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Lower Trapped Modes in the SLAC Rotatable Collimator

Lower Trapped Modes in the SLAC Rotatable Collimator. Liling Xiao Aug. 22, 2011. SLAC Rotatable Collimator. R_beampipe=30.5mm. Jaw’s opening=2mm / 60mm. Larger EM foils are adopted to reduce the Ez fields along the beam path, thus the longitudinal modes have smaller shunt impedances.

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Lower Trapped Modes in the SLAC Rotatable Collimator

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  1. Lower Trapped Modes in the SLAC Rotatable Collimator Liling Xiao Aug. 22, 2011

  2. SLAC Rotatable Collimator R_beampipe=30.5mm Jaw’s opening=2mm / 60mm • Larger EM foils are adopted to reduce the Ez fields along the beam path, thus the longitudinal modes have smaller shunt impedances. • The most dangerous longitudinal mode shunt impedance in the SLAC collimator is 2 orders magnitude lower than that one in the CERN collimator I. • But the lowest transverse mode, which has highest shunt impedance, is a concern in the current SLAC collimator. 2

  3. Parameters Assuming bunch length Longitudinal Trapped Modes R/Q and Q (calculated from Omega3P): Transverse Trapped Modes R/Q_T and Q (calculated from Omega3P): Loss factor: Kick factor: Longitudinal Impedance (including the Gaussian form-factor) Transverse Impedance (including the Gaussian form-factor) Vacuum tank is made of stainless steel (sigma=0.116e7s/m); jaws and EM foils are made of copper (sigma=5.8e7s/m) 3

  4. Longitudinal Modes in SLAC Collimator 1.5m 215MHz 98.7MHz * The Gaussian form-factor is not included. 4

  5. The Lowest Transverse Mode E-field Gap=2mm Gap=60mm 150 6 yoffset@ 0.5mm yoffset@ 0.5mm Ey @ Gap=2mm Ey @ Gap=60mm Ey profile for normalized stored energy • The lowest transverse mode is a gap mode and exists mainly in the gap region; • It has stronger Ey fields between the two jaws for fully inserted jaws; • The EM foil shape would not affect the lowest transverse mode significantly. 5

  6. Kick Factor vs. offset r0 @ gap=2mm • The transverse modes’ kick factors are slightly different at different offset r0; • The lowest transverse mode has the highest kick factor; • In a real collimator, the kick factor should be of the same order of those shown in this plot. 6

  7. Transverse Modes in CERN Collimator e3 Gap=5mm CERN Design, AB-Note-2005-042 RF 7

  8. Transverse Modes in CERN/SLAC Collimators CERN collimator SLAC collimator with larger EM foils • The lower transverse modes in SLAC collimator are gap modes; • They have lower frequencies and higher kick factors than those in the CERN collimator; • The form-factor is not including. 8

  9. Transverse Modes in TCTV/SLAC Collimators CERN TCTV @ gap=3mm SLAC collimator with larger EM foils gap=3mm • The lowest transverse mode in SLAC collimator has lower frequency and higher shunt impedance than the most critical trapped mode in the CERN TCTV. • Elias’s e-mail: If we have values, as we could may be expect from your slides, close to the ones mentioned in the following talk http://ab-abp-rlc.web.cern.ch/ab-abp-rlc/Meetings/2006/2006.02.10/CBIAtTopEnergy_TCTVOnly_RLC_10-02-06.pdf, then we would like you to considerably reduce the impedances of these modes (meaning by at least a factor ~ few hundreds * The Gaussian form-factor is not included. 9

  10. Summary • In the current SLAC collimator design with larger EM foils, the longitudinal modes have lower shunt impedances than those in the CERN collimator I. Therefore, the heating due to the longitudinal trapped modes would not be a problem. • However, the lowest transverse mode has lower frequency and highest kick factor in the SLAC collimator than the critical mode in the CERN collimator and TCTV. It should be reduced at least one or two factors. • Why the transverse impedances are quite different in CERN collimator I and TCTV (see Slides 8 and 9)? 10

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