# Where do the peaks in the impedance of a flange come from?

When you are computing wakepotentials and impedances of a beampipe flange, you will see not decaying signals in the wakepotentials and therefore peaks in the impedance. This writeup is an attempt to explain what kind of fields are responsible for these.

# Computing Wakepotentials

The wakepotentials are computed when you perform a time domain computation with a relativistic line charge as excitation. The relevant part of such an inputfile is:
 -fdtd
-ports
name= beamlow,  plane= zlow,  modes= 0, npml= 30, doit
name= beamhigh, plane= zhigh, modes= 0, npml= 30, doit
-lcharge
charge= 1e-12
xposition= 0
yposition= OFFSET  # The y-offset of the relativist line charge
shigh= 6   # Perform a long range wakepotential computation.

We start the computation of the time dependet fields with the command:
    single.d1 -host=ALL < flange0.gdf | tee out

The parameter  -host=ALL  tells single.gd1 to perform the computation in parallel on all processors that are specified in the parallel virtual machine. The computation will take some hours on a single CPU of a 2003 workstation.

The inputfile for this flange is flange0.gdf

# Looking at the results

We start the postprocessor to compute the wakepotentials and impedance from the data which were recorded during the time domain computation.

We start the postprocessor, gd1.pp, and use him interactively:
Input for gd1.pp:

     -general, infile= @last

-wakes
impedance= yes
doit

 -------
Thats it.

When we change the parameter DS1 in the inputfile, we are changing the gap width of the flange. We will now study how the impedance depends on that gap width.

# Resonant fields in a closed structure

The structure itself is symmetric with respect to the plane z=0. We model only half of the structure, the lower half, by specifying  pzhigh= 0, czhigh= electric. The lower border of the computational volume is specified as a magnetic wall.

The computed resonant frequencies of the first 10 resonant modes in a structure where the condition at the lower plane of the computational volume (in the beampipe) is a magnetic wall, are 1.77, 1.83,, 3.9, 4.1, 4.4, 5.5, 5.6, 6.3, 6.5, and 6.7 GHz.