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RF aspects of module vacuum system Riccardo Zennaro CERN

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Contents Wakefield study in the main linac vacuum chamber Wakefile study in the AC-QUAD main linac intramodule interconnection Wakefield study in the main linac intermodule interconnection

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Simple geometry and constant transverse section (with the exceptions of the spacers) 2D problem (HFSS) + longitudinal dependence Problem: resonator in a beam line; (standing waves excited) resistive wakes is the main problem: Copper layer

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TE 11 TE TM 01 TM 11 TE

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No spacers, r=2.5 mm, dx=1mm x y E H TE 11 TM 11 cutoff=73 GHz TE11 cutoff 2*V/(pC*mm) TE 11 cutoff=35 GHz

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x y E H No spacers, r=2.5 mm, dy=1mm TM 11 2*V/(pC*mm)

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No spacers, r=2.5 mm beam on axis x y H H 4*V/(pC*mm) TM 01 cutoff=46 GHz

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No Spacers Spacers; periods=50 mm, length=2.5mm x y E H

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F=36.59 GHz F=36.58GHz

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x y E H x y E H x y H H Problem solved (no trapped modes in the pillbox approximation) ?.. In case damping Variation of the beam pipe radius (3.7 mm instead of 2.5 mm) Problem solved (no trapped modes in the pillbox approximation) TE 11 cutoff= from 35 GHz (r=2.5mm) to 24 GHz (r=3.7mm) TM 01 cutoff= from 46 GHz (r=2.5mm) to 31 GHz (r=3.7mm)

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Mind the scale x y E H 2*V/(pC*mm)

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CLIC module AS/AS QUAD/AS AS/BPM IC (or AS/AS IC) Free space: 30mm20 mm 15mm

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Main beam – QUAD/AS intramodule (intermodule) interconnections QUAD/AS intermodule is the same with longer bellows and flexible element Continuous solution Solution with a gap and damping material (under study) From Cedric: CLIC two beam module review 15/09/09

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f=12.197 GHz Q=1125 f=15.438 GHz Q=1310 f=2.020 GHz Q=444 V/pC/mm/2m NB: limit at 2 nd bunch is 7 V/pc/mm/m

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mode12345678910 F (GHz)2.0203.6745.3216.6288.7979.31310.59712.19714.02715.438 Q444599721101294911201006112511921310 K (V/nC/mm)3.4510.26.948.911.5155.344.9171.928.496.5 r x ( Ohm/mm ) 483105959747507871188827161009315345212

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7 45 3.7 13 31 88 5 Loads: r =20, tg =0.2

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V/pC/mm/2m

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Sealed version with gap Welded version with flexible element Pro: Good RF continuity Con: “dirty” Specific tooling (welding and cutting machine) Axial and radial space needed Pro: “clean” Easy maintenance Availability of linac (procedure tbs) Con: RF properties (to be checked) Damping material Main beam – AS/AS (or AS/BPM) intermodule interconnections From Cedric: CLIC two beam module review 15/09/09

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V/pC/mm/2m NB: limit at 2 nd bunch is 7 V/pc/mm/m f: 11.882, Q=4279, kick factor 693 V/nC/mm, r x = 159048 Ohm/mm

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No load Single load Double load V/pC/mm/2m (m) 22 152 56 30 140 8 3

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f=22.05 GHz Q~145 Single load Double load

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Double load gap=9mm Double load gap =5mm V/pC/mm/2m Gap=5mmGap=9mm Double load gap=9mm Double load gap =5mm

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The transverse wake amplitude due to interconnections seems to be relatively small but, since it is completely undamped (Q~1000), it could be critical (beam dynamics computation to evaluate the criticality). Damping is anyway easy to implement and with good results. Possible optimization for compactness Low impedance of the chamber and small wakefield but large Q factor (~9000); problems in case of build-up Negligible effects of the spacers The geometry can be considered as a simple pillbox for the case of beam on axis or horizontal offset. For this reason the obvious solution is to use a beam pipe of the same radius This solutions provides good results also for the other plane Conclusions Quad vacuum chamber Interconnections

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