1. The Cockcroft Institute and The University of Manchester
WP HOM CD
I.R.R.Shinton, R.M.Jones
Contribution from
The Cockcroft Institute and
The University of Manchester

2. Normalisation in HFSS
In the normalisation process it is important to note that HFSS renormalized the port impedance values to a specific impedance value (denoted by the user). This has the effect of removing the frequency dependency from the port impedances.
where
• S is the n x n generalized S-matrix.
• I is an n x n identity matrix.
• Z0 is a diagonal matrix having the characteristic impedance (Z0) of each port as a diagonal value.
where
• Z is the structure’s unique impedance matrix.
• ZÙ and YÙ are diagonal matrices with the desired impedance and admittance as diagonal values. For example, if the matrix is being renormalized to 50 ohms, then ZÙ would have diagonal values of 50.
Visualize the generalized S-matrix as an S-matrix that has been renormalized to the characteristic impedances of the structure. Therefore, if a diagonal matrix containing the characteristic impedances of the structure is used as ZÙ in the above equation, the result would be the generalized S-matrix again.

3. HFSS 11.2 Transmission pipe test – longer pipe
Use HFSSv11.2
Driven modal sweep
Modelled with one mode the TE11 mode
Used parameters in table
All values are Un-normalised
Manual meshed with 5000 volume elements at 5GHz
Pipe draw from (0,0,0)

4. HFSS 11.2 Transmission pipe test – longer pipe
Use HFSSv11.2
Driven modal sweep
Modelled with one mode the TE11 mode
Used parameters in table
All values are Normalised to 50Ω/m per port
Manual meshed with 5000 volume elements at 5GHz
Pipe draw from (0,0,0)
Note that CST has a similar option for the renormalisation of modes

5. 3.9GHz 4 cavity string
Dipole band 1
1MHz frequency step
Cascade
Results

6. Increasing computational throughput
Now with the correct geometry for the 1 leg HOM coupler I can generate some results using the cascading scheme.
Given the time constraints it would not be possible to run discrete sweeps with a 1MHz frequency step – although the method is accurate and is stable below cut-off, it is too slow i.e. a frequency range of 4GHz to 5GHz at 10MHz steps would take 7hrs per unit cell, there are 7 unit cells so 7x10x7=~21days….
In order to speed up the process I have re-looking into using the fast frequency sweep (uses ALPS method) in HFSS. This method although quick is prone to errors and has difficulty in calculations below cut-off.
I have re-run and cross-checked some of the Discrete sweeps against their Fast sweep comparisons in order to check that the results, given the meshing, are believable.

7. 3.9GHz unit cells C8 HOM power C8 HOM pickup C3 HOM power - Redrawn
All unit cells are calculated in HFSS using 30um surface mesh and volume mesh
Fast frequency sweep is used – mesh at 5GHz, in order to reduce calculation time
First band sweep is between 4GHz and 5GHz
1MHz frequency step is used
10 modes per port
C8 HOM power
C8 HOM pickup
C3 HOM power
- Redrawn
Middle cell
C3 HOM pickup
- Redrawn

8. Throughput book keeping

9. HOM coupler book keeping

10. 3.9GHz unit cells Cavity mode polarisation imposed alignment1 2 3 4 5 7 8 10 6 9

11. 3.9GHz unit cells Coaxial mode polarisation imposed alignment1 2 3 4 5 6 8 10 7 9

12. 3.9GHz unit cells Imposed polarisation alignment
1,4,7,9
3,5,8,10
2,5,8,10
1,2,4,6,7,9

13. Cascade Benchmarking: C3 HOM pickup to a Middle cell
Dominant Coaxial TM mode into Dominant cavity TE11 mode
Cascade Calculation time: 22s
Time per Unit cell in HFSS: ~7hrs
Full HFSS simulation time: ~14hrs

14. Cascade Benchmarking: C3 HOM pickup to a Middle cell
Dominant Pipe TE11 mode into Dominant cavity TE11 mode
Cascade Calculation time: 22s
Time per Unit cell in HFSS: ~7hrs
Full HFSS simulation time: ~14hrs

15. Cascade Benchmarking: Remarks
Since there are no TE “Cavity” modes propagating below the cut-off of ~4.4GHz we would expect to see a discrepancy in the Cascade below this value
This is because the Cascade propagation is based on there being at least one propagating mode for the calculation to work

16. Dominant Coaxial TM mode into Dominant coaxial TM mode
Full 4 cavity stringC3 HOM pickup of Cavity 1 to HOM pickup of Cavity 4
Dominant Coaxial TM mode into Dominant coaxial TM mode
No Pipes…. Renormalized to 1Ω
Cascade Calculation time: 4000s
Time per Unit cell in HFSS: ~4hrs for MHz steps

17. Dominant Coaxial TM mode into Dominant coaxial TM mode
Full 4 cavity stringC3 HOM pickup of Cavity 1 to HOM pickup of Cavity 4
Dominant Coaxial TM mode into Dominant coaxial TM mode
Renormalized to 1Ω
Cascade Calculation time: 4000s
Time per Unit cell in HFSS: ~4hrs for MHz steps
Here the data file that it is compared to is c1p2c4p2 – i.e. complete 4 cavity string.
Question of Zo normalisation to use
Cascading results below cut-off suspect – due to aforementioned propagation requirements.

18. Cable values from our friend Pei in DESY?
At present my calculations rely upon correctly setting the value for Zo so that the results can be directly compared to the experimental results i.e. I need to renormalize my results….

19. Things to do for LINAC2010 with Cascade calculations
1) Determine HOM port intrinsic impedances (Zo) from experimental data (Pei? More results other than SOL?)
2) Cascade full 3.9GHz module for first dipole band - DONE
3) Put in errors/change pipe lengths and look at variations in HOM’s
4) Repeat steps 3) and 4) for the second dipole band – IN PROGRESS
5) Repeat all results with finer frequency steps (time permitting) – DONE
The Pipe sections will be added analytically to the calculation.