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2006/9/25-26 ILCDR06, Cornell University 1 DESIGN STUDY OF A MOVABLE COLLIMATOR WITH LOW BEAM IMPEDANCE Yusuke Suetsugu*, Kyo Shibata KEKB Vac. Group Introduction Simulation Test Model Summary (Application to clearing electrode)

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2006/9/25-26 ILCDR06, Cornell University 2 Movable Collimator (Mask) –A vacuum component to shut off spent electrons, which circulating out of a nominal orbit Indispensable to reduce background of detector Introduction Beam Bellows Chamber Mask Chamber Bellows Chamber Head [Ex. Collimator Ver.4 in operation at KEKB]

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2006/9/25-26 ILCDR06, Cornell University 3 Problems in high current machine –High impedance –Damage of head by beam Introduction Ceramics Metal Beam duct Support Head SiC Beam SiC One idea –Ceramics support + thin conductive layer Little interference with beam No charge up –Ceramics head Little damage by beam Ex. Al 2 O 3 ： R.L. = 75 mm –SiC HOM absorbers Absorption of HOM

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2006/9/25-26 ILCDR06, Cornell University 4 Introduction Studied here –RF properties Simulation by Mafia 4.2 [MAFIA] 、 Microwave Studio 6.0 [MWS] f r (resonance frequency), Q, R S, R T (shunt impedance) of trapped modes CBI growth rate (Longitudinal, Transverse) Tolerable conductivity of coating –Estimation of head temperature Input power, temperature –Manufacturing of a test model (atmosphere version) Manufacturing of head, dielectric support (BN, Al 2 O 3 ) Measurement of f r 、 Q of trapped modes, and comparison with calculation Clearing electrode

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2006/9/25-26 ILCDR06, Cornell University 5 Simulation Model for MWS Head (W:8 mm,T:7 mm, L:90 mm) –Copper, 10 mm from beam Support –BN (W: 4 mm, T: 6mm) r = 4.0, tan = 0.0008 –Al 2 O 3 (W: 4 mm, T: 4mm) r = 9.0, tan = 0.0001 –Thin layer (t = 0.1mm) with conductivity ( ), as a coating Duct – 94, L: 300 - 500 mm SiC –Deby first-order dispersion – s = 110, = 14, = 1 10 -9 s Port 1 Port 2 Beam duct Support Head SiC Calculation –S 11 between Port 1 and Port 2 Antenna: 10 mm –Frequency mode Debye type

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2006/9/25-26 ILCDR06, Cornell University 6 Beam duct Support Head Beam SiC Simulation Model for MAFIA Head (W: 8 mm, T: 7 mm,L:90 mm) –Copper, 10 mm from beam Support –BN (W: 4 mm, T: 6mm) r = 4.0 –Al 2 O 3 (W: 4 mm, T: 4mm) e r = 9.0 –Thin layer (t = 0.8mm) with conductivity ( ) as a coating Duct – 94, L: 3200 mm SiC –Deby First-order dispersion – s = 110, = 14, = 1 10 -9 s Calculation – x= 2mm, y =1mm, z =0.8mm –Wake calculation up to 32 m –Beam: x = 0, y = 0 –Bunch length: z = 4 - 8 mm Debye type

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2006/9/25-26 ILCDR06, Cornell University 7 Simulation S 11 spectrum (MWS) –Two modes, Mode-1 and Mode-2 are trapped under the cut-off frequency (1.87 GHz) –Mode-1 disappears for ceramics support Mode 2 ~1.38 GHz TE 111 of 94 pipe Mode 1 ~0.69 GHz 1 0.995 0.99 0.985 0.98 0.975 0.5 1 1.5 2 Frequency [GHz] Amplitude Mode 2 ~1.38 GHz 0.5 1 1.5 2 Frequency [GHz]

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2006/9/25-26 ILCDR06, Cornell University 8 Simulation H distribution of modes Current goes up and down along support High impedance f~0.69 GHz I [H][H] Depend on of support [ Mode-1 (only for metal) ] [H][H] f~1.37 GHz [ Mode-2 (both for metal and ceramics) ] I I Current go and back along head

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2006/9/25-26 ILCDR06, Cornell University 9 Simulation R S and Q for Mode-1 calculated by MWS Expressed as a function of (skin depth) / t (thickness) R S is larger for large . Q is also high. At /t ~1, R S ~ 1k .Q ~ 20. Almost constant at R S /Q ~ 50 Calculation was impossible at /t >2 –Disappear ! Little dependence on SiC at /t > 0.2 [MWS]

