From: Joachim Tuckmantel
Sent: Tuesday, September 30, 2003 4:30 PM
To: Frank Zimmermann
Subject: Re: LHC cavity impedance data

Hello, Frank

1) The LHC 200 MHz capture and damper cavity was RF-wise designed by me and the total design is published in LHC-Project-Report 368. Evidently I have calculated the f and R/Q values for this cavity (part of the optimization), monopole numbers are given there; for dipoles (up to to
decapoles) I have the longitudinal R/Q at the edge of the beam tube, but not published. The Q-values (and shunt imp.) are for the bare cavity without HOM dampers, they are upper limit, cannot become worse. But there have to be HOM dampers which will be made in a far future as modifications of the existing HOM dampers kept from the SPS 200 MHz cavities (cavities given away) but which do not have enough power handling capability for the LHC beam. Hence there are no definite numbers known ....
The report 2001-044-HRF was done in time domain and Fourier Transform by a Chinese visitor assuming a certain geometry of the HOM coupling loop, I am reluctant to take these numbers as rock-solid basis, but they give an idea.
In any case these 200 MHz cavities are staged and will not be in LHC during the first years, we have to do without and we hope - after some success in the SPS as injector - that we can survive up to the nominal current without them.

2) Concerning the LHC superconducting cavities, they have the property that all monopoles do propagate through the large beam tube, hence a module with 4 single cell cavities is in fact for the HOMs a 4-cell supercavity. But then the age-old problem cames back: Due to fabrication tolerances the indicidual cavity HOM frequencies have a non-negligible scatter and hence the field-profile - i.e. here the excitation of the different single cavities - can be anything for the 4 modes to be expected. The worse that can happen is that one of these modes is synchronous over the full module and thus appears - each 'cell' of the supercavity has its own HOM damper - as if you would have 4 times a single cavity with dampers.
The R/Q of the fundamental mode is 45 (circuit) Ohm and if I remember right the worst HOM should be about 1/3 of that. But Ernst Haebel has done his best to keep the damped Q-values of those bad guys very low (see SL-98-008 RF) - also for power output reasons. Sounds strange but is true: the better you couple, the less power you extract.
And remember concerning measurements: You cannot do a (bead-pull) HOM measurement in a superconducting cavity/module without spoiling it
(dust) !!!

3) In fact the ideal TE (= Transversal Electric) MONOpole modes do not have an Ez component, but if a cavity is not perfectly symmetric, the real-world TE-like modes are mixtures of a lot of TE and a little of TM, hence may have some coupling to the beam. Also an ideal cavity badly aligned has a small component in the beam direction.
For multipoles the longitudinal field (of a perfectly symmetric well aligned cavity) always vanishes on the axis and rises linearly with the distance for dipoles, square of distance for quads ....

I hope this info helps, I cannot supply more. Concerning the LHC sc. 
cavity design, I was mainly distant spectator occupied that LEP got some good sc. cavities running there. Unfortunately the main actors of the LHC cavity design are retired or back to their labs elsewhere ....

   Cheers   Joachim
 
 


Frank Zimmermann wrote:

>
>Hallo Joachim,
>
>ich bin von Francesco beauftragt worden, die LHC impedance database 
>input  fuer die cavities auf Vordermann zu bringen. Und ich sehe, dass 
>Deepa Angal- Kalinin in LHC Projetc Report 595, R und Q Werte fuer die 
>Monopole und Dipol Moden der 200 und 400 MHz cavities angibt, mit den 
>folgenden Referenzen.
>Ich fuege ein paar Fragen hinzu, die ich bei der Lektuere hatte. 
>Vielleicht kannst Du mir ja helfen, einige davon zu beantworten, oder 
>mir raten, an wen ich mich sonst wenden koennte.
>
>200 MHz:
>T. Linnecar et al., CERN SL-Note-2001-044-HRF. 
>
>This paper gives data for damped and undamped longitudinal modes.
>
>For dipole modes undamped values are plotted, but there are
>
>no numbers. D. Angal's paper also gives some number (from where?).
>
>There is no information on the damped dipole modes.
>
>
>
>400 MHz.
>
>E. Haebel et al., CERN-SL-98-008-RF. 
>
>Damped and undamped longitudinal and dipole modes.
>
>But there are only Q values, if I am not mistaken,
>
>where would I find the R_sh or R/Q? (D. Angal also
>
>quotes R value - correct and from where?)
>
>
>
>Sorry a further question, I remember slightly that only
>
>TM modes couple to the beam, but not the TE
>
>modes (or was it the other way round?). 
>
>Are the dipole modes given in these  papers
>
>of either type? Do you have any suggestions how
>
>to proceed in this enterprise? 
>
>
>
>Vielen Dank fuer Deine Hilfe!
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>Gruss,
>
>           Frank
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