Frequencies as a function

Transverse Kickfactors

Since our structure is no longer rotational symmetric, the shunt-impedance of the monopole-mode is no longer independent of the position of the testcharge. Since a real charge cloud has a finite extension in the x-y plane, the charges at different (x,y) positions will experience a different accelerating voltage. This gives rise to an energy spread. We can again use the shell-script of page to compute the variation of the accelerating voltage as a function of the x-position. For convenience, the shell script '/usr/local/gd1/Tutorial-SRRC/x-voltages.x' is shown here again:

#!/bin/sh

 #
 # feed the postprocessor with a 'here'-document,
 # 'tee' the output of the postprocessor to the file "pp.out"
 #

 (gd1.pp | tee pp.out) << EOF

    nomenu, noprompt, nomessage     # no unneccessary output
    -general, infile= @last
    -lintegral
       symbol= e_1
       direction= z, component= z
       do ix= 1, @nx
          startpoint= ( @x(ix), 0, @zmin )
          doit
          echo @x0 @vreal @vimag # <= x, vreal, vimag
       enddo
    end
EOF

 #
 # Write a PlotMtv-header to "x-voltages.mtv".
 #
 # Process the file "pp.out":
 # 'grep' the lines with the pattern "vreal"
 #
 echo \$ DATA= COLUMN  >  x-voltages.mtv
 echo x vreal  vimag   >> x-voltages.mtv

 grep vreal pp.out     >> x-voltages.mtv

 #
 # now start "mymtv2" to display the data:
 #
 mymtv2 -mult -landscape x-voltages.mtv

The resulting plot is shown in figure 7.1.

Figure 7.1: A plot of the real part and imaginary part of the accelerating voltage of the monopole mode in the cavity with plungers. Only the real part would be nonzero, if the symmetry plane at z=0 would not have been used. One can clearly see that the accelerating voltage no longer is independent of the x-position.

There will of course be a variation of the voltage on the y-position as well. One could analyse this with a similiar shell script. Frequencies as a function