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2006/9/25-26 ILCDR06, Cornell University 10 Simulation MWS and MAFIA At /t ~1, R S ~ 1 k ( MWS). But, Q~5 (~1/4 of MWS), R S /Q~200. Little effect of Q: Too short calculation length of wake? At /t ~1, R S =1 k . R S /Q = 50~200 [MWS] [MAFIA]

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2006/9/25-26 ILCDR06, Cornell University 11 Simulation R S and Q of Mode-2 by MWS Q does not so depends on SiC as that for Mode-1 At /t =1~10, R s =100~10 , Q= 1000~500 (with SiC). At /t =1~10, R s /Q = 0.1~ 0.02 。 R s /Q decreases at /t >2. [MWS]

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2006/9/25-26 ILCDR06, Cornell University 12 Simulation MWS and MAFIA At /t =1~10, R s =100~10 ( MWS), but Q ~200 (1/5~1/3 of MWS) At /t =1~10, R s /Q =0.5~ 0.05 R s /Q decreases at /t >1. [MAFIA] At /t =1~10, R S =100~10 , R S /Q=0.5~0.02 [MWS]

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2006/9/25-26 ILCDR06, Cornell University 13 Simulation Summary of f r, Q, R S and R T

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2006/9/25-26 ILCDR06, Cornell University 14 Simulation Growth rate of Longitudinal CBI –For a uniform bunch filling, : Mode number e : Electron charge N : Number of electrons in a bunch M : Number of bunches : Momentum compaction factor T 0 : Revolution time [s] E 0 : Beam energy [J] s : 2 Synchrotron frequency R S : Shunt impedance [ ] Q 0 : Q value r : 2 Resonance frequency I b : Beam Current [A] = eNM/T 0

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2006/9/25-26 ILCDR06, Cornell University 15 Simulation Tolerable growth rate –KEKB(LER) Damping time = 21.5 msec, = 3.39 10 -4, f s =2 10 3 Hz -1 < 50 s -1 (@ 2.6 A) Then, -1 < 3 s -1 (@ #16 masks) –SKEKB Damping time = 30 msec, = 2.7 10 -4, f s =3.1 10 3 Hz -1 < 30 s -1 (@ 9.4 A) Then, -1 < 1 s -1 (@2.6A, #16, =3.4 10 -4, f s =2 10 3 Hz)

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2006/9/25-26 ILCDR06, Cornell University 16 Simulation Maximum -1 for a 2.6A beam @KEKB m = 1~5120, M =5120, T 0 =1 10 -5 [s], I b = 2.6 [A] =3.4 10 -4, E 0 =3.5 [GeV], : 2 2 10 3 Mode-1 Mode-2 500 200 Maximum within f r 0.1GHz 1 1

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2006/9/25-26 ILCDR06, Cornell University 17 Simulation Necessary /t –Mode 1 R S < 500 /t > 2 –Mode 2 R S < 200 OK if with SiC 、 /t > 3 if without SiC (MWS) For Cu ( = 5.8 10 7 -1 m -1 ), /t =2 Possible material –1 m Ti coating ( =1.7 10 6 -1 m -1 ), for example ： – = 1 10 -5 m @1.38GHz – /t = 10 – R S ~10, R S /Q =0.02 ~ 0.05 (Mode-2)

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2006/9/25-26 ILCDR06, Cornell University 18 Simulation Similar discussion can be made for transverse CBI. Tolerable growth rate: –Damping time ~50 turn (SKEKB) – -1 35 s -1 (@2.6A, #16) Mode 1 –R T 2 Mode 2 –R T 1 if without SiC (MWS) Realized by 1 m Ti coating

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2006/9/25-26 ILCDR06, Cornell University 19 Simulation Loss factor (MAFIA) At /t ~10 ( ~10 -1 m -1 ) 、 z = 4mm, 1/4 of Ver.4 @KEKB But, the loss factor is still large (Without SiC) KEKB Ver.4 =10

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2006/9/25-26 ILCDR06, Cornell University 20 Simulation Loss factor: Comparison with R S Similar behaviour to R S (Without SiC)

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2006/9/25-26 ILCDR06, Cornell University 21 Simulation Heating of Mask head (only results) –Joule loss by wall current ~30 W –Input power from trapped mode (Only Mode-2) ~25 W at most –Heat transfer: Only radiation –Expected temperature: Input ~ 50 W ~600 C for 1 =0.5 1 : emissivity Tolerable range 5000 bunches, 10 A, KEKB

