1. MDI: Trapped modes and other power losses
Alexander Novokhatski, Eleonora Belli, Miguel Gil Costa
Michael K. Sullivan and Roberto Kersevan
CERN and SLAC National Accelerator Laboratory
FCC week 2017
May 31, 2017, Berlin
A. Novokhatski 5/31/17

2. Outline
Why do we need to pay attention to the shape of the Interaction Region beam pipe?
An unavoidable trapped mode
Possible smooth pipe connections
Status of the trapped mode analyses
A proposal to use a HOM absorber
Prediction for IR HOMs heating
Conclusion and future steps
A. Novokhatski 5/31/17

3. Why do we need to pay attention to the shape of the IR beam pipe?
In terms of collective effects, the dominant issue is the relatively high beam current (1.45 A) that must be supported in each ring of the electron-positron FCC for Z-production.
A beam circulating in a storage ring interacts with its surroundings electromagnetically by inducing image currents in the walls of the vacuum chamber and exciting Higher Order Modes in the chamber elements, such as RF cavities, kickers, vacuum valves, collimators, bellows, BPM electrodes and the Interaction Region.
Beam pipes of two rings are combined into one pipe in the IR.
Because of the complicated IR geometry a lot of electromagnetic power can be radiated. Some part of radiation will propagated out of the IR, but some may stay inside in the form of trapped wake fields.
A. Novokhatski 5/31/17

4. Main HOMs effects in IR (all are negative)
The frequency of some HOMs can be in a resonance with a harmonic of the revolution frequency and the amplitude will grow exponentially and can reach a high value.
In practice this happens often.
Heating of the beam pipe walls
Temperature and vacuum rise
Decreasing the pumping speed due to the large temperature rise
Pipe deformations and vacuum leaks
Melting of thin shielded fingers
Breakdowns and multipacting
Vacuum spikes
Beam aborts
Electromagnetic waves can go outside vacuum chamber through pump high voltage electrodes
Interaction with sensitive detector electronics
All effects lead to increasing the background or unstable operation.
Examples from the PEP-II operation can be found in NIM A 735(2014)349–365
A. Novokhatski 5/31/17

5. An unavoidable trapped mode
Trying to find an optimum geometry for IR with minimum electromagnetic wave excitation (minimum impedance), we discovered one mode, which stays even in a very smooth geometry.
First calculations were done using a flat version of the code NOVO for a flat geometry of IR. This mode is situated near the connection of the two pipes.
This mode has a longitudinal electrical component and can be easily excited by electron and positron beams. + -
Pipe
connection
Metal walls
electric field lines
beam
A surface current has also a longitudinal slope
beam
A. Novokhatski 5/31/17

6. Possible smooth pipe connections
Among other configurations for the geometry of the IR beam pipe, which has the smallest impedance, we considered three different models of IR with the same diameter of incoming pipes and of a central pipe – 30 mm in a diameter.
The incoming pipes are smoothly squeezed to the half circle shape in order to merge into the central pipe with a constant diameter.
The incoming pipes near the connection are circular pipes. The central part near the pipe connection has a transition to an approximately elliptical shape of a double size in the horizontal direction. The connection of two pipes and the elliptical shape contains some small sharp transitions.
Each pipe near the connection has a transition to a half of a special shape determined by the shape of the transition from the central pipe (a proposal from Oide Katsunobu). A full smooth geometry.
We will show details of these models and make a comparison between the smoothed geometries 1 and 3.
A. Novokhatski 5/31/17

7. All models are based on the M
All models are based on the M. Sullivan design: MDI mini workshop, CERN, January 2017, updated May 2017
A. Novokhatski 5/31/17

8. Current status of the HOMs analyses
Eleonora Belli did a tremendous work for electromagnetic calculations in Interaction Region.
We calculate wake potentials of a 4m long main part of the IR.
Initially we designed the IR model using the CST code editor, but we had a problem with the mesh distribution for a smooth IR geometry.
As this was an important point we decided to use CAD files as an input file for CST and HFSS codes.
We got a support and professional files from Miguel Gil Costa.
New approach for the wake field and eigen mode simulation using CAD files from “CATIA” for Interaction Region.
Established the file format and additional file description for better communication between “CATIA” and “CST”.
A. Novokhatski 5/31/17

9. Model 1. Squeezed incoming pipes.
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10. We found one trapped mode
30 mm
Electric field line distribution
Same field structure as for the unavoidable mode
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11. Wake potential and spectrum
Wake potential describes the integrated effect of the wake fields along the beam trajectory
f=5.78 GHz
A note: a positive value of the real part of the wake field spectrum shows a good quality of the calculation of the wake potential.
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12. Model 2. Small sharp transition. We found also one trapped mode at 5
Model 2. Small sharp transition. We found also one trapped mode at 5.67 GHz.
A. Novokhatski 5/31/17

13. Model 3. Transitions design. Miguel Gil Costa
General view
Central round pipe 30 mm
Transition from round to an “ellipse”
Transition of incoming circular pipes 30 mm to half of an “ellipse”
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14. All smooth geometrical transitions.
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15. Inner view
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16. We also found one mode, but less frequency 3.46 GHz
Model 3
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17. Loss frequency integral calculated from the spectrum of wake potential of a 2.5 mm bunch
Model 3
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18. A trapped mode. Same field structure.
65 mm
electric field lines
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19. The structure of the mode field distribution shows how we can capture it with minimum disruption of the image currents of the beam field.
Electric field lines in this place are perpendicular to the beam trajectory
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20. We can make longitudinal slots oriented perpendicular to the HOM electric field, which allow the mode field to easily propagate though these slots. At the same time, the beam field will not pass through. Then we can put a water-cooled absorber above the slots.
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21. We have already found some initial positions for the slots.
cupper blocks
absorbing tiles
inner view
water pipes
slots
HOM absorber will not only absorb the mode, but also capture some propagating fields
A. Novokhatski 5/31/17

22. To calculate the radiation power we use a loss frequency integral
Model 1
propagating mode loss factor,
depends upon the bunch length
trapped mode loss factor
propagating transverse modes can be captured by the HOM absorbers
propagating longitudinal modes
cut-off frequencies
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23. Estimates for HOM and propagating power. Comparison of the models
Model 3 is 5 times better than model 1.
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24. Resistive wall wake potential
Electric field
Eleonora Belli
Multi-bunch regime. Losses may be increased several times
conductivity /Ohm/mm
Al 35000
Cu 58000
SS 1400
Au 48800
Be 25000
Ni 14600
NEG
single bunch
More information is needed about layers of the beam pipe (Au,Be)
Current estimate is 200 W/m
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25. Conclusion and future steps
We have designed a smooth geometry of the IR vacuum chamber, which has a relatively small HOMs impedance.
Each beam of 1.45 A will produce electromagnetic power of approximately 5 KW from both connections. This power will be mainly absorbed in the two sets of HOM absorbers.
More work will be needed to further optimize the HOM absorbers.
Beam pipe requires water or air cooling.
Need more analyses.
This optimal shape of the
IR beam pipe can be also used in other circular colliders (scaled if needed)
A. Novokhatski 5/31/17

26. Acknowledgement
We would like to thank Frank Zimmerman, Manuela Boscolo and especially Michael Benedikt for their great support of this work. We are also happy to thank Oide Katsunobu, Mauro Migliorati and the MDI team for many useful discussions and help. Thank you!
A. Novokhatski 5/31/17