =    -1.0000e+30, bbzlow =    -1.0000e+30  #
 # bbxhigh=     1.0000e+30, bbyhigh=     1.0000e+30, bbzhigh=     1.0000e+30  #
 #                                                                            #
 #                                                                            #
 # @muepower : undefined               (symbol: undefined, m: 1)              #
 # @epspower : undefined               (symbol: undefined, m: 1)              #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################


-flux: Compute Flux of Fields through rectangular Areas

In this Section you may compute the Flux of a Field through a rectangular Area.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -flux                                                             #
 ##############################################################################
 # symbol  = h_1                                                              #
 # quantity= h                                                                #
 # solution= 1                                                                #
 #                                                                            #
 # normal  = z                     -- [x|y|z]                                 #
 # cutat   = undefined             -- Coordinate of the integration Plane     #
 # xlow= undefined            , xhigh= undefined                              #
 # ylow= undefined            , yhigh= undefined                              #
 # zlow= undefined            , zhigh= undefined                              #
 #    ( used: @cutat : undefined )                                            #
 #    ( used: @xlow  : undefined        , @xhigh  : undefined )               #
 #    ( used: @ylow  : undefined        , @yhigh  : undefined )               #
 #    ( used: @zlow  : undefined        , @zhigh  : undefined )               #
 # @flux : undefined [undefined]                                              #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################


-clouds: Analyse Properties of free moving Charges

This Section is for analysing the Results of a Time Domain Computation with free moving Charges.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -clouds                                                           #
 ##############################################################################
 # symbol  = h_1                                                              #
 # quantity= h                                                                #
 # solution= 1                                                                #
 #                                                                            #
 # position = no                   -- 3D Plot of Particle Positions           #
 #   showbox= yes                  -- Show computational Box with 3D Plot     #
 # gamma    = yes                  -- 2D Plot of Gamma                        #
 # hgamma   = yes                  -- 2D Plot of Gamma-density                #
 #   ihgamma= 30                   -- Number of hgamma Bins                   #
 # current  = yes                  -- 2D Plot of Q*Velocity                   #
 #  binwidth=  5                   -- Bin-Width of Current Average / ChargeSiz#
 #   normal = z                    -- Direction of 2D Plots (gamma, current)  #
 # phase    = yes                  -- Plots of Velocities vs Position         #
 # export   = no                   -- Export raw Cloud Data                   #
 #   outfile= ./gdfidl-exported-clouds                                        #
 ##############################################################################
 # 2dplotopts= -geometry 690x560+10+10                                        #
 # showtext     = yes         -- (yes | no)                                   #
 # onlyplotfiles= no          -- (yes | no)                                   #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################


-sparameters: Computes scattering Parameters from Time Domain Data

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section -sparameter                                                        #
 ##############################################################################
 # ports      = all                                                           #
 #               -- (all | LIST )                                             #
 # modes      = ( 1 )                         -- (all | LIST )                #
 # timedata   = no                            -- ( yes | no )                 #
 #   tsumpower= no                            -- ( yes | no )                 #
 #   tintpower= no                            -- ( yes | no )                 #
 #   usample  = 5                             -- Undersample for t-Plots      #
 # freqdata   = yes                           -- ( yes | no )                 #
 #   wantdf   = auto                          -- ( auto | REAL )              #
 #   windowed = yes                           -- ( yes | no )                 #
 #     edgeofwindow= 0.70              -- At what Frac. start to apply Window #
 #   fsumpower= yes                           -- ( yes | no )                 #
 #   magnitude= yes                           -- ( yes | no )                 #
 #     slog   = no                            -- ( yes | no )                 #
 #     xlog   = no                            -- ( yes | no )                 #
 #   fintpower= no                            -- ( yes | no )                 #
 #   phase    = no                            -- ( yes | no )                 #
 #   smithplot= no                            -- ( yes | no )                 #
 #     markerat= undefined              -- Want a Marker at .. in Smith-Chart #
 #   groupvelocity= no                        -- ( yes | no )                 #
 #   fri      = no                            -- ( yes | no )                 #
 # excdata    = yes                     -- Show the Data of the Excitation    #
 # upto       = auto                    -- [s]   ( auto | REAL )              #
 # tfirst     = 0.0                     -- [s]                                #
 # flow       = auto                    -- [1/s] ( auto | REAL )              #
 # fhigh      = auto                    -- [1/s] ( auto | REAL )              #
 # ignoreexc  = no                            -- ( yes | no )                 #
 # details    = no                            -- ( yes | no )                 #
 ##############################################################################
 # 2dplotopts= -geometry 690x560+10+10                                        #
 # showtext     = yes         -- (yes | no)                                   #
 # onlyplotfiles= no          -- (yes | no)                                   #
 ##############################################################################
 # return, help, end, ls, clearmarkers, doit                                  #
 ##############################################################################

Example To Compute and Plot the scattering Parameters of only the first two Modes of the Ports with Names Input, Output, we say:
 -sparameter
     modes= ( 1, 2 )
     ports= ( Input, Output )
  doit

Example In the first Step, we compute the Time Domain Amplitudes with gd1:
 gd1 < /usr/local/gd1/examples-from-the-manual/arndt.MTT90.p1854.fig5.gdf
 # /usr/local/gd1/examples-from-the-manual/arndt.MTT90.p1854.fig5.gdf

define(INF,10000.0)
define(MAG, 2) define(PEL, 1) define(CU, 3) define(PER,0)

define(FREQ,15e9)

define(WGH, 15.8e-3)
define(WGW0, 7.9e-3)
define(T0, 6.6e-3)

define(CSW1, 4.2e-3)
define(T1, 6.2e-3)

define(STPSZE, 0.5e-3 )
define(XHIGH, 30e-3) define(XLOW, -XHIGH )
define(ZHIGH, 12e-3) define(ZLOW, -ZHIGH )

########
########
########
 -general
   outfile= /tmp/UserName/arndt
   scratch= /tmp/UserName/arndt-scratch-

 -mesh
   spacing= STPSZE
#   graded= on, qfgraded= 1.2, dmaxgraded= 3e8/FREQ/20
   pxlow= XLOW, pxhigh= XHIGH
   pylow= -WGH/2-STPSZE, pyhigh= 0   # Weg damit
   pylow= 0, pyhigh= WGH/2+STPSZE
   pzlow= ZLOW, pzhigh= ZHIGH
   cxlow= el, cxhigh= el
   cylow= el, cyhigh= mag   # Weg damit
   cylow= mag, cyhigh= ele
   czlow= el, czhigh= mag

 -material
   material= PEL, type= electric
   material= CU,  type= electric

#
# Fill everything with material CU
#
-brick
   material= CU,
   volume= ( -INF, INF, \
             -INF, INF, \
             -INF, INF)
   doit
#
# Upper and lower waveguide
#
   material= 0,
   volume= ( -INF,INF, -WGH/2,WGH/2, T0/2,T0/2+WGW0 ), doit
   vol (-INF,INF, -WGH/2,WGH/2, -(T0/2+WGW0),-T0/2 ), doit

#
# coupling slits
#
   vol ( -CSW1/2,CSW1/2, -WGH/2,WGH/2, -(T0/2+WGW0),T0/2+WGW0 ), doit
   vol ( -(4.2e-3/2+3.0e-3),\
          (4.2e-3/2+3.0e-3),\
          -WGH/2,WGH/2,\
          T0/2,T0/2+WGW0 ),
   doit

   vol ( -(4.2e-3/2+3.0e-3),4.2e-3/2+3.0e-3, -WGH/2,WGH/2, -(T0/2+WGW0),-T0/2 ), do
define(XDUM, 4.2e-3/2+3.0e-3 )
   vol ( -(XDUM+3.2e-3),-XDUM, -WGH/2,WGH/2, -(T0/2+WGW0),T0/2+WGW0 ), do
   vol ( XDUM,XDUM+3.2e-3, -WGH/2,WGH/2, -(T0/2+WGW0),T0/2+WGW0 ), do

define(XDUM, 4.2e-3/2+3.0e-3+3.2e-3+4.2e-3 )
   vol ( -(XDUM+1.6e-3),-XDUM, -WGH/2,WGH/2, -(T0/2+WGW0),T0/2+WGW0 ), do
   vol ( XDUM,XDUM+1.6e-3, -WGH/2,WGH/2, -(T0/2+WGW0),T0/2+WGW0 ), do

 -volumeplot,
#   eyeposition= ( 1.0, 2.0, 0.5) 
   scale= 4.5
   doit

-fdtd
  -ports
     name= xlow1,  plane= xlow,  pzlow = 0, modes= 1, doit
     name= xlow2,  plane= xlow,  pzhigh= 0, modes= 1, doit
     name= xhigh1, plane= xhigh, pzlow = 0, modes= 1, doit
     name= xhigh2, plane= xhigh, pzhigh= 0, modes= 1, doit

  -pexcitation
     port= xlow1,
     mode= 1, amplitude= 1, frequency= 15e9, bandwidth= 10e9,

  -time
     tmin=    100/FREQ
     tmax=  10000/FREQ
     firsts= 10/FREQ
     lasts = 11/FREQ
     distancesave= 0.10/FREQ
     amptresh= 1e-3