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2006/9/25-26 ILCDR06, Cornell University 22 Test Model A test model for air version was manufactured. –Aluminum alloy pipe –Head ： Aluminum 、 Graphite –Support ： Aluminum 、 BN 、 BN+Ti coating, Al 2 O 3 –SiC ： W:20mm L:90mm 8 pieces Graphite head (Non rectangular) Graphite BN SiC

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2006/9/25-26 ILCDR06, Cornell University 23 Test Model S 12 between two antennae was measured Frequency spectrum 、 Q 、 f r of trapped modes were compared to the calculated ones [HP Network Analyzer 8753]

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2006/9/25-26 ILCDR06, Cornell University 24 Test Model Frequency spectrum –Mode-1 disappeared for ceramics support as expected S12 Metal Support (Al) Ceramics (BN) Support 0.4 GHz 2 GHz 0.4 GHz 2 GHz Mode 1 (~0.7 GHz) Mode 2 (~1.4GHz) Mode 2 (~1.4GHz)

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2006/9/25-26 ILCDR06, Cornell University 25 Test Model Simulation Model for test model SiC Case 1 Case 2 Case 3 Case 4 Case 5 Case 6 f r and Q were measured changing number and position of SiC Al [MWS] Al SiC

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2006/9/25-26 ILCDR06, Cornell University 26 Test Model f r and Q (Al support) Difference of f r is within 2.5%. The behaviour is similar, but the change of f r is larger. Q of Mode-2 is also good agreement. Q for Mode-1 is smaller by a factor of 3 - 4. –Due to bad electric contact between support and head, duct Mode-1 Mode-2

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2006/9/25-26 ILCDR06, Cornell University 27 Test Model Thin tapes at one side of support Simulation of a thin coating Cu : t = ~30 m, = 5 10 7 -1 m -1 / t = 0.09 Al -alloy: t = ~50 m, = 1 10 7 -1 m -1 / t = 0.12 SUS : t = ~40 m = 1 10 6 -1 m -1 / t = 0.48

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2006/9/25-26 ILCDR06, Cornell University 28 Test Model Frequency spectrum: BN→SUS → Al → Cu BN SUS Al Cu 0.4 – 2.0 GHz Case-3

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2006/9/25-26 ILCDR06, Cornell University 29 Cold Model Ti coated Al 2 O 3 support Mode-1 disappears for t = 1 m (86 for 30 mm) 0.4 – 2.0 GHz t = 10 m ( /t ~1) t = 1 m ( /t ~10)

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2006/9/25-26 ILCDR06, Cornell University 30 Summary Proposal –Head supported by ceramics with a thin coating Simulation –For a case of Al 2 O 3 support with 1 m Ti coating – / t ~10 @1.38GHz –R S ~10 、 R T ~1 k m -1 (Only for Mode-2) –Longitudinal, Transverse CBI : OK (for SKEKB) –Loss factor @ z = 4 mm ~ 0.3 V pC -1 (~1/4 of KEKB Ver.4) –Head temperature ~600 ℃ @ 1 = 0.5 (~50 W input power) Promising

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2006/9/25-26 ILCDR06, Cornell University 31 Summary Test Model –f r and Q (Except for Mode-1) agreed well with calculation –Behavior of Q (Mode-1) against coincides with calculation –1 m Ti coating actually showed no peak of Mode-1 Next step –Optimization of dimensions of head to reduce loss factor –Trial model for KEB LER is under manufacturing, and will be installed next year.

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2006/9/25-26 ILCDR06, Cornell University 32 Summary Plan (under manufacturing)

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2006/9/25-26 ILCDR06, Cornell University 33 Summary Application to a clearing electrode –If finite is ok, the structure can be applied to clearing electrode. –Electrode based on similar concept has been tried in DA NE Clearing electrode for ion Electrode was supported by ceramics with conductive painting –Calculation is undergoing –Test using existing B chamber?

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2006/9/25-26 ILCDR06, Cornell University 34 Clearing Electrode Model for clearing electrode –Electrode: 1mm 1mm 1000 mm rod –Support: 2mm 2 mm 2* One support:Al 2 O 3 + thin conductive layer –10 mm from wall L.Wang et al., EPAC2006 [MAFIA] (*Note: Several additional ceramics supports will be required)

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2006/9/25-26 ILCDR06, Cornell University 35 Clearing Electrode Z // =10 -1 m -1 ~150 MHz (~ /2 resonance) Metal Ceramics R S <~1 Q ~ 2/0.06~30 @2GHz

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2006/9/25-26 ILCDR06, Cornell University 36 Clearing Electrode Z T R T <~3000 Q ~ 2/0.06~30 @2GHz =10 -1 m -1 Metal Ceramics

