Modelling the geometry

Figure 1.2: A drawing of the main cavity.

The cavity we want to analyse is essentially a body of revolution. There are two plungers attached, that are presumably for tuning the cavity. In addition, a small tube is attached, that is probably used for maintaining the vacuum.

In the first step we model the cavity and the beam-pipes. We do this by specifying a polygonal description of the boundary in the r-z-plane. The inputfile that describes the boundary is:

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

 #
 # We define symbols that will be used to describe our cavity:
 # The names of the symbols can be up to 32 characters long,
 #
 define(OuterRadius   , 46.23e-2/2 )
 define(InnerRadius   , 13.00e-2/2 )
 define(GapLength     , 27.60e-2   )
 define(CurveRadius   ,  0.585e-2  )
 define(BeamPipeRadius, 14.17e-2/2 )
 define(TaperLength   , 13.2e-2    )

 -brick
     material= EL
     xlow= -INF, xhigh= INF
     ylow= -INF, yhigh= INF
     zlow= -INF, zhigh= INF
     doit
 
 #
 # we carve out the body of the cavity
 #

 -gbor
    material= 0
    origin= (0,0,0)
    zprimedirection= (0,0,1)
    rprimedirection= (1,0,0)
    range= (0,360)

    clear      # clear any old polygon-description
      # point= (z,r)
    point= ( -(GapLength/2+TaperLength+10e-2), 0              ) # p1
    point= ( -(GapLength/2+TaperLength+10e-2), BeamPipeRadius )
    point= ( -(GapLength/2+TaperLength      ), BeamPipeRadius )
    point= ( -(GapLength/2+CurveRadius      ), InnerRadius    )
      arc, radius= CurveRadius, size= small, type= counterclockwise
    point= ( -(GapLength/2                  ), InnerRadius+CurveRadius )
    point= ( -(GapLength/2                  ), OuterRadius    )
     ## crossing z=0 plane
    point= (  (GapLength/2                  ), OuterRadius    )
    point= (  (GapLength/2                  ), InnerRadius+CurveRadius )
      arc, radius= CurveRadius, size= small, type= counterclockwise
    point= (  (GapLength/2+CurveRadius      ), InnerRadius    )
    point= (  (GapLength/2+TaperLength      ), BeamPipeRadius )
    point= (  (GapLength/2+TaperLength+10e-2), BeamPipeRadius )
    point= (  (GapLength/2+TaperLength+10e-2), 0              )
 show= now
 doit

 -volumeplot
    doit

This inputfile can be found as "/usr/local/gd1/Tutorial-SRRC/doris00.gdf". When we feed this file into gd1 via the command "gd1 $<$ doris00.gdf", we get a desktop similiar to the one shown in figure 1.3

Figure 1.3: Screenshot of the desktop when the inputfile doris00.gdf has been fed into gd1. gd1 has popped up an instance of mymtv2 that shows the outline of the specified polygon.

gd1 does not what we want, we do not get a "volumeplot", although we requested one. But gd1 gives us a hint what we made wrong:

 volumeplot>     doit
 # I am checking the mesh settings..
   .. plane x= xlow  in "-mesh" is undefined..
   .. plane x= xhigh in "-mesh" is undefined..
   .. plane y= ylow  in "-mesh" is undefined..
   .. plane y= yhigh in "-mesh" is undefined..
   .. plane z= zlow  in "-mesh" is undefined..
   .. plane z= zhigh in "-mesh" is undefined..
 *** section -mesh: "spacing= undefined"..
 *** errors in "mesh"..
 *** Since this not seems to be an interactive session,
 *** I decide to treat this as a fatal error.
 *** Fix the input.
 stop

When we say "doit" in the section "-volumeplot", gd1 tries to generate the mesh. But in order to generate the mesh, gd1 needs to know

• what the extreme coordinates of the computational volume shall be,
• what the default mesh spacing shall be.

All these informations have to be given to gd1 before a volumeplot is requested. Since gd1 has detected that it is fed by an inputfile and is not used interactively, it stops as soon some essential information is not available. When not run interactively, gd1 also stops when some syntax error is present in the inputfile.

To give gd1 the needed information, we change our inputfile. We insert the following lines somewhere before "-volumeplot":

 ###
 ### We define the borders of the computational volume,
 ### and we define the default mesh-spacing.
 ###
 -mesh
     spacing= InnerRadius/15
     pxlow= -1.1*OuterRadius, pxhigh= 1.1*OuterRadius
     pylow= -1.1*OuterRadius, pyhigh= 1.1*OuterRadius
     pzlow = -(GapLength/2+TaperLength+9e-2)
     pzhigh= +(GapLength/2+TaperLength+9e-2)

The so edited inputfile can be found as "/usr/local/gd1/Tutorial-SRRC/doris01.gdf".

When we feed gd1 with this inputfile (gd1 $<$ doris01.gdf) we get a screen similiar to the one shown in figure 1.4

Figure 1.4: Screenshot of the desktop when the inputfile doris01.gdf has been fed into gd1. gd1 has popped up an instance of gd1.3dplot that shows the generated mesh.