  -fdtd
     doit
In the next Step, we start gd1.pp to compute the scattering Parameters from the Time Domain Amplitudes, that were computed by gd1. The Input we give to gd1.pp is:
 -gen, inf @last
 -3da, sy e_1, scal 4.5, arr 5000, fonmat yes, doit
 -spa, window yes, doit
       window no, doit
The resulting Plots are shown in the Figures 2.3 to 2.13.
Figure 2.3: The Time Domain electric Field at an early Time.
\begin{figure}\epsfig{figure=arndt.MTT90.p1854.fig5.ps,width=18cm,bbllx=0pt,bblly=0pt,bburx=747pt,bbury=554pt,clip=}\end{figure}
Figure 2.4: The computed Reflection when a Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-window-xlow1_out_1-freq-abs.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.5: A computed Transmission when a Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-window-xlow2_out_1-freq-abs.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.6: A computed Transmission when a Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-window-xhigh1_out_1-freq-abs.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.7: A computed Transmission when a Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-window-xhigh2_out_1-freq-abs.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.8: The computed Reflection when no Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-nowindow-xlow1_out_1-freq-abs.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.9: A computed Transmission when no Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-nowindow-xlow2_out_1-freq-abs.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.10: A computed Transmission when no Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-nowindow-xhigh1_out_1-freq-abs.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.11: A computed Transmission when no Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-nowindow-xhigh2_out_1-freq-abs.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.12: The Sum of the Squares of the computed scattering Parameters when a Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-window-sum-power-freq.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.13: The Sum of the Squares of the computed scattering Parameters when no Window has been applied.
\begin{figure}\epsfig{figure=arndt-res-nowindow-sum-power-freq.ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}

Example This Example demonstrates the Usage of tfirst. A Computation with a relativistic Line Charge is performed. The Device is a Button-Beam-Position-Monitor. Only a Quarter of the Device is modeled. There are three Ports where Energy can flow away from the Button. The TEM-Line which is connected to the Button, and the lower and upper Beam-Pipe. The Amplitudes at these Ports is recorded when modes at these Ports is specified larger than Zero.
 gd1 < /usr/local/gd1/examples-from-the-manual/Button-LineCharge.gdf
 # /usr/local/gd1/examples-from-the-manual/Button-LineCharge.gdf

define(INF, 10000)

define(SIGMA, 4.6e-3)
define(STPSZE, 0.15e-3 )

define(A,    40e-3)
define(B,    37e-3)

define(ZYL1, 100e-3)

define(RADO, 3.8e-3)
define(RADI, 3.5e-3)  
define(FEED, 0.33e-3)

define(BUTTON,4.0e-3)
define(CERMA, 4.5e-3)
define(CERME, 6.5e-3)
define(BLOCK, 7.5e-3)

define(EXT, 85e-3)

     
###############################################################

 -general
    outfile= /tmp/UserName/Resultfiles
    scratch= /tmp/UserName/scratch-

 -mesh
    spacing= STPSZE, perfectmesh= no
    graded= yes, dmaxgraded= 4*STPSZE

 define(BUTTONX0, 9.065e-3)
 define(X1, BUTTONX0-RADO)
 define(X2, BUTTONX0+RADO)
 define(NX, 1+(X2-X1)/STPSZE)
    xfixed( NX, X1, X2 )
    zfixed( NX, -RADO, +RADO )

    pxlow= 0, pxhigh= EXT+5e-3
    pylow= 0, pyhigh= 25e-3
    pzlow = -0.01
    pzhigh= +0.01

    cxlow= mag, cxhigh= ele
    cylow= mag, cyhigh= ele
    czlow= el,  czhigh= ele

 #########################################################################
 -material
    material= 3, type= electric
    material= 4, type= electric
    material= 5, type= normal, epsr= 9, muer= 1

-brick
  # Fill the universe with metal..
  material=4 
     volume= (-INF,INF, -INF,INF, -INF,INF)
  doit
 ################################################################
 #vacuum chamber

 -ggcylinder
     material= 0
     originprime= ( 0, 0, 0 )
     xprimedirection= ( 1, 0, 0 )
     yprimedirection= ( 0, 1, 0 )
     range= (-ZYL1/2, ZYL1/2)
 show= later
     clear
       point= ( -36e-3,      -5e-3)
       point= ( -36e-3,       5e-3)
       point= (-20.415e-3,   14e-3)             
       point= ( 20.415e-3,   14e-3)
       point= (  36e-3,       5e-3)
       point= (  56e-3,       5e-3)
       point= (  56e-3,      14e-3)
       point= ( EXT,         14e-3) 
       point= ( EXT,        -14e-3) 
       point= (  56e-3,     -14e-3)
       point= (  56e-3,      -5e-3)
       point= (  36e-3,      -5e-3)
       point= ( 20.415e-3,  -14e-3)
       point= (-20.415e-3,  -14e-3)    
       point= ( -36e-3,      -5e-3)
     doit


 #
 # All four Buttons are modelled, although
 # only one of them is inside the selected Quarter.
 #
 do i= -1, 1, 2
    do j= -1, 1, 2

       #The vacuum part containing the bpm's
       -gbor
           material= 0
           originprime= ( j * BUTTONX0, 14e-3*i, 0 )
           zprimedirection= ( 0, i, 0 )
           rprimedirection= ( 1, 0, 0 )
           range= (0, 360)
 show= later
           clear
              point= (0,       0.)
              point= (0,       4.25e-3)
              point= (27e-3,   4.25e-3)
              point= (27e-3,   0.)
           doit


       # the bpm's
       #the outside shell _1

        material= 3
           clear
              point= (0,        RADO)
              point= (0,        4.25e-3)
              point= (17.5e-3,  4.25e-3)
              point= (17.5e-3,  4.25e-3)
              point= (27e-3,    4.25e-3)
              point= (27e-3,    2.05e-3)
              point= (BLOCK,    2.05e-3) 
              point= (BLOCK,    RADO) 
              point= (0,        RADO)
            doit

       #inner part of the bpm's
            clear
               point= (0,       0.0)
               point= (0,       RADI)
               point= (BUTTON,  RADI)
               point= (BUTTON, 1.65e-3)
               point= (CERMA,  1.65e-3) 
               point= (CERMA,  FEED)  
               point= (CERME,  FEED)  
               point= (CERME,  0.89e-3)  
               point= (27e-3,  0.89e-3)
               point= (27e-3,  0.0e-3)
            doit

       #Al203 part_1
         material= 5
            clear
               point= (CERMA,  FEED)
               point= (CERMA,  RADO)
               point= (CERME,  RADO)
               point= (CERME,  FEED)
            doit
   end do
 end do
###############################################
-volumeplot
      scale=3
      doit
##########################################################################
#
# Wake-Parameters..
#
# For Ports where the Beam passes through, npml=40 or larger is recommended.
#
-fdtd
  -ports
    name= lower_end, plane= zlow,  modes= 10, npml= 40, doit
    name= upper_end, plane= zhigh, modes= 10, npml= 40, doit
    name= bpmho,     plane= yhigh, modes= 1, doit

 -lcharge 
    xpos= 0, ypos= 0,
    charge= 1e-12, sigma= SIGMA
    shigh= 2

 #
 # The Storing of the Fields is just for the nice plot for the Manual.
 #
 -time
    firstsaved= SIGMA / @clight
    lastsaved= (ZYL1 + 20 * SIGMA) / @clight
    distance= SIGMA / @clight

 -fdtd
    doit
The time Data of the Modes at the lower and upper Beam-Pipes are contaminated by the Passing of the Beam through these Ports at small time Values. The Beam has significant Charge ie more than 1e-7 than the Maximum, for times less than $ t = 8 \times SIGMA / c $ for the lower Beam Pipe, where it enters. The Beam reaches the upper Beam Pipe after $ \Delta t = (z_{max} - z_{min}) / c$. The Input for gd1.pp to create the following Plots (and some more Plots not shown) is:
 -general,
     infile= @last
     scratch= ./Resultfile-
 -3darrow, sy e_11, arr 1e4, lena 100, fonmat yes, scale 4, doit
 -spa,
       freqdata= no, timedata= yes, tintpower= yes, modes= all

    ports= ( lower_end )
       tfirst= 0, doit
       tfirst= 8 * SIGMA / 3e8, doit
    ports= ( upper_end )
       tfirst= 0, doit
       tfirst= ( @zmax - @zmin + 8 * SIGMA ) / 3e8, doit
    ports= ( bpmho )
       tfirst= 0, doit
Figure 2.14: The Time Domain electric Field at an early Time.
\begin{figure}\epsfig{figure=Button-LineCharge.ps,width=18cm,bbllx=0pt,bblly=0pt,bburx=747pt,bbury=554pt,clip=}\end{figure}
Figure 2.15: The computed Amplitude of the sixth Mode at the lower Beam-Pipe.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-0-port-lower_end-e_amp_of_...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.16: The computed Amplitude of the sixth Mode at the lower Beam-Pipe, the time Data while the Beam passes through the Port is replaced by Zeros.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-XX-port-lower_end-e_amp_of...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.17: The integrated Power of all Modes at the lower Beam-Pipe.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-0-port-lower_end-integral-...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.18: The integrated Power of all Modes at the lower Beam-Pipe, the time Data while the Beam passes through the Port is replaced by Zeros.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-XX-port-lower_end-integral...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.19: The computed Amplitude of the sixth Mode at the upper Beam-Pipe.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-0-port-upper_end-e_amp_of_...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.20: The computed Amplitude of the sixth Mode at the upper Beam-Pipe, the time Data while the Beam passes through the Port is replaced by Zeros.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-XX-port-upper_end-e_amp_of...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.21: The integrated Power of all Modes at the lower Beam-Pipe.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-0-port-upper_end-integral-...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.22: The integrated Power of the all Modes at the upper Beam-Pipe, the time Data while the Beam passes through the Port is replaced by Zeros.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-XX-port-upper_end-integral...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}
Figure 2.23: The integrated Power of all Modes at the BeamPositionMonitor-Port.
\begin{figure}\epsfig{figure=Button-LineCharge-tfirst-0-port-bpmho-integral-sum-...
....ps,width=15cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}\end{figure}