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2006/9/25-26 ILCDR06, Cornell University 37 Clearing Electrode Loss Factor [ -1 m -1 ] k [V C -1 ] 0 (ceramics)3.85x10 8 18.31x10 8 101.59x10 9 Metal3.88x10 9 (~TiN?) (~Ti)

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2006/9/25-26 ILCDR06, Cornell University 38 Clearing Electrode Ref: DA NE type Loss Factor –~6x10 10 V C -1 ( z = 8 mm) R S ~ 40 Q ~ 30 Electrode: 50mm x 50mm x t 1mm Support: 10mm x10mm x10mm+Coating (t = 0.8 mm, =1 -1 m -1 )

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2006/9/25-26 ILCDR06, Cornell University 39 Clearing Electrode What should be considered next? –Instabilities (CBI, Microwave Instability?) –Heating –Structure (More realistic one) –Experiments at KEKB (in B, Wiggler)? –etc.

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2006/9/25-26 ILCDR06, Cornell University 40 end

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2006/9/25-26 ILCDR06, Cornell University 41 Simulation Calculation of Q, R S and R T by MWS –Q: Frequency spectrum of S １１ between two antennae –R S : Longitudinal –R T : Transverse [][] [ /m]

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2006/9/25-26 ILCDR06, Cornell University 42 Simulation W s ( ): FFT of Wake Potential (at x = 0, y = 0) ( ): FFT of bunch profile Z s ( ): Longitudinal impedance –R S and Q are calculated fitting to [][] [][] Calculation of Q, R S by MAFIA –From wake potential

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2006/9/25-26 ILCDR06, Cornell University 43 Simulation Example of Z S at z = 8 mm, = 1 10 3 -1 m -1 Real Part Imaginary Part Mode-1 Mode-2 Longitudinal Impedance [MAFIA]

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2006/9/25-26 ILCDR06, Cornell University 44 Wake Wake(z) at =1 10 7 、 1 10 3 Little damping Little difference for 32m calculation –Calculation error increased for longer calculation length: Limit of MAFIA Damped withiin 32m →OK for /t > 1 = 1 10 7 = 1 10 3

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2006/9/25-26 ILCDR06, Cornell University 45 Heating of head Surface current density at 10A, 5000 bunches –q = 2 10 -8 C → B x ~6 10 -5 T → H x = 48 A/m Surface resitance, R (f r = 1.5 GHz) –Cu: = 5.8 10 7 1/ m Joule loss at surface, P –P = I 2 R = (48 8 10 -3 ) 2 (1.0 10 -2 90 10 -3 /8 10 -3 ) 4 = 0.066W –Too small ・・ Main input was from wall current –No frequency component of Mode-1

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2006/9/25-26 ILCDR06, Cornell University 46 Heating of head Refernce

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2006/9/25-26 ILCDR06, Cornell University 47 Heating of Head Estimation of temperature Only radiation Generally, radiation power, P 12, from an object with an area of A 1, Emissivity of 1, temperature of T 1 to another one with an area of A 2, Emissivity of 2, temperature of T 2 s b ： Stefan-Boltzmann constant = 5.67 10 -8 W/m 2 K 4 A1A1 A2A2

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2006/9/25-26 ILCDR06, Cornell University 48 Heating of Head A 1 =2.8 10 -3 m 2 、 A 2 = 1.55 10 -1 m 2 (500mm long pipe) 、 T 2 = 293 K 、 1 = 0.2 - 0.8(copper) 、 2 = 0.5 (Rough SS) for 50Winput, ~600 ℃ at 1 ~0.5, ~850 ℃ 1 ~0.2. Blazing is possible? A1A1 A2A2 1 =0.2 1 =0.8 1 =0.5

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2006/9/25-26 ILCDR06, Cornell University 49 Simulation –R T and Q are calculated fitting to Calculation of Q, R T by MAFIA –From wake potential W T ( )=W T [y=y 1 ]( )-W T [y=-y 1 ]( ), y 1 →0: Z T ( ): Transverse (y) impedance [ m -1 ]

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2006/9/25-26 ILCDR06, Cornell University 50 Simulation Example at z = 8 mm, = 1 10 3 -1 m -1 Real Part Imaginary Part Mode 1 Mode 2 Transverse Impedance

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2006/9/25-26 ILCDR06, Cornell University 51 Cold Model Dependence of Q (Mode-1) on / t Two SiC bars (Case-3) Tendency is in good agreement with calculation Measured Q was 1/10~1/20 of calculation.

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