-material: Conductivities of electric Materials

This Section allows the Changing of the Conductivities of Materials with type= electric. These Conductivities are used for estimating the Wall Losses in the Section -losses.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -material                                                          #
 ##############################################################################
 # material=  1        epsr....: infinity      kappa    =      58.0e+6        #
 # type: electric         xepsr: infinity        xkappa =      58.0e+6        #
 #                        yepsr: infinity        ykappa =      58.0e+6        #
 #                        zepsr: infinity        zkappa =      58.0e+6        #
 #                     muer....:       0.0     mkappa   :       0.0           #
 #                        xmuer:       0.0       xmkappa:       0.0           #
 #                        ymuer:       0.0       ymkappa:       0.0           #
 #                        zmuer:       0.0       zmkappa:       0.0           #
 ##############################################################################
 # return, help, ls                                                           #
 ##############################################################################
In gd1.pp, the Values for type, epsr, muer, mkappa cannot be changed.
Example To specify that Wall Loss Computations in the Section -wlosses shall use a Conductivity of $30 \times 10^6$ for the Material '10', we say:
 -material
    material= 10
    kappa= 30e6


-wakes: longitudinal and transverse Wakepotentials

This Section allows the Computation of longitudinal and transverse Wake Potentials from Data that were computed by gd1. These Data are only recorded by gd1 when you did specify a Charge in the Section -lcharge of gd1.

gd1 computes the Integral of the $E_z$ component along the outermost Paths where a Witness-Particle can travel and stores the Result in the Database. Since from these Data the longitudinal and transverse Wakepotentials everywhere in the Beam Pipe can be computed, you can specify an unlimited Number of Positions (x,y) where you are interested in the Wakepotentials. The (x,y) Position of the exciting Charge cannot be changed afterwards, though.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section -wakes                                                             #
 ##############################################################################
 # set =     0      -- What Dataset (windowwake only)                         #
 # watq      = yes  -- Process all Wakes at Positions of Line-Charges         #
 # awtatq    = yes  -- Use the Average of the two nearest transverse Wakes    #
 #                  -- as the transverse Wakes at the Positions of Charges    #
 # impedances= no   -- Compute Impedances.                                    #
 #    wantdf = auto           -- Wanted freq Resolution => SIN(f)/f Interpol. #
 #    window = yes  -- Apply Hann-Window when computing Impedances.           #
 #     fhigh =  undefined               -- fhigh of Impedances.               #
 # uselu     = yes  -- Use Sparse LU-Factorisation (not MG).                  #
 #   niter =   2 -- nIter for MG                                              #
 #   omega =    1.10 -- Omega for MG                                          #
 #   Omega2=    1.10 -- Omega2 for MG                                         #
 #   mgdetails= no  -- Show Number of its etc                                 #
 # uselowpass= no   -- Use lowpass Filtering.                                 #
 # usehighpass= no  -- Use highpass Filtering.                                #
 # showchargemax= no     -- Show Value of Charge Maximum.                     #
 # centerbunch= yes      -- Shift Data. Bunch Center will be at s=0.          #
 # peroffset= no         -- Scale Wx by x, Wy by y.                           #
 # xyref     = ( 0.0, 0.0)                      -- refpoint for ??atxy-Data   #
 # usexyref  = no                               -- Use refpoint?              #
 # clear            -- Clears all the "w*at*" Values.                         #
 # watxy = ( undefined, undefined)                  -- want wz(xi,yi,s), i= 1 #
 # wxatxy= ( undefined, undefined)                  -- want wx(xi,yi,s), i= 1 #
 # wyatxy= ( undefined, undefined)                  -- want wy(xi,yi,s), i= 1 #
 # watsi = undefined                  -- want w(x,y,si), i= 1                 #
 # watxi = undefined                  -- want w(xi,y,s), i= 1                 #
 #   liny= 20                         -- Number of Lines in y-Direction.      #
 # watyi = undefined                  -- want w(x,yi,s), i= 1                 #
 #   linx= 20                         -- Number of Lines in x-Direction.      #
 # wxatxi= undefined                  -- want wx(xi,y,s), i= 1                #
 # wxatyi= undefined                  -- want wx(x,yi,s), i= 1                #
 # wyatxi= undefined                  -- want wy(xi,y,s), i= 1                #
 # wyatyi= undefined                  -- want wy(x,yi,s), i= 1                #
 # istrides= 3                        -- Distance of s-Points of the Plots    #
 #                                    --                 in Units of "ds".    #
 # slow =        0.0                  -- Lowest s-Value to consider.          #
 # shigh=  undefined                  -- Highest s-Value to consider.         #
 # watsfiles = -none-
 #   xlowwats =       -1.0e+30                                                #
 #   xhighwats=        1.0e+30                                                #
 #   ylowwats =       -1.0e+30                                                #
 #   yhighwats=        1.0e+30                                                #
 # frequency=  undefined ( @ufrequency :  undefined )                         #
 #   ( @zxesrf:  undefined )                                                  #
 #   ( @zxesrf:  undefined )                                                  #
 #   ( @zxesrf:  undefined )                                                  #
 #  ( @xloss :  undefined ) [VAs]                                             #
 #  ( @yloss :  undefined ) [VAs]                                             #
 #  ( @zloss :  undefined ) [VAs]                                             #
 #  ( @charge:  undefined ) [As]                                              #
 ##############################################################################
 # 2dplotopts= -geometry 690x560+10+10                                        #
 # showtext     = yes         -- (yes | no)                                   #
 # onlyplotfiles= no          -- (yes | no)                                   #
 ##############################################################################
 # return, help, end, clear, doit                                             #
 ##############################################################################

Note: The longitudinal and transverse Lossfactors are printed in the Plots. They are also available as the Symbols @zloss, @xloss, @yloss after a Wakepotential Computation.
Example To have plotted the longitudinal Wakepotential at the Planes x=1e-3 and x=2e-3:
 -wake
    watxi= 1e-3
    watxi= 2e-3


-totouchstone: Convert fri-data to TouchStone Format

This Section allows the Combination of scattering Parameters in fri-Files to TouchStone Files.
The Section -sparameter may be used to generate the fri-Files.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section: -totouchstone                                                     #
 ##############################################################################
 # outfile= ./s-matrix.sXp                                                    #
 # ports= 2                                                                   #
 # normalise= no                                                              #
 #                                                                            #
 # ij= (1,1)                  -- Index of S-Parameter.                        #
 # file=  -none-
 #                            -- Filename of S-Parameter.                     #
 # factor= 1.0                -- Factor to apply.                             #
 # iport=  1, fcutoff= 0.0                                                    #
 # ###                                                                        #
 # Already specified Files:                                                   #
 # ij: (1,1), factor: 1.0, fcutoff: 0.0                                       #
 #   file:  -none-
 # ij: (1,2), factor: 1.0, fcutoff: 0.0                                       #
 #   file:  -none-
 # ij: (2,1), factor: 1.0, fcutoff: 0.0                                       #
 #   file:  -none-
 # ij: (2,2), factor: 1.0, fcutoff: 0.0                                       #
 #   file:  -none-
 ##############################################################################
 # clear, doit, ?, return, end, help, ls                                      #
 ##############################################################################

Note: All fri-Files must have the same frequency Resolution (use wantdf= DF), and must have the same frequency Range.
Example The following Shell-Script computes the four Rows of the scattering Matrix of a four-Port Device, by exciting four times a different Port. The computed scattering Parameters are stored as fri-Files and are combined to one TouchStone-File.
#!/bin/sh

#
# First Step:
# Computation of the four rows of the scattering matrix.
# The results of each computation are stored in a different file.
#
#    In the inputfile "arndt.00.x.gdf", the outfile is defined as
#       outfile= /tmp/bruw1931/garbage/arndt-excitation-at-PEXC
#
#
# At each computation, a different port is excited.
#
#    In the inputfile, the excitation is defined via:
#  -pexcitation
#     port= PEXC,
#     mode= 1, amplitude= 1, frequency= 17e9, bandwidth= 20e9,
#

 for PEXC in xlow1 xhigh1 xlow2 xhigh2
 do
    gd1 -DPEXC=$PEXC < arndt.00.x.gdf | tee out-excitation=$PEXC
 done

#
# Fouriertransform, and generating fri-files.
# The names of the fri-files are defined via
#
#  -general, scratch= /tmp/bruw1931/garbage/exc-at-$PEXC-
#
# Frequency resolution is 10 MHz  (wantdf= 10e6)
#
 for PEXC in xlow1 xhigh1 xlow2 xhigh2
 do
    gd1.pp << EOF
      -general
         infile= /tmp/bruw1931/garbage/arndt-excitation-at-$PEXC
         scratch= /tmp/bruw1931/garbage/exc-at-$PEXC-
      -sparameter
         window= yes, edgeofwindow= 0.7
         wantdf= 10e6
         flow= 5e9, fhigh= 25e9
         timedata= no, fsumpower= no, magnitude= no, phase= no, smithplot= no
         fri= yes
         onlyplotfiles= yes
         doit
EOF
 done

#
# Second step.
# Combining the rows of the scattering matrix to one TouchStone-file.
#

 gd1.pp << EOF
 -totouchstone
    clear     # file= - undefined -
    ports= 4

 sdefine(BASE, /tmp/bruw1931/garbage/exc-at)
    sdefine(P1, xlow1) sdefine(P2, xhigh1)
    sdefine(P3, xlow2) sdefine(P4, xhigh2)
      ij= (1,1), file= [BASE]-[P1]-[P1]_out_1.fri
      ij= (1,2), file= [BASE]-[P1]-[P2]_out_1.fri
      ij= (1,3), file= [BASE]-[P1]-[P3]_out_1.fri
      ij= (1,4), file= [BASE]-[P1]-[P4]_out_1.fri

      ij= (2,1), file= [BASE]-[P2]-[P1]_out_1.fri
      ij= (2,2), file= [BASE]-[P2]-[P2]_out_1.fri
      ij= (2,3), file= [BASE]-[P2]-[P3]_out_1.fri
      ij= (2,4), file= [BASE]-[P2]-[P4]_out_1.fri

      ij= (3,1), file= [BASE]-[P3]-[P1]_out_1.fri
      ij= (3,2), file= [BASE]-[P3]-[P2]_out_1.fri
      ij= (3,3), file= [BASE]-[P3]-[P3]_out_1.fri
      ij= (3,4), file= [BASE]-[P3]-[P4]_out_1.fri

      ij= (4,1), file= [BASE]-[P4]-[P1]_out_1.fri
      ij= (4,2), file= [BASE]-[P4]-[P2]_out_1.fri
      ij= (4,3), file= [BASE]-[P4]-[P3]_out_1.fri
      ij= (4,4), file= [BASE]-[P4]-[P4]_out_1.fri

     outfile= /tmp/bruw1931/garbage/touchstone.s4p

    doit
EOF

##############


-combine: Build scattering Matrices via scattering other scattering Matrices

This Section allows the Combination of scattering Matrices of several Devices to the resulting scattering Matrix of the combined Device.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section: -combine                                                          #
 ##############################################################################
 # outfile= ./s-matrix.sXp
 # show= yes                            -- Give a Plot of the resulting       #
 #                                      -- Scattering Parameters.             #
 # kdevice= 1, smatrix=  -none-
 # kdevice= 2, smatrix=  -none-
 # kdevice= 3, smatrix=  -none-
 # p1ik= ( 1, 1 ), p2ik= ( 1, 2 ), factor= 1.0                                #
 #  fcutoff= 0.0, epsmue= 1.0, linelength= 0.0                                #
 # rpi= 1, pik= ( 1, 1 )                                                      #
 # ####                                                                       #
 # Specified Port Connections:                                                #
 #     -- none so far --                                                      #
 # ####                                                                       #
 # Specified outer Ports:                                                     #
 #     -- none so far --                                                      #
 ##############################################################################
 # connect, assign, clear, doit, ?, return, end, help                         #
 ##############################################################################

Example
 -combine
  outfile= ./filter.s2p
    kdevice= 1, smatrix= /tmp/UserName/ipart=1.s2p
    kdevice= 2, smatrix= /tmp/UserName/ipart=2.s2p
    kdevice= 3, smatrix= /tmp/UserName/ipart=1.s2p
 
 
   # Connect the Ports at the Cutplanes.
   # i: Port, k: Device
    p1ik = (2,1), p2ik = (1,2), fcutoff= 3.2e9,
         epsmue= 1, linelength= -5e-3, factor= 1, connect
    p1ik = (2,2), p2ik = (2,3), fcutoff= 3.2e9,
         epsmue= 1, linelength= -5e-3, factor= 1, connect
 
   # rpi : Resulting Port I
   # pik : Port I of device K
   rpi= 1, pik= (1,1), assign
      # The port '1' of the resulting device shall be the port '1' of device '1'.
   rpi= 2, pik= (1,3), assign
      # The port '2' of the resulting device shall be the port '1' of device '3'.
 doit

-smonitor: Analyse scalar Time Domain Signals

This Section is for analysing Data monitored via gd1's section -smonitor, ie. scalar Flux Quantities.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # section: -smonitor                                                         #
 ##############################################################################
 # symbol  = - none -                                                         #
 # timedata   = yes                    -- ( yes | no )                        #
 # upto       = auto                   -- [s]   ( auto | REAL )               #
 # freqdata   = yes                    -- ( yes | no )                        #
 #   wantdf   = auto                   -- ( auto | REAL )                     #
 #   windowed = yes                    -- ( yes | no )                        #
 #     edgeofwindow= 0.70              -- At what Frac. start to apply Window #
 #   flow     = auto                   -- [1/s] ( auto | REAL )               #
 #   fhigh    = auto                   -- [1/s] ( auto | REAL )               #
 ##############################################################################
 # 2dplotopts= -geometry 690x560+10+10                                        #
 # showtext     = yes                  -- (yes | no)                          #
 # onlyplotfiles= no                   -- (yes | no)                          #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################

-fexport: Export 3D-Fields to ASCII Files

3D E and H Fields can be exported to ASCII files. Also Portmode Fields can be exported.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -fexport                                                          #
 ##############################################################################
 # symbol  = h_1                                                              #
 # quantity= h                                                                #
 # solution= 1                                                                #
 #   phase =  45.0000         -- Only for Portmodes.                          #
 # bbxlow  =    -1.0000e+30, bbylow =    -1.0000e+30, bbzlow =    -1.0000e+30 #
 # bbxhigh =     1.0000e+30, bbyhigh=     1.0000e+30, bbzhigh=     1.0000e+30 #
 # outfile = ./gdfidl-exported-field                                          #
 ##############################################################################
 # doit, ?, return, end, help, ls                                             #
 ##############################################################################


-2dmanygifs: Create many GIF Files

3D-Fields which were exported via gd1's section -fexport or gd1.pp's Section -fexport can be used to create GIF-Files.

 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -2dmanygifs                                                       #
 ##############################################################################
 # 1stinfile = /tmp/UserName/fexported--000000000.gz                          #
 # outfiles  = auto                                                           #
 # mpegfile  = 2dmanygifs.mpeg                                                #
 # uptonfiles= 1000000000                                                     #
 # ixoffset  = 0                                                              #
 # iyoffset  = 0                                                              #
 # stride    = 1                                                              #
 # width     = 1000                                                           #
 # scale     = 1.0                                                            #
 # what      = rHy                      -- rHx, rHy, Hx, Hy                   #
 # log       = no                       -- plot log(1+|scale*f|)              #
 # zerolines = yes                      -- Plot Lines at f=0                  #
 # show      = yes                      -- Show the mpeg.                     #
 ##############################################################################
 # doit, ?, return, end, help                                                 #
 ##############################################################################


-3dmanygifs: Create many GIF Files

Datasets of H-Fields on Surfaces exported via gd1's Section -fexport, what=honmat can be used to create GIF-Files.
 ##############################################################################
 # Flags: nomenu, noprompt, nomessage,                                        #
 ##############################################################################
 # Section: -3dmanygifs                                                       #
 ##############################################################################
 # 1stinfile = /tmp/UserName/H-onmat--000000001.gz                            #
 # outfiles  = auto                                                           #
 # uptonfiles= 1000000000                                                     #
 # what      = abs                      -- abs, logabs, loglogabs             #
 # mpegfile  = ./3dmanygifs.mpeg                                              #
 # xrot = -30.0                                                               #
 # yrot = 40.0                                                                #
 # zrot = 0.0                                                                 #
 # dxrot= 0.0                                                                 #
 # dyrot= 0.0                                                                 #
 # dzrot= 0.0                                                                 #
 # scale= 1.0                           -- Plot scale*f.                      #
 # width= 1000                          -- Width of the GIFs.                 #
 # boxed= yes                           -- Display Volume Box                 #
 # show= yes                            -- Show the mpeg                      #
 ##############################################################################
 # doit, ?, return, end, help                                                 #
 ##############################################################################

GdfidL's command Language

Variables

A Variable has a Name and a Value. You define or redefine a Variable with the Sequence sdefine(name, value) or a Sequence define(name, value). Whenever gd1 or gd1.pp encounter the Name of an already defined Variable, the Name is substituted by the Value of the Variable, and the Line is interpreted again.

Defining Variables from Outside

Both gd1 and gd1.pp can be supplied Options that define Variables from outside an Inputfile. The Syntax is gd1 -Dname=value. This way, you can e.g. compute Sispersion relations with simple Shell Scripts. Variables defined in this way are not automatically evaluated. ( sdefine(..,..) )
Example
#!/bin/sh
  # Given the proper "inputfile.gdf", this shell-Script computes the
  # dispersion Relation of some periodic Structure.
  for PHASE in 0 20 40 60 80 100 120 140 160 180
  do
      gd1 -DThisPhase=$PHASE < inputfile.gdf > out.Phase=$PHASE
  done

Arithmetic Expressions

Whenever gd1 or gd1.pp encounter the String eval(, the matching closing Brace is searched and the String inside the enclosing Braces is interpreted as an arithmetic Expression. The Value of the expression is transformed to a String and substituted for eval(expression).
Example
 echo (2*3)      # this outputs "(2*3)"
 echo eval(2*3)  # this outputs "6"
The arithmetic Expression may contain the arithmetic operators +,-,*,/,**,%. In addition to that, the boolean Operators ==,!=,<,>,<=,>= are handled. The result of applying a boolean Operator is an integer 0 or 1. Zero stands for false, and 1 for true.

The Functions abs(x), min(x,y), max(x,y), log(x), cos(x), sin(x), tan(x),
atan(x), atan2(x,y), mod(x,y), pow(x,y) are recognised and evaluated.

In every Context where a Number is required as a Parameter, an arithmetic Expression may be used. In these Contexts, enclosing the Expression in eval() is not required.

do-loops

Sections of the Input can be interpreted repeatedly via do loops: The Structure of a do loop is the same as in Fortran.
  do M1, M2, M3
     # Loop-Body
  enddo  # or 'end do'
The Loop-Body may itself contain do-loops, Macro Calls, whatever. The iteration Variable M1 is not restricted to Integer Values.
  do i= 1, 100, 1   # count upwards
     echo I is i
  end do
  do i= 100, 1, -1  # count downwards
     echo I is i
  end do
  do i= 1, 2, 0.1   # non integer step
     echo I is i
     echo 2*I is eval(2*i)
  end do

if elseif else endif

Conditional Interpretation of Part of an Inputfile is possible with if Blocks.
An if Block is:
  if (ARITHMETIC-EXPRESSION) then
     #
     # if-body
     #
  endif # or 'end if'
If the ARITHMETIC-EXPRESSION evaluates to something else than '0' then the Body of the If-Block is interpreted.

A general if block is:

  if (ARITHMETIC-EXPRESSION) then
     #
     # if-body
     #
  elseif (ARITHMETIC-EXPRESSION) then
     #
     # elseif-body
     #
  else
     #
     # else-body
     #
  endif

If-Blocks may be nested.

Macros

Anywhere in your Input you can define Macros. A Macro is enclosed between two Lines: The first Line contains the Keyword macro followed by the Name of the Macro. All Lines until a Line with only the Keyword endmacro are considered the Body of the Macro. When gd1 or gd1.pp find such a Macro, they read it and store the Body of the Macro in an internal Buffer.
Example
   #
   # This defines a macro with name 'foo'
   #
   macro foo
      echo I am foo, my first argument is @arg1
      echo The total number of arguments supplied is @nargs
   endmacro
When gd1 or gd1.pp find a Call of the Macro, the Number of the supplied Arguments is assigned to the Variable @nargs, and the Variables @arg1, @arg2, .. are assigned the Values of the supplied Parameters of the Call. Similiar to the user definable Variables (via sdefine), the Values of the Arguments are Strings. Of course, it is possible to have a String, e.g. '1e-4', which happens to be interpreted in the proper Context as a real Number.
Example
   #
   # this calls 'foo' with the arguments 'hi', 'there'
   #
   call foo(hi, there)
Macro Calls may be nested. The Body of a Macro may call another Macro.

Result-variables

gd1.pp makes its Results accessible as symbolic Variables. The Names of these Variables all start with @. The exact Name can be found in the Description of the Sections of gd1.pp. There are some other Variables as well that have not yet been described. The following Variables are defined as soon as a Database has been specified: gd1.pp has a special Variable @path. Its Value is a command String that would enter the current Section.

Supplied Macros

This Section documents four Macros that define a Sequence of secondary Computations to be performed in the Postprocessor gd1.pp. All four Macros are contained in the File
/usr/local/gd1/postprocessor-macros.

Q-Values

The quality Factor Q is defined as
\begin{displaymath}
Q = \frac{\omega W}{P}
\end{displaymath} (4.1)

where In the Section -wlosses we compute the wall Wosses via the Perturbation Formula. In the Section -energy we compute the stored Energy in the H-Field.

Q-Values: Real valued Fields

The following macro contains the Commands to evaluate the above Formula for a given resonant Field. This Macro is contained in the file /usr/local/gd1/postprocessor-macros.
macro QValue
  pushflags, noprompt, nomenu, nomessage
  define(QValue_PATH, @path)                  # remember current section
  -base                                       # goto the base of the branch-tree
  -energy                                     # compute stored energy
      quantity= h                             # ... we dont need to compute the
      solution= @arg1                         #     energy in the electric field
      doit                                    #     -- it has to be the same
  -wlosses                                    # Wall-losses
      doit
 echo
echo *** h-Energy   is @henergy
echo *** metalpower is @metalpower
  return
  define(QValue_value, eval(2*@pi*@frequency*2*@henergy/@metalpower))
  echo *** mode number       is @arg1
  echo *** frequency         is @frequency {Hz}
  echo *** QValue            is QValue_value {1}
# echo return path is : QValue_PATH
  QValue_PATH                                 # back to where we came from ...
  undefine(QValue_PATH)
  popflags
endmacro
With the Definition of the Macro available, we can compute the Q-Value of the first resonant Mode by saying:
   call QValue(1)
To compute the Q-Values of the first five Modes, we may say:
 do i= 1, 5
    call QValue(i)
 enddo

Q-Values: Complex valued Fields

For complex Fields (resonant fields computed with periodic boundary conditions or lossy resonant Fields), we have to integrate over the Real and imaginary Part separately:
macro perQValue
  pushflags, noprompt, nomenu, nomessage
  define(perQValue_PATH, @path)               # remember current section
  -base                                       # goto the base of the branch-tree
  -energy                                     # compute stored energy
      quantity= hre                           # ... we dont need to compute the
      solution= @arg1                         #     energy in the electric field
      doit                                    #     -- it has to be the same
# echo *** W_h of real part is @henergy
      define(hre_energy, @henergy)
      quantity= him
      doit
      define(him_energy, @henergy)
define(htot_energy, eval(hre_energy+him_energy) )
  -wlosses                                    # Wall-losses
      quantity= hre, doit
      define(hre_metalpower, @metalpower)
      quantity= him, doit
      define(him_metalpower, @metalpower)
      define(htot_metalpower, eval(hre_metalpower+him_metalpower))
# echo *** total h-Energy   is htot_energy
# echo *** total metalpower is htot_metalpower
  define(perQValue_value, eval(2*@pi*@frequency*2*htot_energy/htot_metalpower))
  echo
  echo *** mode number       is @arg1
  echo *** frequency         is @frequency {Hz}
  echo *** QValue            is perQValue_value {1}
# echo return path is : perQValue_PATH
  perQValue_PATH                              # back to where we came from ...
  undefine(perQValue_PATH)
  popflags
endmacro
With the definition of the Macro available, we can compute the Q-Value of the first resonant Mode by saying:
   call perQValue(1)
To compute the Q-Values of the first five Modes, we may say:
 do i= 1, 5
    call perQValue(i)
 enddo

Computing normalised Shunt Impedances $R/Q$

There are several Definitions for a normalised Shunt Impedance floating around. We take this one:
\begin{displaymath}
R/Q = \frac{V V^*}{2 \omega W}
\end{displaymath} (4.2)

where If one evaluates the Voltage seen by the Witness Particle, one arrives at the Result
\begin{displaymath}
V = \int\limits_{z=z_1}^{z=z_2}
E_z(x,y,z) e^\frac{{\rm j}\omega z}{\beta c_0}\; dz
\end{displaymath} (4.3)

for a Particle that travels in positive z-Direction from $z=z_1$ to $z=z_2$.

R/Q: Real valued Fields

The following macro contains the Commands to evaluate the above Formula for a given Real-Valued resonant Field. This Macro is contained in /usr/local/gd1/postprocessor-macros.
macro rshunt
  pushflags, noprompt, nomenu, nomessage
  define(rshunt_PATH, @path)                # remember current section
  -base                                     # goto the base of the branch-tree
  -energy                                   # compute stored energy
      quantity= e                           # ... we dont need to compute the
      solution= @arg1                       #     energy in the magnetic field
      doit                                  #     -- it has to be the same
# echo *** W_e is @eenergy
  return
  -lintegral                                # accelerating voltage
      direction= z, component= z
      startpoint= (0,0, @zmin)
      length= auto
      doit
# echo *** vabs is @vabs
  return
  define(rshunt_value_a, eval(@vabs **2/(2*@pi*@frequency*(2*2*@eenergy))))
  define(rshunt_value_r, eval(@vreal**2/(2*@pi*@frequency*(2*2*@eenergy))))
  define(rshunt_value_i, eval(@vimag**2/(2*@pi*@frequency*(2*2*@eenergy))))
  echo
  echo *** mode number         is @arg1
  echo *** frequency           is @frequency {Hz}
  echo ***
  echo *** shunt impedances as computed from | U * conjg(U) | :
  echo *** Shunt Impedance/Q   is rshunt_value_a {Ohms}
  echo *** Shunt Impedance/Q/m is eval(rshunt_value_a/@length) {Ohms/m}
  echo ***
  echo *** shunt impedances as computed from | Re(U) * Re(U) | :
  echo *** Shunt Impedance/Q   is rshunt_value_r {Ohms}
  echo *** Shunt Impedance/Q/m is eval(rshunt_value_r/@length) {Ohms/m}
  echo ***
  echo *** shunt impedances as computed from | Im(U) * Im(U) | :
  echo *** Shunt Impedance/Q   is rshunt_value_i {Ohms}
  echo *** Shunt Impedance/Q/m is eval(rshunt_value_i/@length) {Ohms/m}

## echo return path is : rshunt_PATH
  rshunt_PATH                               # back to where we came from ...
  undefine(rshunt_PATH)
## echo return path is : rshunt_PATH
  popflags
endmacro

R/Q: Complex valued Fields

For complex valued Fields, we evaluate separately the real Part and the imaginary Part of the Field. This is done with the following macro:
macro perrshunt
  pushflags, noprompt, nomenu, nomessage
  define(rshunt_PATH, @path)                  # remember current section
  -base                                       # goto the base of the branch-tree
  -energy                                     # compute stored energy
      quantity= ere                           # ... we dont need to compute the
      solution= @arg1                         #     energy in the magnetic field
      doit                                    #     -- it has to be the same
# echo *** W_e of real part is @eenergy
      define(ere_energy, @eenergy)
      quantity= eim
      doit
      define(eim_energy, @eenergy)
define(etotenergy, eval(ere_energy+eim_energy) )
  return
  -lintegral                                  # accelerating voltage
      direction= z, component= z
      startpoint= (0,0, @zmin)
      length= auto
      quantity= ere, doit
# echo *** vabs of real part is @vabs
      define(V_ere_re, @vreal) define(V_ere_im, @vimag)
      quantity= eim, doit
# echo *** vabs of imaginary part is @vabs
      define(V_eim_re, @vreal) define(V_eim_im, @vimag)
  return
define(vztotre, eval(V_ere_re-V_eim_im))
define(vztotim, eval(V_ere_im+V_eim_re))
define(vztotabs, eval((vztotre**2+vztotim**2)**0.5) )
  define(rshunt_value, eval(vztotabs**2/(2*@pi*@frequency*(2*etotenergy))))
  echo
  echo *** mode number       is @arg1
  echo *** frequency         is @frequency {Hz}
  echo *** Shunt Impedance   is rshunt_value {Ohms}
  echo *** Shunt Impedance/m is eval(rshunt_value/@length) {Ohms/m}
# echo return path is : rshunt_PATH
  rshunt_PATH                                 # back to where we came from ...
  undefine(rshunt_PATH)
  popflags
endmacro

stp2stl: Converts STEP File to STL-File

A OpenCascade-based STEP to STL File Converter is provided. The Converter reads a STEP-File and writes a STL-File. The Parameter '-deflection=XX' controls the Accuracy of the generated STL-File. A sample Shell Script which generates two STL-Files from the same STEP-File but with different Values for '-deflection=XX' is shown below.

#!/bin/sh

 for DEFL in 1e-4 1e-5
 do
    $GDFIDL_HOME/Linux-x86_64/stp2stl \
        -infile=/usr/local/gd1/examples/Vac-Quart_12WNSDVG1.8.stp \
        -deflection=$DEFL -outfile=/tmp/UserName/$DEFL.stl
 done
Parts of the generated STL-Data are shown in Figures 5.1 and 5.2.

Figure 5.1: A Part of the STL-Data generated with deflection set to 1e-4
\begin{figure}\epsfig{figure=stp2stl1.ps,width=18cm,bbllx=174pt,bblly=107pt,bburx=587pt,bbury=457pt,clip=} \end{figure}

Figure 5.2: A Part of the STL-Data generated with deflection set to 1e-5
\begin{figure}\epsfig{figure=stp2stl2.ps,width=18cm,bbllx=174pt,bblly=107pt,bburx=587pt,bbury=457pt,clip=} \end{figure}

Examples

This Chapter shows some Examples for the Interplay of Device Description, Computation, and Postprocessing.

There is no Example for computing Eigenvalues, as this is mentioned in great Detail in the Tutorial.

Wake Potentials

The Computation of Wakepotentials occurs in two Steps.

As a simple Example, we use a very strange Device where we want to compute the Wakepotentials of. The Input for gd1 is

 # /usr/local/gd1/examples-from-the-manual/wake-example-1.gdf

define(LargeNumber, 1000)
#
# The following picture shows a cut through the structure to be
# modelled and the variables associated to the lengths.
#
#
#                a               a               a
#        |<------------->|<-------------->|<----------->|
#
#                 -      ------------------
#                 ^      |                |
#               b |      |                |
#                 |      |                |
#        -----------------                ---------------  -
#        |                     beam                     |  |
#        |<-------------------------------------------->|  | d
#        |                                              |  |
#        ------------------------------------------------  -
#
#    x^
#    |-> z
#
 define( a, 1e-2 )
 define( b, 5e-3 )
 define( c, 5e-3 )
 define( d, 1e-2 )

 -general
    outfile= /tmp/UserName/wake-example
    scratch= /tmp/UserName/wake-example-scratch

    text()= A strange Device,
    text()= it serves only as an Example
    text()= for computing Wakepotentials.

 -mesh
define(STPSZE, 3*a/60 )
    spacing= STPSZE
    perfectmesh= no

    pxlow= 0, pxhigh= c+b
    pylow= -STPSZE, pyhigh= d
    pzlow= 0, pzhigh= 3*a

    cxlow= ele, cxhigh= ele
    cylow= ele, cyhigh= ele
    czlow= ele, czhigh= ele

    #
    # We enforce a Meshline at the Position of the Linecharge
    # by enforcing two Meshplanes.
    #
    xfixed(1, c/2, 0)
    yfixed(1, d/2, 0)

 -brick
    #
    # Fill the universe with Metal.
    #
    material= 1
       volume= (-LargeNumber, LargeNumber,\
                -LargeNumber, LargeNumber,\
                -LargeNumber, LargeNumber)
    doit

    #
    # Carve out the Waveguide.
    #
    mat 0
       xlow= 0, xhigh= c
       ylow= 0, yhigh= LargeNumber
       zlow= -LargeNumber, zhigh= LargeNumber
    doit

    #
    # Carve out the Resonator Box.
    #
    mat 0
       xlow= 0, xhigh= c+b
       ylow= 0, yhigh= LargeNumber
       zlow= a, zhigh= 2*a
    doit

 -volumeplot
   eyepos= ( 1.0, 2.30, 0.5 )
   showlines= yes
   scale= 2.5
   doit

 -fdtd
    -ports
       name= zlow, plane= zlow, modes= 0, doit
       name= zhigh, plane= zhigh, modes= 0, doit

    -lcharge
       charge= 1e-12   # 1 pAs
       sigma= 5e-3
       xposition= c/2
       yposition= d/2

 -fdtd
     doit
Figure 6.1: This Volumeplot shows the discretised Device. Although gd1 allows an inhomogeneous Mesh even when a particle Beam is present, this is not explicitely used here.
\begin{figure}\centerline{
\psfig{figure=wake-example00.ps,width=18cm,bbllx=25pt,bblly=197pt,bburx=586pt,bbury=802pt,clip=}
}\end{figure}
We start gd1 with the UNIX-Command:
   gd1 <  wake-example-1.gdf | tee out

The next Step is to tell the Postprocessor that we wish to see the Wakepotentials: The Commands for the Postprocessor gd1.pp are:

 -general, infile= @last
 -wakes
    doit
We get three Plots for the three Components of the Wakepotential at the (x,y) Position where the Line-Charge was travelling.
Figure 6.2: The z-Component of the Wakepotential at the (x,y)-Position where the exciting Line-Charge was travelling. For Reference, the Shape of the exciting Charge is plotted as well.
\begin{figure}\centerline{
\psfig{figure=wake-example00.wz.ps,width=14cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=}
}\end{figure}

\begin{figure}\centerline{ \psfig{figure=wake-example00.wx.ps,width=14cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} } \end{figure}
Figure 6.3: The two transverse Components of the Wakepotential at the (x,y)-Position where the exciting Line-Charge was travelling. For Reference, the Shape of the exciting Charge is plotted as well. The transverse Wakepotentials are computed as the Average of the transverse Wakepotentials nearest to the Position where the Line-Charge was travelling. The y-Component of the Wakepotential vanishes, as it should be.
\begin{figure}\centerline{ \psfig{figure=wake-example00.wy.ps,width=14cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}

Scattering Parameters

The Computation of scattering Parameters is via two Steps.

As a simple Example, we use a somewhat strange Device where we want to compute the scattering Parameters of. The Input for gd1 is
 # /usr/local/gd1/examples-from-the-manual/spar-example-1.gdf

 define(LargeNumber, 1000)

 define( a, 1e-2 )
 define( b, 5e-3 )
 define( c, 5e-3 )
 define( d, 1e-2 )

 define(FREQ, 20e9)

 -general
    outfile= /tmp/UserName/spar-example
    scratch= /tmp/UserName/spar-example-scratch

    text()= A strange Geometry, just an Example.

 -mesh
 define(STPSZE, 3*a/60 ) # Too large for MPI
# define(STPSZE, a/60 )
    spacing= STPSZE
    graded= yes, qfgraded= 1.2, dmaxgraded= @clight / FREQ / 40
    perfectmesh= no

    pxlow= 0, pxhigh= c+b
    pylow= -STPSZE, pyhigh= d
    pzlow= 0, pzhigh= 3*a

    cxlow= ele, cxhigh= ele
    cylow= ele, cyhigh= ele
    czlow= ele, czhigh= ele

 -brick
    #
    # Fill the Universe with Metal.
    #
    material= 1
       volume= (-LargeNumber, LargeNumber,\
                -LargeNumber, LargeNumber,\
                -LargeNumber, LargeNumber)
    doit

    #
    # Carve out the Waveguide.
    #
    mat 0
       xlow= 0, xhigh= c
       ylow= 0, yhigh= LargeNumber
       zlow= -LargeNumber, zhigh= LargeNumber
    doit

    #
    # Carve out Resonator Box.
    #
    mat 0
       xlow= 0, xhigh= c+b
       ylow= 0, yhigh= LargeNumber
       zlow= a, zhigh= 2*a
    doit

 -volumeplot
   eyepos= ( 1.0, 2.30, 0.5 )
   showlines= yes
   scale= 3
   doit

 -fdtd
    -ports
       name= Input, plane= zlow, modes= 1, doit
       name= Output, plane= zhigh, modes= 1, doit

    -pexcitation
       port= Input
       mode= 1
       amplitude= 1
       frequency= FREQ
       bandwidth= 0.7*FREQ

    -time
       #
       # tminimum: the minimum Time to be simulated
       # tmaximum: the maximum Time to be simulated
       #   If the Amplitudes have died down sufficiently
       #   at a Time between tmin and tmax,
       #   the Computation will stop.
       #
       tmin=   10/FREQ
       tmax= 1000/FREQ
       amptresh= 1e-3

 -fdtd
     doit
Figure 6.4: This Volumeplot shows the discretised Geometry.
\begin{figure}\centerline{ \psfig{figure=spar-example00.ps,width=18cm,bbllx=25pt,bblly=197pt,bburx=586pt,bbury=803pt,clip=} }\end{figure}
We start gd1 with the Unix-Command:
   gd1 < spar-example-1.gdf | tee out

The next Step is to tell the Postprocessor that we wish the scattering Parameters to be computed and plotted. In addition to the default Values, we want to see (Parts of) the Timedata that were recorded during the Time-Domain Computation, and we want to see the scattering Parameters in a Smith-Chart. The Commands for the Postprocessor gd1.pp are:

 -general, infile= @last
 -sparameter
    ports= all, modes= 1
    timedata= yes
    smithplot= yes, markerat 19e9, markerat 20e9, markerat 21e9
    doit
We get in total 9 Plots.
\begin{figure}\centerline{ \psfig{figure=spar-example00-excitation.0001.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} } \end{figure}
Figure 6.5: The Data of the Excitation. Above: The time History of the Amplitude that was excited in the Port with Name 'Input'. Below: The Spectrum of this Excitation.
\begin{figure}\centerline{ \psfig{figure=spar-example00-excitation.0002.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}

\begin{figure}\centerline{ \psfig{figure=spar-example00-Input-e_amp_of_mode-eq-0...
...ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} } \end{figure}
\begin{figure}\centerline{ \psfig{figure=spar-example00-Input_out_1-freq-abs.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} } \end{figure}
Figure 6.6: The Data of the scattered Mode '1' in the Port with Name 'Input'. Above: The time History of its Amplitude. This was computed by gd1. Below: The scattering Parameter as Amplitude Plot, and in a Smith-Chart. These Data are computed by gd1.pp by Fourier-Transforming the time History of this Mode, and dividing by the Spectrum of the Excitation.
\begin{figure}\centerline{ \psfig{figure=spar-example00-Input_out_1-freq-smith.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}

\begin{figure}\centerline{ \psfig{figure=spar-example00-Output-e_amp_of_mode-eq-...
...ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} } \end{figure}
\begin{figure}\centerline{ \psfig{figure=spar-example00-Output_out_1-freq-abs.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} } \end{figure}
Figure 6.7: The Data of the scattered Mode '1' in the Port with Name 'Output'. Above: The time History of its Amplitude. This was computed by gd1. Below: The scattering Parameter as Amplitude Plot, and in a Smith-Chart. These Data are computed by gd1.pp by Fourier-Transforming the time History of this Mode, and dividing by the Spectrum of the Excitation.
\begin{figure}\centerline{ \psfig{figure=spar-example00-Output_out_1-freq-smith.ps,width=10cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}

Figure 6.8: The Sum of the squared scattering Parameters. Since the Device is loss-free, this Sum should ideally be identical to '1' above the cut-off Frequency. The Sum of the computed Parameters is only very near the cut-off Frequency of the Modes unequal '1'.
\begin{figure}\centerline{ \psfig{figure=spar-example00-sum-power-freq.ps,width=14cm,bbllx=0pt,bblly=43pt,bburx=776pt,bbury=575pt,clip=} }\end{figure}

Computing Brillouin-Diagrams

Brillouin Diagrams are Plots of Eigenvalues (resonante Frequencies) as a Function of the Phase-Shift in periodic Structures. GdfidL allows Computation with specified Phase Shifts in x- y- and z-Direction simultaneously. So we can compute Brillouin diagrams in 3D-Periodic Structures, where the Plane-Normals of the Planes of Periodicity are in x- y- and z-Direction simultaneously.

The following Input defines an elemental Cell of such a periodic Structure.

 # /usr/local/gd1/examples-from-the-manual/brillo.gdf

 #
 # Assign a value to "PHASE", if it is not yet defined
 # via  "gd1 -DPHASE=XX"
 #
 if (! defined(PHASE) ) then
    define(PHASE, 45)
 endif

 #
 # What Part of the Brillouin-diagram do we want to compute?
 #
 #
 # part==1 : from Gamma to H : 0<kx<pi/d, ky=0,      kz=0
 # part==2 : from H to N     : kx=pi/d,   0<ky<pi/d, kz=0
 # part==3 : from N to P     : kx=pi/d,   ky=pi/d,   0<kz<pi/d
 # part==4 : from P to Gamma : 0 < (kx=ky=kz) < pi/d
 #

 #
 # Get the Value of PART by inclusion of a File:
 # the Content of the File is just
 #    "define(PART, 1)"
 # or "define(PART, 2)"
 # or "define(PART, 3)"
 # or "define(PART, 4)"
 include(this-part-of-brillo)

 if ( PART == 1 ) then
    define(XPHASE, PHASE)
    define(YPHASE, 000)
    define(ZPHASE, 000)
 endif

 if ( PART == 2 ) then
    define(XPHASE, 180)
    define(YPHASE, PHASE)
    define(ZPHASE, 000)
 endif

 if ( PART == 3 ) then
    define(XPHASE, 180)
    define(YPHASE, 180)
    define(ZPHASE, PHASE)
 endif

 if ( PART == 4 ) then
    define(XPHASE, PHASE)
    define(YPHASE, PHASE)
    define(ZPHASE, PHASE)
 endif

 define(INF, 10000.0 * @clight)
 define(MAG, 2) define(EL, 1)

 ##
 ## Geometry definitions
 ##
 define(LATTICE_D, @clight / 2 )
 define(RADIUS, LATTICE_D * 0.375 )

 #
 # Default Mesh Spacing.
 #
 define(STPSZE, RADIUS/10 )

 ##############
 ##############
 ##############
 ##############
 ##############
 -general
    outfile= /tmp/UserName/outfile
    scratchbase= /tmp/UserName/delete-me-

    text()= Lattice Constant d= LATTICE_D
    text()= Radius of the Spheres= RADIUS
    text()= r/d = eval(RADIUS/LATTICE_D)
    text()= 2r/d = eval(2*RADIUS/LATTICE_D)
    text()= stpsze= STPSZE
    text()= xphase: XPHASE
    text()= yphase: YPHASE
    text()= zphase: ZPHASE

 -mesh
    spacing= STPSZE
    graded= yes, dmaxgraded= 10*STPSZE
    qfgraded= 1.3
    perfectmesh= yes
 perfectmesh= no

    pxlow= -0.5*LATTICE_D, pxhigh= 0.5*LATTICE_D
    pylow= -0.5*LATTICE_D, pyhigh= 0.5*LATTICE_D
    pzlow= -0.5*LATTICE_D, pzhigh= 0.5*LATTICE_D

    xperiodic= yes, xphase= XPHASE
    yperiodic= yes, yphase= YPHASE
    zperiodic= yes, zphase= ZPHASE

    do ii= -1, 1, 1
       xfixed( 2, ii*LATTICE_D-RADIUS, ii*LATTICE_D+RADIUS )
       xfixed( 2, (ii-0.1)*LATTICE_D, (ii+0.1)*LATTICE_D )

       yfixed( 2, ii*LATTICE_D-RADIUS, ii*LATTICE_D+RADIUS )
       yfixed( 2, (ii-0.1)*LATTICE_D, (ii+0.1)*LATTICE_D )

       zfixed( 2, ii*LATTICE_D-RADIUS, ii*LATTICE_D+RADIUS )
       zfixed( 2, (ii-0.1)*LATTICE_D, (ii+0.1)*LATTICE_D )
    enddo

 ##############

 -brick
    #
    # Fill the Universe with Vacuum.
    #
    material= 0
       volume= (-INF,INF, -INF,INF, -INF,INF)
    doit


 define(M3, 1)
 #
 # Define square Lattice.
 # Only a Part of these Spheres end up being within
 # computational Volume.
 #
 do iz= 0, 1, 1
    do ix= 0, 1, 1
       do iy= 0, 1, 1
          #
          # A Sphere with Center at
          # ( ix*LATTICE_D, iy*LATTICE_D, iz*LATTICE_D )
          #
          -gbor
             material= M3
                origin= ( ix*LATTICE_D, \
                          iy*LATTICE_D, \
                          iz*LATTICE_D )
                rprimedirection= ( 1, 0, 0 )
                zprimedirection= ( 0, 0, 1 )
                range= ( 0, 360 )

                clear
                point= ( -RADIUS, 0 )
                   arc, radius= RADIUS, type= clockwise, size= small
                point= ( RADIUS, 0)
             doit
       enddo
    enddo
 enddo

 #
 # The connecting Rods in x-Direction.
 #
 do iz= 0, 1, 1
    do iy= 0, 1, 1
       -gccylinder
          material= M3
             radius= 0.1*LATTICE_D
             length= INF
             origin= ( -INF/2, \
                       iy*LATTICE_D, \
                       iz*LATTICE_D )
             direction= ( 1, 0, 0 )
          doit
    enddo
 enddo

 #
 # The Connecting Dods in y-Direction.
 #
 do iz= 0, 1, 1
    do ix= 0, 1, 1
       -gccylinder
          material= M3
             radius= 0.1*LATTICE_D
             length= INF
             origin= ( ix*LATTICE_D, \
                       -INF/2, \
                       iz*LATTICE_D )
             direction= ( 0, 1, 0 )
          doit
    enddo
 enddo

 #
 # The connecting Rods in z-Direction.
 #
 do ix= 0, 1, 1
    do iy= 0, 1, 1
       -gccylinder
          material= M3
             radius= 0.1*LATTICE_D
             length= INF
             origin= ( ix*LATTICE_D, \
                       iy*LATTICE_D, \
                       -INF/2 )
             direction= ( 0, 0, 1 )
          doit
    enddo
 enddo

 #
 # Definition of the Material Properties.
 #
 -material
    material= M3, type= electric


 #
 # What does the Materialdistribution look like?
 #
 -volumeplot
##    doit

 #################
 #
 # Computation of the Eigenvalues.
 #
 -eigenvalues
    solutions= 20
    estimation= 2.8
    pfac2= 1e-2
    passes= 2

    doit

 end
To compute the four Parts of the Brillouin-Diagram, we use a Shell-Script. This Shell-Script starts a Program four times. That Program starts gd1 several times to compute the Frequencies for different Phase-Shifts. This is the Shell-Script:
#!/bin/sh

 #
 # Compile the program which starts "gd1" several times
 #
 f77 brillo.f -o brillo.a.out

 for part in 1 2 3 4
 do
    #
    # (re)create the file that defines which part of the
    # Brillouin diagram is to be computed:
    #
    echo "define(PART, $part)" > this-part-of-brillo

    #
    # compute..
    ./brillo.a.out

    #
    # save the result, and display
    #
    cp brillo.mtv brillo.part=$part.mtv
    mymtv brillo.part=$part.mtv &

 done

 #
 # compile the program that combines the four parts
 # to a single Brillouin diagram of a 3D structure,
 # execute it,
 # and display the result..
 #
 f90 a3dbrillo.f
 cat brillo.part=[1-4].mtv | a.out
 mymtv2 3D-brillo.mtv &

The following is the Source of the Program that starts gd1 several times to compute the Frequencies for different Phase-Shifts:

!
! /usr/local/gd1/examples-from-the-manual/brillo.f90
!
 PROGRAM Bla

 IMPLICIT NONE
 CHARACTER(LEN= 400) cmd

 REAL, DIMENSION(300,1000) :: f0
 REAL, DIMENSION(1000) :: ph0

 INTEGER :: i11, i19, NMode, np, ip, Mode, iDum
 REAL :: af, ap, p0, p1, Phase, Acc, f

    i11= 11
    i19= 19
    OPEN (UNIT= i19, &
          FILE= 'brillo.mtv')

    WRITE (UNIT= i19, FMT= 90)
 90 FORMAT( &
      '$ DATA= CURVE2D NAME= "Brillouin-Diagramm"',/, &
      '% linetype= 0',/, &
      '% markertype= 3',/, &
      '% equalscale= false',/, &
      '% fitpage= false',/, &
      '% xyratio= 3',/, &
      '% xlabel= "Phase-shift"',/, &
      '% ylabel= "Frequency"',/, &
      '% comment= "no comment"',/  )

    af= 0
    ap= 0

    NMode= 15

! p0: First Phase
! p1: Last Phase
! np: Number of Phases

    p0= 0.
    p1= 180.
    np= 41

    DO ip= 1, np, 1
       Phase= p0+(ip-1)*(p1-p0)/FLOAT(np-1)
       ph0(ip)= Phase
       WRITE (UNIT= cmd, FMT= 81) Phase
 81    FORMAT( &
         ' gd1 "-DPHASE=', F8.2, '"< brillo.gdf ', &
         '| tee brillo.tmp | grep "for me" > brillo.out' )
 write (UNIT= 0, FMT= '(1X,4711(A))') ' cmd:', TRIM(cmd)
       CALL system( cmd )
       OPEN (UNIT= i11, &
             FILE= 'brillo.out')
       Mode= 0
  100    CONTINUE
       DO
          READ (UNIT= i11, FMT= *, ERR= 199, END= 199) iDum, f, acc
          IF (acc < 0.5) THEN
             Mode= Mode+1
             IF (Mode <= NMode) f0(Mode,ip)= f
             WRITE (UNIT= i19, FMT= 71) Phase,f
 write (0,*) Phase, f, acc
             af= MAX(af, f)
             ap= MAX(ap, Phase)
          END IF
       END DO
 199   CONTINUE
       CLOSE (UNIT= i11)
    END DO

 71 FORMAT( '@ point x1=', 1P, E12.6, ' y1=', E12.6, &
            ' z1= 0 markertype=1', ' markersize= 1' )

    DO Mode= 1, NMode, 1
       WRITE (UNIT= i19, FMT= *)
       DO ip= 1, np, 1
          WRITE (UNIT= i19, FMT= *) ph0(ip),f0(Mode,ip)
       END DO
    END DO
    WRITE (UNIT= i19, FMT= *)
    WRITE (UNIT= i19, FMT= 99) 0., 0., 0., af, ap, af
 99 FORMAT( 3(1X, 1P, 2(E12.6, 1X), /), /)
!
!   **
!   ** write the uninterpreted data
!   **
!
    DO ip= 1, np, 1
       WRITE (UNIT= i19, FMT= '(//,A,F14.2)') ' # Phase:', ph0(ip)
       DO Mode= 1, NMode, 1
          WRITE (UNIT= i19, FMT= '(A,1X,1P,E20.7)') '#', f0(Mode,ip)
       END DO
    END DO

 END PROGRAM Bla
The resulting Plots are presented in figure 6.9.
Figure 6.9: The four Parts of the Brillouin-Diagram.
\begin{figure}\centerline{ \psfig{figure=brillo.part1-4.PS,width=10.5cm} }\end{figure}

The following is the Sourcecode of the Program that combines the four Parts of the Brillouin-Diagram into a single Plot:

*
* /usr/local/gd1/examples-from-the-manual/a3dbrillo.f
*
* usage:
*
* cat brillo.part=[1-4].mtv | a.out
* mymtv2 3D-brillo.mtv
*
*
      DIMENSION f0(300,1 000), ph0(1 000)
      REAL, DIMENSION(100) :: Phase0, scale
      CHARACTER(LEN=1000) :: str
*
      i11= 11
      i19= 19
      OPEN (UNIT= i19
     1    , FILE= '3D-brillo.mtv')
*
      WRITE (UNIT= i19, FMT= 9000)
 9000 FORMAT(
     1 '$ DATA= CURVE2D NAME= "Brillouin-Diagramm"',/,
     2 '% linetype= 0',/,
     3 '% markertype= 3',/
     4 '% equalscale= false',/,
     5 '% fitpage= false',/,
     6 '% xyratio= 3',/,
     7 '% xlabel= "normalised Phase-shift"',/,
     8 '% ylabel= "Frequency"',/,
     9 '% comment= "no comment"',/
     x )
*
      af= 0.
      ap= 0.
*
      NMode= 10
*
      phase0(1:4)= (/ 0.0,
     1                1.0,
     2                2.0,
     3                4.0  /)
      scale(1:4)= (/ 1./180.0,    !! Gamma to H
     2               1./180.0,    !!     H to N
     3               1./180.0,    !!     N to P
     4              -1./180.0 /)  !!     P to Gamma
*
      Phase Last= 0.
      np= 1
      str= ' '
      DO
         DO
            IF (INDEX(str, '# phase:') .NE. 0) THEN
               jj= INDEX(str, '# phase:')+LEN('# phase:')
               READ (UNIT= str(jj:), FMT= *) phase
               IF (phase .LT. Phase Last) THEN
                  np= np+1
               ENDIF
               Phase Last= phase
               EXIT
            ENDIF
            READ (UNIT= *, FMT= '(A)', END= 10) str
         ENDDO
      write (*,*) ' phase:', phase
         pp= Phase0(np)
         ph0(np)= pp+phase*scale(np)
*
         mode= 0
         DO mode= 1, NMode, 1
            READ (UNIT= *, FMT= '(A)', END= 10) str
            READ (UNIT= str(2:), FMT= *, IOSTAT= iostat) f
            IF (iostat .NE. 0) EXIT
      write (*,*) ' pp, f:', pp+phase*scale(np), f
            f0(mode,np)= f
            WRITE  (UNIT= i19, FMT= 7010) pp+phase*scale(np),f
            af= MAX(af,f)
            ap= MAX(ap,pp+phase*scale(np))
         ENDDO
      ENDDO
   10 CONTINUE
*
 7010 FORMAT(
     1 '@ point x1=',E12.6,' y1=',E12.6,' z1= 0 markertype=1',
     2 ' markersize= 1')
*
      WRITE (UNIT= i19, FMT= *)
      WRITE (UNIT= i19, FMT= 99) 0.,0.,0.,af,ap,af
 99 FORMAT(3(' ',2(E12.6,' ')/),/)
*
      END
The resulting Plot is presented in Figure 6.10.
Figure 6.10: The four Parts of the Brillouin-Diagram combined.
\begin{figure}\centerline{ \psfig{figure=a3dbrillo.PS,width=10.5cm} }\end{figure}

This is the End of this Document


Footnotes

... File1.1
This will actually be a Directory. The Reason is: For current (2014) Workstations, it is quite easy to generate Data in excess of 2GBytes. But many current Filesystems and OS-Tools cannot handle Files larger than 2GBytes. So we chose to organise the computed Data as a Hierarchy of Files. A Directory is a Hierarchy of Files, so we used just that.
... stop.1.2
This was implemented for some User who uses this Facility to use a Queue for short running Jobs for his long running Jobs. He puts a Computation which will run for eg 10 Hours into a Queue where Jobs are killed after running for more than 1 Hour. He instructs GdfidL to write these Restartfiles and stop after writing them. After a Job was run for less than 1 Hour, a Script inspects the Logfiles, and if the Computation needs to continue, the next Job is put into the short-Runner Queue, which uses the previously written Restartfiles to continue the Job.
... System1.3
AutoCAD can export its Data as a STL-file. The Command is 'stlout'.
... T\"uckmantel1.4
J. Tückmantel, `Urmel with a High Speed and High Precision Eigenvector Finder', CERN/EF/RF 83-5, 11 July 1983
...41.5
J. Tückmantel `An improved version of the eigenvector processor SAP applied in URMEL', CERN/EF/RF 85-4, 4 July 1985